Background: Until recently it has not been possible to isolate the mechanical behavior of individual muscles during passive stretching. Muscle shear modulus(an index of muscle stiffness) measured using ultrasound shea...Background: Until recently it has not been possible to isolate the mechanical behavior of individual muscles during passive stretching. Muscle shear modulus(an index of muscle stiffness) measured using ultrasound shear wave elastography can be used to estimate changes in stiffness of an individual muscle. The aims of the present study were(1) to determine the shear modulus—knee angle relationship and the slack angle of the vastus medialis oblique(VMO), rectus femoris(RF), and vastus lateralis(VL) muscles;(2) to determine whether this differs between the muscles.Methods: Nine male rowers took part in the study. The shear modulus of VMO, RF, and VL muscles was measured while the quadriceps was passively stretched at 3°/s. The relationship between the muscle shear modulus and knee angle was plotted as shear modulus—knee angle curve through which the slack angle of each muscle was determined.Results: The shear modulus of RF was higher than that of VMO and VL when the muscles were stretched over 54°(all p < 0.01). No significant difference was found between the VMO and VL(all p > 0.05). The slack angle was similar among the muscles: 41.3°± 10.6°, 44.3°± 9.1°, and 44.3°± 5.6° of knee flexion for VMO, RF, and VL, respectively(p = 0.626).Conclusion: This is the first study to experimentally determine the muscle mechanical behavior of individual heads of the quadriceps during passive stretching. Different pattern of passive tension was observed between mono-and bi-articular muscles. Further research is needed to determine whether changes in muscle stiffness are muscle-specific in pathological conditions or after interventions such as stretching protocols.展开更多
In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and g...In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.展开更多
文摘Background: Until recently it has not been possible to isolate the mechanical behavior of individual muscles during passive stretching. Muscle shear modulus(an index of muscle stiffness) measured using ultrasound shear wave elastography can be used to estimate changes in stiffness of an individual muscle. The aims of the present study were(1) to determine the shear modulus—knee angle relationship and the slack angle of the vastus medialis oblique(VMO), rectus femoris(RF), and vastus lateralis(VL) muscles;(2) to determine whether this differs between the muscles.Methods: Nine male rowers took part in the study. The shear modulus of VMO, RF, and VL muscles was measured while the quadriceps was passively stretched at 3°/s. The relationship between the muscle shear modulus and knee angle was plotted as shear modulus—knee angle curve through which the slack angle of each muscle was determined.Results: The shear modulus of RF was higher than that of VMO and VL when the muscles were stretched over 54°(all p < 0.01). No significant difference was found between the VMO and VL(all p > 0.05). The slack angle was similar among the muscles: 41.3°± 10.6°, 44.3°± 9.1°, and 44.3°± 5.6° of knee flexion for VMO, RF, and VL, respectively(p = 0.626).Conclusion: This is the first study to experimentally determine the muscle mechanical behavior of individual heads of the quadriceps during passive stretching. Different pattern of passive tension was observed between mono-and bi-articular muscles. Further research is needed to determine whether changes in muscle stiffness are muscle-specific in pathological conditions or after interventions such as stretching protocols.
文摘In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.
