The Behavior of the Patella Tendon under Dynamic Situations - Article Example

Abstract The human knee is essential for natural locomotion and so understanding of the knee is essential to the science of movement. In cases of large deformations, strain rates increase to pose trouble for the viscoelastic constitution of the knee. By establishing a measure of the strain rate in cases of deformation, some authors have proposed a change in how scientists model and conceptualize such issues. New parameters for these tests match empirical results with regards to the human cruciate ligaments and patellar tendons. These models are informed by an understanding of strain placed on the knee in terms of the moment arm of the knee-extensor mechanism. Differences in patellar tendon moment arm result from differences in femoral condyle width, which is an anatomical variable sometimes changed in individuals with deformities. Models of strain and tension in the patellar tendon are consistent with results indicating the position and orientation of the screw axis of the tibia relative to the femur, where the tendon originates. In their original research, Pioletti et al. (1998) performed traction tests on soft tissues to reevaluate existing models of strain. The gap in the research literature this work attempted to fill existed in terms of deformations—a case in which there is no acceptable model for strain to work with. What Pioletti et al. developed by the end of their study was a comprehensive model of strain that not only works under the normal condition, but does so under the deformed condition, and does so in accordance with principles of thermodynamics (Pioletti, Rakotomanana, Benvenuti, & Leyvraz, 1998). Their model incorporates information about tendon elasticity and viscosity in terms of strain placed on the human cruciate ligaments and patellar tendons, the latter of which is particularly important for understanding strain and function in the human knee. The law described in Pioletti et al. (1998) is set up to model the viscoelastic behavior of ligaments and tendons under any condition, and so provides a useful, if not essential in some cases, stepping stone to effective understanding. Years later in a study of the patellar tendon specifically, Krevolin, Pandy and Pearce (2004) explained the moment arm of the knee in terms of the patellar tendon, the tibia, and the femur. The screw axis and the action of the patellar tendon are used to determine this moment arm calculation. Newer technologies make this sort of measurement possible in full three dimensions, such that positions of bones can be precisely obtained from calculations. One important result from Krevolin et al. (2004) is that the shortest distance between the patellar tendon’s line of action and the axis of rotation of the knee is equal to the moment arm of the patellar tendon. This equivalence degrades as the measurement approaches full extension of the knee, at which point the moment arm becomes less than the shortest, or perpendicular, distance. The moment arm, with few exceptions, is relatively constant between individuals, counting still the kinds of deformations encountered by Pioletti et al. in their research. A variable controlled for by Krevolin et al. is the femoral condyle width, which may be different in individuals with the kinds of deformations seen by Pioletti et al., which may affect the kinds of strain measured in that latter study. It is important to evaluate these two studies in terms of their merits and in terms of their ability to add (or fill in) details to paint a complete picture of the knee such that we arrive at a comprehensive view of the patellar tendon and the entire knee-extensor mechanism. Firstly, it should be noted that the purposes of the two studies are compatible. In the case of Krevolin et al. (2004), the researchers set out (1) to measure the moment arm of the patellar tendon in three dimensions for comparison to other studies (a “primary” goal), and (2) to account for variability in the moment arm due to anatomical dissimilarities (a “secondary” goal). This secondary goal is compatible with the purpose of the Pioletti et al. (1998) research insofar as Pioletti et al. set out to create a “three-dimensional” viscoelastic constitutive law describing strain in soft tissue, such as the patellar tendon. In that respect, both studies looked at variation in the anatomies of the human knee and attempted to derive general principles for wider application. In addition to this primary similarity, a secondary similarity between the two studies is the method by which the researchers derived their results: through the use of three-dimensional analysis, which both studies cite as an important, if not essential, tool for understanding these variables. Understanding anatomical variability as it relates to the results of these studies is central to determining how the patellar tendon and the knee mechanism functions in both normal cases and in deformed cases as analyzed in the Pioletti et al. (1998) study. In the following cross-analysis, the conclusions of both studies are compared and, at times, contrasted. Methods Pioletti et al. (1998) first describes the general theory, and the assumptions, upon which they base their research, first with a description of general constitutive law, and second with a description of thermodynamic principles as reduced to a single inequality (p. 754). Ending with an equation, as given by “Eq. (6)”, the authors propose a novel solution to deriving correct results in the case of large deformations. Against this theoretical backdrop, the authors studied the cruciate ligaments and patellar tendons of four males whose mean age equaled 75 years. Taking care to control