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PubMed · 8614746

Polynomials with asymptotes for longitudinal data.

R H Jones
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Abstract

I use Laguerre polynomials to model growth curves or time--response curves known to approach an asymptote as time approaches infinity. An example is with measurements on a variable or variables from subjects recovering from surgery. These variables can often vary in a non-monotonic fashion for which a functional form of the curve is unknown. Using a longitudinal data mixed model, one can include in the model random subject effects, within-subject serial correlation and fixed or time varying covariates. I present two examples that involve groups of subjects recovering from surgery.

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Anterior Cruciate LigamentAnterior Cruciate Ligament InjuriesBiasData Interpretation, StatisticalEffect Modifier, EpidemiologicHumansLikelihood FunctionsLinear ModelsLiver TransplantationLongitudinal StudiesMathematicsSoftwareTime FactorsTreatment OutcomeJournal ArticleResearch Support, U.S. Gov't, P.H.S.

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R H Jones. 1996-01-15. Polynomials with asymptotes for longitudinal data.. https://doi.org/10.1002/(sici)1097-0258(19960115)15%3A1%3C61%3A%3Aaid-sim140%3E3.0.co%3B2-r

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PubMed2007

Effects of initial graft tension on the tibiofemoral compressive forces and joint position after anterior cruciate ligament reconstruction.

BACKGROUND: The initial tension applied to an anterior cruciate ligament graft at the time of fixation modulates knee motion and the tibiofemoral compressive loads. PURPOSE: To establish the relationships between initial graft tension, tibiofemoral compressive force, and the neutral tibiofemoral position in the cadaveric knee. STUDY DESIGN: Controlled laboratory study. METHODS: The tibiofemoral compressive forces and joint positions were determined in the anterior cruciate ligament-intact knee at 0 degrees , 20 degrees , and 90 degrees of knee flexion. The anterior cruciate ligament was excised and reconstructed with a patellar tendon graft using graft tensions of 1, 15, 30, 60, and 90 N applied at 0 degrees , 20 degrees , and 90 degrees of knee flexion. The compressive forces and neutral positions were compared between initial tension conditions and the anterior cruciate ligament-intact knee. RESULTS: Increasing initial graft tension increased the tibiofemoral compressive forces. The forces in the medial compartment were 1.8 times those in the lateral compartment. The compressive forces were dependent on the knee angle at which the tension was applied. The greatest compressive forces occurred when the graft was tensioned with the knee in extension. An increase in initial graft tension caused the tibia to rotate externally compared with the anterior cruciate ligament-intact knee (1.5 degrees and 7.7 degrees of external rotation when tensioned to 90 N at 0 degrees and 90 degrees of knee flexion, respectively). Increases in initial graft tension also caused a significant posterior translation of the tibia relative to the femur (0.9 and 5.3 mm of posterior translation when tensioned to 90 N at 0 degrees and 90 degrees of knee flexion, respectively). CONCLUSION: Different initial graft tension protocols produced predictable changes in the tibiofemoral compressive forces and joint positions. CLINICAL RELEVANCE: The tibiofemoral compressive force and neutral joint position were best replicated with a low graft tension (1-15 N) when using a patellar tendon graft.

Anterior Cruciate Ligament↗
PubMed2007

Double-bundle "anatomic" anterior cruciate ligament reconstruction: a cadaveric study of tunnel positioning with a transtibial technique.

PURPOSE: The aim of this study was to examine whether a double-bundle anterior cruciate ligament (ACL) reconstruction with a transtibial approach could position the tibial and femoral tunnels accurately in the native bundle attachments. METHODS: In 21 fresh-frozen knees the tibial and femoral attachments of the anteromedial (AM) and posterolateral (PL) bundles were outlined. The AM tibial tunnel guidewire was drilled with the 65 degree Howell tibial guide (Arthrotek, Warsaw, IN) located against the femur in the extended knee. The PL tibial wire was drilled through a prototype attachment to the Howell guide. Of the knees, 14 were available for the femoral part of the study. The AM femoral guidewire used an aimer offset 3 mm from the over-the-top position. The PL wire was drilled transtibially at 70 degrees of flexion, with external rotation and posterior drawer loads being applied. The plateaus and condyles were photographed and the wire positions measured. RESULTS: With regard to the tibia, 17 of 21 AM wires were in the AM bundle attachment (at 61% and 36% of the natural ACL posteroanterior and mediolateral length, respectively) and 19 of 21 PL wires were in the PL bundle attachment (at 28% and 36% of the posteroanterior and mediolateral length, respectively). With regard to the femur, 12 of 14 AM wires and 9 of 14 PL wires were in the correct native bundle attachment. The AM wire was 3% more shallow than the center of the AM attachment (P = .03) and 6% more superior (P < .001), where 100% was the diameter of the posterior lateral condyle. The PL wire was 4% more shallow than the center of the PL attachment (P = .026) and 6% more superior (P < .001). CONCLUSIONS: Anatomic and reproducible tibial guidewire positioning was achieved. Femoral wires were reproducibly positioned, but both were superior to and more shallow than the natural ACL bundle attachments, so further development or a different approach is appropriate. CLINICAL RELEVANCE: The double-bundle reconstruction aims to restore anterior drawer and rotational stability. This technique ensures anatomic tibial positioning. Further improvements are needed with regard to the femur.

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