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      Comprehensive, Population-Based Sensitivity Analysis of a Two-Mass Vocal Fold Model

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      PLoS ONE
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          Abstract

          Previous vocal fold modeling studies have generally focused on generating detailed data regarding a narrow subset of possible model configurations. These studies can be interpreted to be the investigation of a single subject under one or more vocal conditions. In this study, a broad population-based sensitivity analysis is employed to examine the behavior of a virtual population of subjects and to identify trends between virtual individuals as opposed to investigating a single subject or model instance. Four different sensitivity analysis techniques were used in accomplishing this task. Influential relationships between model input parameters and model outputs were identified, and an exploration of the model’s parameter space was conducted. Results indicate that the behavior of the selected two-mass model is largely dominated by complex interactions, and that few input-output pairs have a consistent effect on the model. Results from the analysis can be used to increase the efficiency of optimization routines of reduced-order models used to investigate voice abnormalities. Results also demonstrate the types of challenges and difficulties to be expected when applying sensitivity analyses to more complex vocal fold models. Such challenges are discussed and recommendations are made for future studies.

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          Probabilistic sensitivity analysis using Monte Carlo simulation. A practical approach.

          The data for medical decision analyses are often unreliable. Traditional sensitivity analysis--varying one or more probability or utility estimates from baseline values to see if the optimal strategy changes--is cumbersome if more than two values are allowed to vary concurrently. This paper describes a practical method for probabilistic sensitivity analysis, in which uncertainties in all values are considered simultaneously. The uncertainty in each probability and utility is assumed to possess a probability distribution. For ease of application we have used a parametric model that permits each distribution to be specified by two values: the baseline estimate and a bound (upper or lower) of the 95 percent confidence interval. Following multiple simulations of the decision tree in which each probability and utility is randomly assigned a value within its distribution, the following results are recorded: (a) the mean and standard deviation of the expected utility of each strategy; (b) the frequency with which each strategy is optimal; (c) the frequency with which each strategy "buys" or "costs" a specified amount of utility relative to the remaining strategies. As illustrated by an application to a previously published decision analysis, this technique is easy to use and can be a valuable addition to the armamentarium of the decision analyst.
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            Bifurcations in an asymmetric vocal-fold model.

            A two-mass model of vocal-fold vibrations is analyzed with methods from nonlinear dynamics. Bifurcations are located in parameter planes of physiological interest (subglottal pressure, stiffness of the folds). It is shown that a sufficiently large tension imbalance of the left and right vocal fold induces bifurcations to subharmonic regimes, toroidal oscillations, and chaos. The corresponding attractors are characterized by phase portraits, spectra, and next-maximum maps. The relevance of these simulations for voice disorders such as laryngeal paralysis is discussed.
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              Voice simulation with a body-cover model of the vocal folds.

              A simple, low-dimensional model of the body-cover vocal-fold structure is proposed as a research tool to study both normal and pathological vocal-fold vibration. It maintains the simplicity of a two-mass model but allows for physiologically relevant adjustments and separate vibration of the body and the cover. The classic two-mass model of the vocal folds [K. Ishizaka and J. L. Flanagan, Bell Syst. Tech. J. 51, 1233-1268 (1972)] has been extended to a three-mass model in order to more realistically represent the body-cover vocal-fold structure [M. Hirano, Folia Phoniar. 26, 89-94 (1974)]. The model consists of two "cover" masses coupled laterally to a "body" mass by nonlinear springs and viscous damping elements. The body mass, which represents muscle tissue, is further coupled laterally to a rigid wall (assumed to represent the thyroid cartilage) by a nonlinear spring and a damping element. The two cover springs are intended to represent the elastic properties of the epithelium and the lamina propria while the body spring simulates the tension produced by contraction of the thyroarytenoid muscle. Thus contractions of the cricothyroid and thyroarytenoid muscles are incorporated in the values used for the stiffness parameters of the body and cover springs. Additionally, the two cover masses are coupled to each other through a linear spring which can represent vertical mucosal wave propagation. Simulations show reasonable similarity to observed vocal-fold motion, measured vertical phase difference, and mucosal wave velocity, as well as experimentally obtained intraglottal pressure.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                4 February 2016
                2016
                : 11
                : 2
                : e0148309
                Affiliations
                [1 ]Division of Engineering, New York University–Abu Dhabi, Abu Dhabi, United Arab Emirates
                [2 ]Department of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaiso, Chile
                The University of Chicago, UNITED STATES
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: DR DC MZ. Performed the experiments: DR DC MZ. Analyzed the data: DR DC MZ. Contributed reagents/materials/analysis tools: DR DC MZ. Wrote the paper: DR DC MZ.

                Article
                PONE-D-15-28536
                10.1371/journal.pone.0148309
                4742229
                26845452
                a1ee3f73-8f6d-41f0-b740-5c904d6e8e81
                © 2016 Robertson et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 30 June 2015
                : 15 January 2016
                Page count
                Figures: 6, Tables: 5, Pages: 19
                Funding
                The authors have no support or funding to report.
                Categories
                Research Article
                Biology and Life Sciences
                Behavior
                Research and Analysis Methods
                Research Design
                Experimental Design
                Physical Sciences
                Mathematics
                Probability Theory
                Probability Distribution
                Biology and Life Sciences
                Physiology
                Sensory Physiology
                Medicine and Health Sciences
                Physiology
                Sensory Physiology
                Research and Analysis Methods
                Simulation and Modeling
                Research and analysis methods
                Mathematical and statistical techniques
                Statistical methods
                Monte Carlo method
                Physical sciences
                Mathematics
                Statistics (mathematics)
                Statistical methods
                Monte Carlo method
                Physical Sciences
                Physics
                Classical Mechanics
                Continuum Mechanics
                Fluid Mechanics
                Fluid Dynamics
                Flow Rate
                Physical Sciences
                Mathematics
                Optimization
                Custom metadata
                All relevant data are within the paper.

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