for environment, the authors preconditioned their subjects and then performed their tests with timed intervals in between each. These tests sought to measure two variables: “F”, the deformation gradient, and “P”, a measure of nominal stress. From these and theoretical foundation, “C” strain, “S” stress, and other variables could be calculated and derived. Adding elastic and viscous potentials is part of the authors’ major contribution to the understanding of viscoelastic law, as given by “Eq. (9)” (Pioletti, Rakotomanana, Benvenuti, & Leyvraz, 1998). Krevolin et al. (2004) employed similar experimental conditions but as a means to measuring a different, albeit related, concept. The authors experimented and measured the moment arm about the screw axis on six human cadavers, three male and three female. To measure the position of the tibia and patella relative to the femur, the authors utilized markers on the patellar tendon/tibial tuberosity and the patellar tendon/patella. While applying a force to the quadriceps tendon, three-dimensional measurements of the markers took into account the position and orientation of the screw axis of the tibia relative to the femur (Krevolin, Pandy, & Pearce, 2004). These measurements were verified by running each of cadaver experiment twice on each specimen. Results Krevolin et al. (2004) discovered the distance from one marker to the center of the moment arm vector was approximately 158mm, with a maximum difference of 6mm between repeated measures of the experiment. Peak values of knees tested during the experiment ranged from 40mm to 60mm, with a peak flexion of the moment arm at 45º. Based on their results, the authors determined that for any flexion angle, moment arm measures equal, with minimal variability, the shortest distance (a perpendicular distance) between line of action of the patellar tendon and the axis of rotation of the knee. At full extension, these values are not equal. Likewise, Pioletti et al. (1998) achieved significant results. Their study looked at strain rate effect in stress-strain curves from the ACL, the PCL, and the patella tendon. The results obtained from their study fit along the theorized curve set forth by the authors prior to performing their experiment. In other words, Pioletti et al. verified their proposed constitutive laws accounting for deformations in strain curves. Discussion The Pioletti et al. (1998) and Krevolin et al. (2004) studies each sought to establish new connections between measurements of anatomy and knee function. Both of these connections are made in three-dimension, which in both cases provides a unique perspective on the patellar tendon. In particular, Krevolin et al. (1998) made the first attempt to measure the moment arm of the patellar tendon in three dimensional spaces, leaving two-dimensional accounts inadequate (p. 787). In the end, Krevolin et al. conclude that the patellar tendon’s moment arm is determined, in large part, by the bones of the knee and the movements of the tibia and femur, in addition to other factors. Such other factors may include the viscoelastic nature of the tendon as given by Pioletti et al., and how a different model may produce different results. Both studies managed to comprehensively study the knee, and the patellar tendon, at what Pioletti et al. describe as “dynamic situations” (p. 753). In their study, this term refers to the different circumstances under which their proposed constitutive law was tested. The variables manipulated between these tests were elastic and viscous parameters. This anatomic variability is similar to the anatomic variability seen in the results obtained by Krevolin et al. insofar as the latter study, also conducting tests on “dynamic situations” attributed differences in the moment arm of the knee to anatomic variability having to do with bone geometry. To the extent that each Pioletti et al. (1998) and Krevolin et al. (2004) made use of advanced anatomic imaging, it is noteworthy that both make reference to underlying differences in the patellar tendon, even if both studies measured a separate, though not entirely unrelated, dependent variable. Each study contributes a fair amount of empirical knowledge to the field of biomechanics and, taken together, complete a portion of the picture depicting a reliable and valid knee mechanism model. By providing a general constitutive law, Pioletti et al. incorporates all variables in describing stress and strain on the patellar tendon. By providing an account of the moment arm of the knee through new technologies, Krevolin et al. sheds light on the anatomic sources of variation between individuals. Together, the studies point to the need for further research verifying not only the results of their own studies, but extending these results to other situations the authors may not have considered; for instance, further research could take the advice of Krevolin et al. to study the bone geometry, which is the most significant factor in moment arm variation. Likewise, it may be interesting to see the constitutive law of Pioletti et al, along with its three parameters challenged with its application to other kinds of deformation in the knee mechanism. To fit these studies together, this extension of the research literature might examine the relationship between the moment arm of the knee and the stress-strain curve. References Krevolin, J., Pandy, M., & Pearce, J. (2004). Moment arm of the patellar tendon in the human knee. Journal of Biomechanics, 37, 785–788. Pioletti, D., Rakotomanana, L., Benvenuti, J., & Leyvraz, P. (1998). Viscoelastic constitutive law in large deformations: Application to human knee ligaments and tendons. Journal of Biomechanics, 31, 753-757. Read More