biomec@fcien.edu.uy

Facultad de Ciencias (Paleontología), Facultad de Medicina (Fisioterapia) Universidad de la República, Montevideo, Uruguay.

SUMMARY

In this paper, a biomechanical model is proposed, that optimises the rehabilitation of the knee´s anterior cruciate ligament. (ACL). By using a simple model, an equation was obtained, that allows to establish the point where a determined mass has to be put to make the ACL to withstand a pre-set stress at any angle. This constitutes a fundamental tool during the recovery, as the model includes anthropometric features of the patient as well as physical elements.The considered system includes leg, foot and an added mass. Two external forces, the one exerted by the cuadriceps (Fq) and the weight (W). The analysis was carried out in two dimensions. The origin of the axis system was set on a point on the articular surfaces of the inner femoral condyle, in such a way that the model´s X axis corresponds with the geometrical axis of the tibia at any angle of knee flexion. To calculate the mass of the body segments regression equations were used. The variables were obtained through direct measurements on strictly profiled X-ray photographs. The obtained data was used for calcutations from the ecuations derived from the model. The conclusions drawn give new and more accurate criteria for the first recovery stages.

INTRODUCTION

The anterior cruciate ligament (ACL) is one of the features of the knee that is most frequently injured (Insall, 1995). One element to take into account during the post-surgical recovery is the tone of the quadriceps muscle. The action of this muscular group is risky for the ACL, as one component of the muscular force tends to move the tibia forwards in regard to the femur, yielding stress on the ACL (Kapandji, 1987). The aim of this paper is to develop a tool that permits to control stress on the ACL during the isometric exercises of the quadriceps for any knee angle.

METHODS

The sample was composed by eight male individuals, which ages ranged from 18 to 35 years. Height, body mass and leg length was recorded for each individual. Strictly profiled X-ray were taken at different knee angles. On each X ray picture, an axis system and the line of action of the patellar ligament were drawn, to determine the lever arm of the quadriceps (Fq). Such moment is given by T = Fq (d2 sen f ), where f is the angle of action of the patellar ligament. To determine the stress of the ACL, a system in static condition was considered, composed by leg, foot and added mass. A free body diagram was drawn (Figure 1), considering two external forces, Fq and weight (W). The masses of the segments were determined after regression equations (Zatsiorsky, 1998). Through inverted dynamics, it was determined the place on the leg where a mass should be added to achieve a preset stress on the ACL. Data obtained were processed using Matlab 5.3 and ANCOVA analysis was performed.

RESULTS AND DISCUSSION

Stress on the ACL was controlled by equalising the moment arm of the weight of the system (dl) with the moment arm of the weight of the system, Fq (R/Senf). Significant differences were found in the value of f at different knee angles in individuals of similar anthropometric features. Those differences are associated to the form and position of the patella in regard to the femoral condyles. Therefore, it is concluded that f is a fundamental variable to choose the place and modulus of the added mass during the quadriceps isometric exercises to control stress on the ACL. Free body diagram Figure 1.