Douglas D. Cook

Mathematical Models and Numerical Schemes for the Simulation of Human Phonation

Acoustic data has long been harvested in fundamental voice investigations since it is easily obtained using a microphone. However, acoustic signals alone do not reveal much about the complex interplay between sound waves, structural surface waves, mechanical vibrations, and fluid flow involved in phonation. Available high speed imaging techniques have over the past ten years provided a wealth of information about the mechanical deformation of the superior surface of the larynx during phonation. Time-resolved images of the inner structure of the deformable soft tissues are not yet feasible because of low temporal resolution (MRI and ultrasound) and x-ray dose-related hazards (CT and standard x- ray). One possible approach to circumvent these challenges is to use mathematical models that reproduce observable behavior such as phonation frequency, closed quotient, onset pressure, jitter, shimmer, radiated sound pressure, and airflow. Mathematical models of phonation range in complexity from systems with relatively small degrees of freedom (multi-mass models) to models based on partial differential equations (PDEs) mostly solved by finite element (FE) methods resulting in millions of degrees-of-freedom. We will provide an overview about the current state of mathematical models for the human phonation process, since they have served as valuable tools for providing insight into the basic mechanisms of phonation and may eventually be of sufficient detail and accuracy to allow surgical planning, diagnostics, and rehabilitation evaluations on an individual basis. Furthermore, we will also critically discuss these models w.r.t. the used geometry, boundary conditions, material properties, their verification, and reproducibility.

Ranking vocal fold model parameters by their influence on modal frequencies.

The purpose of this study was to identify, using computational models, the vocal fold parameters which are most influential in determining the vibratory characteristics of the vocal folds. The sensitivities of vocal folds modal frequencies to variations model parameters were used to determine the most influential parameters. A detailed finite element model of the human vocal fold was created. The model was defined by eight geometric and six material parameters. The model included transitional boundary regions to idealize the complex physiological structure of real human subjects. Parameters were simultaneously varied over ranges representative of actual human vocal folds. Three separate statistical analysis techniques were used to identify the most and least sensitive model parameters with respect to modal frequency. The results from all three methods consistently suggest that a set of five parameters are most influential in determining the vibratory characteristics of the vocal folds.

Reducing the number of vocal fold mechanical tissue properties: Evaluation of the incompressibility and planar displacement assumptions

The incompressibility and planar displacement assumptions were used to reduce the number of independent tissue parameters required for the characterization of a structural model of the vocal folds. The influence of these simplifying assumptions on the vibratory properties of the model was investigated. The purpose was to provide estimates of the error introduced by these assumptions. The variability in human tissue properties was accounted for through systematic variation of several material parameters. The modal properties of a vocal fold structural model were computed with each assumption and, in turn, were relaxed to determine their respective effects. The results indicated that the incompressibility assumption introduces little error. Errors introduced by the planar displacement assumption were found to depend on the ratio of the longitudinal stiffness and the transverse stiffness. Criteria for determining the compatibility of tissue property values from independent studies are also presented.

Preventing lodging in bioenergy crops: a biomechanical analysis of maize stalks suggests a new approach

The hypothetical ideal for maize (Zea mays) bioenergy production would be a no-waste plant: high-yielding, with silage that is easily digestible for conversion to biofuel. However, increased digestibility is typically associated with low structural strength and a propensity for lodging. The solution to this dilemma may lie in our ability to optimize maize morphology using tools from structural engineering. To investigate how material (tissue) and geometric (morphological) factors influence stalk strength, detailed structural models of the maize stalk were created using finite-element software. Model geometry was obtained from high-resolution x-ray computed tomography (CT) scans, and scan intensity information was integrated into the models to infer inhomogeneous material properties. A sensitivity analysis was performed by systematically varying material properties over broad ranges, and by modifying stalk geometry. Computational models exhibited realistic stress and deformation patterns. In agreement with natural failure patterns, maximum stresses were predicted near the node. Maximum stresses were observed to be much more sensitive to changes in dimensions of the stalk cross section than they were to changes in material properties of stalk components. The average sensitivity to geometry was found to be more than 10-fold higher than the average sensitivity to material properties. These results suggest a new strategy for the breeding and development of bioenergy maize varieties in which tissue weaknesses are counterbalanced by relatively small increases (e.g. 5%) in stalk diameter that reduce structural stresses.

On measuring the bending strength of septate grass stems.

UNLABELLED • PREMISE OF THE STUDY Reliable testing methodologies are a fundamental tenet of scientific research. However, very little information is found in the literature explaining how to accurately measure the structural bending strength of plant stems. It was hypothesized that the most commonly employed loading configuration used in bending experiments (placement of loading anvil at an internodal region of the stem or stalk) may significantly alter test results and introduce errors in bending strength measurements of plant stems.• METHODS Four types of mechanical tests were performed on bamboo (Phyllostachys aurea), giant reed (Arundo donax), and maize (Zea mays) to investigate how different loading configurations employed during three-point bending experiments affect test results of septate grass stems and to develop a testing protocol that provides reliable measures of stalk bending strength.• RESULTS RESULTS confirmed the hypothesis that internodal-loaded three-point bending test can produce erroneous bending strength measurements. This testing methodology causes plant stems to break prematurely and produces failure types and patterns incongruent with stalks that broke in their natural (in situ) environment. In contrast, a modified test configuration produces natural failure patterns and more accurate measurements of bending strength.• CONCLUSION Reliable measurements of stalk bending strength can be obtained by maximizing the span length of bending tests and placing the loading anvil at stronger and denser nodal tissues. These results are relevant to ecological and evolutionary plant biomechanics studies as well as agronomic breeding studies focused on measuring plant phenotypes such as stalk lodging strength, or on improving bending strength of septate plant stems.

