Tibialis Anterior Muscle: Pedicled Bone Graft for Defect of the Tibia.

Purpose: To report the result of the bone graft retrograde pedicled with the tibialis anterior muscle belly for the treatment of bone defect of tibia. Methods: Between 2017 and 2020, the bone graft pedicled with the tibialis anterior muscle was applied for the treatment of 11 patients with a cortical defect and nonunion of the tibia due to trauma and one patient with segmental bone defect caused by tramatic osteomyelitis. The tibialis anterior has the largest muscle belly, but has not been commonly used due to functional disability following use as transposition muscle flap. New anatomic and clinical data confirm that the distal half of this group of muscles can be transposed with the tendon left intact with no noticeable loss of muscle function. Based on the vascular nutrition of this muscle, we performed a retrograde pedicled bone graft using the muscle belly, thus preserving the function of this muscle. Result: The operation was relatively simple and early bone unions have been achieved without any complications. Conclusion: The bone graft pedicled with the tibialis anterior muscle is useful for the treatment of bone defect of the tibia.

Symmetry-broken coherent state in a ring of nonlocally coupled identical oscillators.

We report on a modulated coherent state in a ring of nonlocally coupled oscillators. Although the identical oscillators are all synchronized under the symmetric coupling, the phase configuration has an inhomogeneous structure. This symmetry-broken coherent state exists only for a nonlocal coupling with both attracting and repulsive interactions, depending on the distance between oscillators, and emerges via a continuous bifurcation from a uniformly coherent state. We analyze the existence and stability of the modulated coherent states on the basis of Ott-Antonsen equations for the local order parameter. Our theoretical results are verified using the numerical simulations.

Chimera and modulated drift states in a ring of nonlocally coupled oscillators with heterogeneous phase lags.

We consider a ring of phase oscillators with nonlocal coupling strength and heterogeneous phase lags. We analyze the effects of heterogeneity in the phase lags on the existence and stability of a variety of steady states. A nonlocal coupling with heterogeneous phase lags that allows the system to be solved analytically is suggested and the stability of solutions along the Ott-Antonsen invariant manifold is explored. We present a complete bifurcation diagram for stationary patterns including the uniform drift and modulated drift states as well as chimera state, which reveals that the stable modulated drift state and a continuum of metastable drift states could occur due to the heterogeneity of the phase lags. We verify our theoretical results using the direct numerical simulations of the model system.

Incoherent chimera and glassy states in coupled oscillators with frustrated interactions.

We suggest a site disorder model that describes the population of identical oscillators with quenched random interactions for both the coupling strength and coupling phase. We obtain the reduced equations for the suborder parameters, on the basis of Ott-Antonsen ansatz theory, and present a complete bifurcation analysis of the reduced system. New effects include the appearance of the incoherent chimera and glassy state, both of which are caused by heterogeneity of the coupling phases. In the incoherent chimera state, the system displays an exotic symmetry-breaking behavior in spite of the apparent structural symmetry where the oscillators for both of the two subpopulations are in a frustrated state, while the phase distribution for each subpopulation approaches a steady state that differs from each other. When the incoherent chimera undergoes Hopf bifurcation, the system displays a breathing incoherent chimera. The glassy state that occurs on a surface of three-dimensional parameter space exhibits a continuum of metastable states with zero value of the global order parameter. Explicit formulas are derived for the system's Hopf, saddle-node, and transcritical bifurcation curves, as well as the codimension-2 crossing points, including the Takens-Bogdanov point.