Although the role of biarticular muscles during squatting and its variations have received considerable attention, the function of these muscles during squatting is not well understood. Closed kinetic chain exercises like squats are commonly preferred for knee rehabilitation and strength training for athletes. Squat exercises require both the hip and knee extensors, such as the gluteus maximus, hamstrings, and quadriceps femoris. For the hip extension strategy, the gluteus maximus and hamstrings have an important role, while the hamstrings and quadriceps co-contract at the knee. The same co-contraction occurs at the hip, between the rectus femoris and the hip extensors. These co-contractions do not seem to be effective, in terms of minimum energy expenditure, minimum muscle fatigue, and minimum sense of effort. However, muscular co-contraction is often seen in human movement, and the co-contractions were measured using electromyography (EMG). Although muscle co-contraction is important to modulate joint stability, the co-contraction cannot be predicted in simulations using a musculoskeletal model where the sum of the muscle activations or metabolic energies is minimized. Thus, the activations of those biarticular muscles are clearly underestimated. In this study, EMG were measured during squatting, and interpretations to understand biarticular muscles activations are discussed.

Phase-contrast magnetic resonance imaging (PC-MRI) allows us to acquire biofluid flow velocity maps, whereas MRI data is restricted by spatiotemporal resolution limitations and contains theoretically inevitable errors. Although various approaches to estimating actual velocity from MR velocity maps using the mass and momentum conservation laws have been proposed, practically reasonable methodologies are still not well established. This study investigates a practical strategy for estimating physically consistent velocities from MR velocity maps based on variational optimal boundary control through examples of the 2D steady Stokes flow as an incompressible viscous fluid. We defined a minimization problem of the sum of squared residuals between MR and the estimated velocity at all pixels (voxels) considering the image data structure with respect to the Dirichlet boundary velocity condition subject to flow governing equations based on variational formulations. This optimization problem is treated as an unconstrained optimization problem by deriving the Lagrange functional, including the cost function, regularization term, and constraint conditions. The optimality condition is computed using the adjoint variable method in a finite element manner. The boundary velocity profile is iteratively updated by the optimality condition using gradient-based optimization until convergence. Numerical examples for 2D Poiseuille flow with noise-free and noisy reference data demonstrated good convergencies of the cost function minimization. The estimated flow velocities were in excellent agreement with reference data. Finally, we demonstrated the viability of the velocity estimation using the actual MR velocity of the cerebrospinal fluid flow. The proposed approach with further considerations specialized for the MRI may be feasible in providing physically consistent velocity profiles in a versatile target of the biofluid flow.

This study as primary research to propose a non-invasive technique to diagnose the Outerbridge grade of cartilage damage by impact signals. A knee model was experimented with the novel attempt instead of a real knee. The knee model is made by a 3D model converted from magnetic resonance images (MRI) and then assembled by true scale and position. The impact signal is input from the calf and output from the thigh, and the absorption of the impact signal is contended differently by different Outerbridge grades of cartilage. The absorbed impact signals collected by sensors were time-frequency analyzed by continuous Gabor transform (CGT). In addition, the absorbed jerk signal is interpreted by the singular spectrum analysis (SSA) for its oscillation components. The analysis of the signals in this study found that the features derived have abilities to distinguish Outerbridge classification. Therefore, the proposed method can be considered for carrying the experiment onto real knees. This study provides a novel idea to make the diagnostic technique of cartilage damage efficient. Combined with the feature engineering and classification technique, it will help in the clinical diagnosis of knees, this study expects that the method can be applied not only to the diagnosis of the overall knee, but also that the method can diagnose more tiny areas in the early stages of the knee disorder.