Biological variability in biomechanical engineering research: Significance and meta-analysis of current modeling practices

Biological systems are characterized by high levels of variability, which can affect the results of biomechanical analyses. As a review of this topic, we first surveyed levels of variation in materials relevant to biomechanics, and compared these values to standard engineered materials. As expected, we found significantly higher levels of variation in biological materials. A meta-analysis was then performed based on thorough reviews of 60 research studies from the field of biomechanics to assess the methods and manner in which biological variation is currently handled in our field. The results of our meta-analysis revealed interesting trends in modeling practices, and suggest a need for more biomechanical studies that fully incorporate biological variation in biomechanical models and analyses. Finally, we provide some case study example of how biological variability may provide valuable insights or lead to surprising results. The purpose of this study is to promote the advancement of biomechanics research by encouraging broader treatment of biological variability in biomechanical modeling.

Visualizing Collagen Network within Human and Rhesus Monkey Vocal Folds Using Polarized Light Microscopy

Objectives: Collagen fiber content and orientation affect the viscoelastic properties of the vocal folds, determining oscillation characteristics during speech and other vocalization. The investigation and reconstruction of the collagen network in vocal folds remains a challenge, because the collagen network requires at least micron-scale resolution. In this study, we used polarized light microscopy to investigate the distribution and alignment of collagen fibers within the vocal folds. Methods: Data were collected in sections of human and rhesus monkey (Macaca mulatta) vocal folds cut at 3 different angles and stained with picrosirius red. Results: Statistically significant differences were found between different section angles, implying that more than one section angle is required to capture the networks complexity. In the human vocal folds, the collagen fiber distribution continuously varied across the lamina propria (medial to lateral). Distinct differences in birefringence distribution were observed between the species. For the human vocal folds, high birefringence was observed near the thyroarytenoid muscle and near the epithelium. However, in the rhesus monkey vocal folds, high birefringence was observed near the epithelium, and lower birefringence was seen near the thyroarytenoid muscle. Conclusions: The differences between the collagen networks in human and rhesus monkey vocal folds provide a morphological basis for differences in viscoelastic properties between species.

Bending Stress in Plant Stems: Models and Assumptions

Analytic expressions for bending stress can be used to predict mechanical stresses and failure of plant stems. However, the nonuniform shape and anisotropic material properties of plant stems contradict several assumptions that are typically used in the derivation of bending stress equations. The purpose of this chapter is to analyze each of these assumptions to determine the accuracy with which beam theory can predict stresses in plant stems. Finite element models of plant stems were used to investigate and quantify the effect of each assumption. Finally, experimental case-study data was used to illustrate the applications of these equations. The goal of this work is to enable researchers to make informed decisions regarding mechanical models of plant stems used to predict of measure mechanical behavior of plants and plant tissues.

What ranges of two-mass model parameters should be used in subject-specific and population-based modeling studies?

Two-mass models have been used in voice research for over 40 years. It is therefore both surprising and somewhat troubling that there is no firm consensus regarding the values of model parameters that should be used to represent human phonation. A knowledge of the parameter ranges that can (or should) be used is essential for scientifically valid studies involving population-based or subject-specific modeling. In this study, four techniques were used to examine the ranges of two-mass model parameter values that produce behavior representative of human phonation. The first approach involved a review of values that have been used in previous modeling studies. The second approach utilized unrestricted Monte Carlo sampling to examine which ranges can be used to simulate human phonation. The third approach also utilized Monte Carlo sampling, but parameters were restricted based on physical features of the vocal folds. Finally, a reduction or order technique was developed that allows the determination of two-ma...

You really can hear the corn grow! Acoustic emissions in the growth and breakage of maize

Corn (or maize) is the leading grain crop in the United States. More than 350 million metric tons are harvested annually, generating twice as much revenue as any other crop. But a lack of understanding of corn stalk mechanics now hinders further improvement of corn production. The most promising new varieties of corn produce high yields, but are often susceptible to wind-induced failure of the stalk. Failure of this kind is prevalent at two distinct periods: in mid-summer during rapid growth, and after physical maturity, but before harvest. This study utilized acoustic measurements to collect new information about corn growth and failure. Measurements during the growth period were conducted in July 2016 at fields in Nebraska. Late-season stalk experiments involved stalks harvested from South Africa. Flexible, shielded piezo film sensors were used in all measurements (SDT1-028K, Measurement Specialties, Hampton, VA). Acoustic emissions were found to occur continuously during corn stalk growth, though typic...