Myoelastic
Arodynamic Theory of Phonation by Ingo R. Titze with
Mathematical Contributions by Fariborz Alipour
Preface
This book is written for the benefit of voice and speech scientists
who use principles of physics, mathematics, and engineering to understand
and simulate the mechanical processes of phonation. Because it summarizes
and assembles fragments of a theory that was developed over half
a century, scattered over many journals, it should be of particular
value to scientists who enter the field. Often the process of gathering
articles, unifying mathematical notation, understanding the many
assumptions, and removing redundancies consumes much time in the
initial phase of getting acquainted with a new field. I hope this
book will shorten that process.
Chapter 1 is the least mathematical. It describes the laboratory
apparrati for excised larynges and physical models that have for
centuries been the basic testing ground for theories of phonation.
It is difficult to describe much of the detail of such laboratory
systems in journal publications because page limitations do not
permit it. However, the chapter is likely to be the most dated,
given that new instrumentation is rapidly developing.
Chapter 2 is the myo portion of the myoelastic-aerodynamic theory
of phonation. Stress-strain properties of the intrinsic laryngeal
muscles are investigated empirically and mathematically. In addition,
some measurements on connective tissue are reported. All of the
data culminate in a generic one-dimensional constitutive equation
for laryngeal tissue that is orthotropic (fibrous) in nature.
Chapter 3 introduces vocal fold posturing, a topic that has not
received much attention by mathematically oriented investigators.
Describing how the vocal folds are positioned and deformed by muscle
activation requires established theories of continuum mechanics
(as opposed to isolated muscle mechanics in Chapter 2). It also
requires joint and connective tissue mechanics, much of which is
still only fragmentary to date. In particular, three-dimensional
models of muscle deformation under active contraction and boundary
constraints are virtually non-existent.
Chapter 4 is the longest and theoretically most advanced chapter
in the book. It covers the elastic portion of the myoelastic-aerodynamic
theory of phonation. The development progresses from low-dimensional
tissue models in the form of bar masses and springs to high-dimensional
point-mass formulations, and finally to finite element formulations.
Emphasis is on normal modes of the tissue, for which a nomenclature
and many graphical sketches are given.
Chapter 5 is the aerodynamic part of the myoelastic-aerodynamic
theory of phonation. Airflow and particle velocity dynamics are
reviewed from basic principles, leading to Euler’s, Bernoulli’s,
and Navier-Stokes’ accounting of momentum conservation in
fluid flow. The core of the chapter is devoted to one-dimensional
flow in a glottal duct, with the corresponding pressure distributions.
The chapter ends with an exploration into two-dimensional flow under
non-steady conditions, a topic that is in need of much more refinement.
Chapter 6 is all about vocal tract acoustics, which cannot easily
be separated from glottal aerodynamics. From this author’s
point of view, the traditional linear source-filter theory of voice
production is passé. One simple experimental discovery, the
narrow epilarynx tube above the vocal folds, turned the tide from
linear to nonlinear source-filter interaction. With this narrow
entry to the vocal tract, supraglottal acoustic pressures are generally
an integral part of the driving pressures on vocal fold tissues.
Had van den Berg been aware of this tight coupling, he may well
have coined his theory the myoelastic-aeroacoustic theory of phonation.
Finally, Chapter 7 is a first attempt to pull all the physical
subsystems together: tissue mechanics, aerodynamics, and acoustics.
The chapter is written from the point of view of nonlinear dynamics.
The primary nonlinearities are first identified, then the parameter
spaces are discussed in terms of variables under human control (primarily
muscle activations), and regions of self-sustained oscillation are
mapped out. Low dimensional tissue models are used because they
are presently more secure in terms of pressure-flow calculations
than the high dimensional finite element models.
Ingo R. Titze
January 20, 2006
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