The effective quadriceps and patellar tendon moment arms relative to the tibiofemoral finite helical axis

Abstract

The moment arm is a crucial parameter for understanding musculoskeletal dynamics as it defines how linear muscle force is transformed into a moment. Yet, for the quadriceps tendon this parameter cannot be directly calculated, as the patella creates a dynamic fulcrum. Thus, the effective quadriceps moment arm (EQma) was developed to define the quadriceps force to tibial moment relationship. In vivo data in regards to the EQma are lacking and the critical question of how patellofemoral kinematics may influence the EQma remains unresolved. Therefore, the purpose of this study was to quantify the in vivo EQma during a knee extension exercise in asymptomatic controls and to correlate the EQma with sagittal plane patellofemoral kinematics. While subjects (30F/10M, 26.5±5.6 years, 167.5±10.2 cm, 62.6±10.7 kg) cyclically flexed-extended their knees within the MR scanner, dynamic cine-phase contrast and cine MR images were acquired. From these data, patellofemoral kinematics, the ratio of the patellar tendon to quadriceps force, the patellar tendon moment arm, and the EQma were quantified. The EQma trended upwards (32.9–45.5mm (females) and 31.5–47.1mm (males)) as the knee angle decreased (50°–10°). The quadriceps had a mechanical advantage (ratio of patellar to quadriceps tendon forces>1.0) for knee angles ≤ 20°. The EQma did not correlate with sagittal plane patellofemoral kinematics. As this is the first study to characterize the EQma in vivo during dynamic volitional activity, in a large group of asymptomatic controls, it can serve as a foundation for future knee joint models and to explore how pathological conditions affect the EQma.

Analysis of the moment arms and kinematics of ostrich (Struthio camelus) double patellar sesamoids

“…However, it is interesting that the moment arms ratios calculated here between input and output moment arms were very similar, regardless of the method used to estimate patellar joint centers of rotation (via a second‐order polynomial curve vs. a circle) and despite the resulting moment arm values and patterns themselves being different (shown in Supplementary Figure S1 in the Supporting Information). In the human literature, using moment arm lengths between the input and output tendon to patellofemoral point of contact (rather than rotation center) also results in moment arm ratios highly consistent with those derived from moment arm lengths to center of rotation or force ratios (Im, Goltzer, & Sheehan, ). The apparent independence of calculated moment arm ratios to rotation center choice or method is thought‐provoking.…”

Normalized patellofemoral joint reaction force is greater in individuals with patellofemoral pain

“…Although PTma and EQma have been used to explain knee joint musculoskeletal dynamics (Brechter and Powers, 2002; Edmonds and Glaser, 2015; Im et al, 2015; Sheehan, 2007), their impact on patellofemoral joint reaction force is dependent on other variables. In contrast, the new normalized patellofemoral joint reaction force (F r /M tib ) gives direct insight into knee kinetics.…”

“…Thirty-three knees were included in the cohort with PFP (30F/3M, 22.3±11.8 years, 57.8±12.3 kg, 162.3±7.4 cm). Data for the control cohort were taken from a previous study (Im et al, 2015). Subjects in the control cohort had no history of PFP or lower leg pathology/injury/surgery.…”

“…MR images for both cohorts were captured and analyzed using the same methodology (Im et al, 2015). To rule out underlying pathology, static 3D MR images were acquired and read by a radiologist.…”

“…To insure that the analysis used the same portion of the patella across all time frames (Shibanuma et al, 2005), the sagittal image with the largest patella was selected for each analysis. The EQma was calculated as previously published (Im et al, 2015; van Eijden et al, 1986; Yamaguchi and Zajac, 1989): $$\mathit{EQma}=\frac{m{a}_q}{m{a}_p}\ast \mathit{PTma}=\frac{F_{pt}}{F_q}\ast \mathit{PTma}$$…”