The Effect of Cricothyroid Muscle Action on the Relation Between Subglottal Pressure and Fundamental Frequency in an In Vivo Canine Model

The relation between subglottal pressure (P_s) and fundamental frequency (F₀) in phonation was investigated with an in vivo canine model. Direct muscle stimulation was used in addition to brain stimulation. This allowed the P_s-F₀ slope to be quantified in terms of cricothyroid muscle activity. Results showed that, for ranges of 0–2 mA constant current stimulation of the cricothyroid muscle, the P_s-F₀ slope ranged from 10 Hz/kPa to 60 Hz/kPa. These results were compared to similar slopes obtained in a previous study on excised larynges in which the vocal fold length was varied instead of cricothyroid activation. A physical interpretation of the P_s-F₀ slope is that the amplitude-to-length ratio of the vocal folds decreases with CT activity, resulting in a smaller time-varying stiffness. In other words, there is less dependence of F₀ on amplitude of vibration when the vocal folds are long instead of short.     

Cooperative Regulation of Vocal Fold Morphology and Stress by the Cricothyroid and Thyroarytenoid Muscles

Voice is produced by vibrations of vocal folds that consist of multiple layers. The portion of the vocal fold tissue that vibrates varies depending primarily on laryngeal muscle activity. The effective depth of tissue vibration should significantly influence the vibrational behavior of the tissue and resulting voice quality. However, thus far, the effect of the activation of individual muscles on the effective depth is not well understood. In this study, a three-dimensional finite element analysis is performed to investigate the effect of the activation of two major laryngeal muscles, the cricothyroid (CT) and thyroarytenoid (TA) muscles, on vocal fold morphology and stress distribution in the tissue. Because structures that bear less stress can easily be deformed and involved in vibration, information on the morphology and stress distribution may provide a useful estimate of the effective depth. The results of the analyses indicate that the two muscles perform distinct roles, which allow cooperative control of the morphology and stress. When the CT muscle is activated, the tip region of the vocal folds becomes thinner and curves upward, resulting in the elevation of the stress magnitude all over the tissue to a certain degree that depends on the stiffness of each layer. On the other hand, the TA muscle acts to suppress the morphological change and controls the stress magnitude in a position-dependent manner. Thus, the present analyses demonstrate quantitative relationships between the two muscles in their cooperative regulation of vocal fold morphology and stress.     

圆形硐室岩爆机制及其突变理论分析

硐室岩爆机制是围岩中处于极限状态的塑性变形集中区承载能力下降时,其中完好岩体部分以弹性方式卸载,当后者释放的弹性能超过前者形变耗散的能量时便发生岩爆．以岩体等效应变为状态变量,建立了硐室岩爆的突变模型,给出岩爆释放地震能计算式．分析表明: 岩爆发生条件与岩体的升降模量比及岩体裂隙发育程度有关;对于特定冲击倾向的岩体,存在相应的临界软化区深度,当满足岩爆发生条件,且软化区深度达到临界深度时会发生岩爆．     

On Vertices, focal curvatures and differential geometry of space curves

The focal curve of an immersed smooth curve γ : θ ↦ γ (θ), in Euclidean space ℝ^m+1, consists of the centres of its osculating hyperspheres. This curve may be parametrised in terms of the Frenet frame of γ (t, n₁, . . . , n_m), as C_γ (θ) = (γ +c₁n₁+ c₂n₂ + • • • + c_mn_m)(θ), where the coefficients c₁, . . . , c_m-1 are smooth functions that we call the focal curvatures of γ . We discovered a remarkable formula relating the Euclidean curvatures κ_i , i = 1, . . . ,m, of γ with its focal curvatures. We show that the focal curvatures satisfy a system of Frenet equations (not vectorial, but scalar!). We use the properties of the focal curvatures in order to give, for ℓ = 1, . . . ,m, necessary and sufficient conditions for the radius of the osculating ℓ-dimensional sphere to be critical. We also give necessary and sufficient conditions for a point of γ to be a vertex. Finally, we show explicitly the relations of the Frenet frame and the Euclidean curvatures of γ with the Frenet frame and the Euclidean curvatures of its focal curve C_γ.     

Validation of a flow–structure-interaction computation model of phonation

Computational models of vocal fold (VF) vibration are becoming increasingly sophisticated, their utility currently transiting from exploratory research to predictive research. However, validation of such models has remained largely qualitative, raising questions over their applicability to interpret clinical situations. In this paper, a computational model with a segregated implementation is detailed. The model is used to predict the fluid–structure interaction (FSI) observed in a physical replica of the VFs when it is excited by airflow. Detailed quantitative comparisons are provided between the computational model and the corresponding experiment. First, the flow model is separately validated in the absence of VF motion. Then, in the presence of flow-induced VF motion, comparisons are made of the flow pressure on the VF walls and of the resulting VF displacements. Self-similarity of spatial distributions of flow pressure and VF displacements is highlighted. The self-similarity leads to normalized pressure and displacement profiles. It is shown that by using linear superposition of average and fluctuation components of normalized computed displacements, it is possible to determine displacements in the physical VF replica over a range of VF vibration conditions. Mechanical stresses in the VF interior are related to the VF displacements, thereby the computational model can also determine VF stresses over a range of phonation conditions.