Computer simulation of pathological vocal-cord vibration* K. Ishizaka Bell Laboratories,Murray Hill, New Jersey07974
N. Isshiki Schoolof Medicine,Kyoto University,Japan (Received26 February 1976;revised6 July 1976) A dynamic model of the vocal cords, namely, a bilaterally symmetric two-mass model, is extended to a bilaterally asymmetrictwo-massmodel to simulatepathologicalconditionsof the vocal cords. Asymmetric behaviorof the computermodel is investigatedfor variousconditionsof imbalancein bilateral tension.The computer model is found to behave in three basic vibratory modes that are similar to those observedin physiologicalexperimentson larynges under tension imbalance. The three distinctive modes are (1) a vibratory pattern with differencesin phase and amplitude of cord vibration; (2) a nearly periodic motion without glottal closure;and (3) an unsteady,dicrotic or tricrotic motion. The three modesare found to be a strong function of the subglottalpressureand the glottal rest area, as well as the imbalanceconditionsof the cord parameters. The asymmetric vocal-cord model is incorporated into a dynamic vocal-tract synthesizerto simulatespeechwith a hoarsevoice. SubjectClassification:[43]70.20, [43]70.50. INTRODUCTION
Isshiki has developed a new laryngeal surgery, which was devised to modify the vocal cord position and ten-
sion by reforming the thyroid cartilage (Isshiki et al., 1974; Isshiki, 1975). This techniquerequires understanding the imbalances
in the vocal cords and the re-
suiting effects on their vibration and voice quality. Toward this end, systematic physiological experiments
were performed with canine larynges (Tanabe, Isshiki, and Kitajima, 1972). Along with the medical study, a computer simulation
of pathologicalvocal-dord vibration and pathological voice production was undertaken. istic
behavior
of a two-mass
model
Specifically, this coupled lumped-constant representation in the thickness (vertical) direction is a first-order approximation of the distributed system of the vocal cords, which vibrate with a vertical phase difference. The glottis is approximated by thin rectangular crosssections and the masses are permitted lateral motion
only.z For direct extension to the asymmetric cord model, we restrict the asymmetric configuration of the pathological vocal cords such that both vocal cords are still on the same level, and the upper and lower masses--in the sense of the two-mass representationmwill col-
Because of the i•eal of the vocal
cords
ml2
(Ishizaka and Flanagan, 1972), and the naturalhess of the syntheticsoundutterances (Flanagan, Ishizaka, and Shipley, 1975), we expandedthe symmetric two-mass model to a bilaterally asymmetric two-mass model for the pathological vocal cords. This permitted a study of the behavior of the computer model under tension imbalance, and a comparison of the model with the physiological results. In this report, we describe the asymmetric two-mass model, some typical behavior of the computer model under tension imbalance, and a computer synthesis of hoarse voices. The physiological and clinical significance of both the medical study and the computer simulation is beyond the scope of the
present paper and is discussedelsewhere (Isshiki et al.,
VOCAL TRACT I •
z22
/
•76). I. ASYMMETRIC
MODEL
OF THE
VOCAL
CORDS
In the two-mass model (Ishizaka and Matsudaira, 1968), a vocal cord is represented by two mechanical resonators coupled by a spring as seen in Fig. 1, and the vocal cords are assumed to be bilaterally symmetric. This is a functionally equivalent representation of the vocal cords on which the intraglottal air pressure acts. This model does not necessarily imply such a distinct inner structure of the cords, corresponding one-to-one to the spring-coupled resonators. 1193
J. Acoust. Soc. Am., Vol. 60, No. 5, November 1976
/
/
Z12
/ /
Ps
TRACHEA
AND
FIG. 1. Schematic diagram of the asymmetric two-mass approximation
of the vocal cords.
Copyright ¸ 1976 by the AcousticalSociety of America
1193
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 131.111.164.128 On: Wed, 24 Dec 2014 01:29:20
1194
K. Ishizakaand N. Isshiki' Simulation of phatologicvocal cord vibrations
Z21 F21
F22
Z22
were obtained from high-speed motion pictures of live
X22
canine larynges (Tanabe, Isshiki, and Kitajima, 1972), andexcisedlarynges(Isshikiet al., 1976).4 The wave-
_LIL,
forms show the motions of the left and right vocal cords
as functionsof time. In the two waveforms of Fig. 3(a),
Zh21 zh22
! '""' -J
o
X21
x**-x,,
N. Isshiki Schoolof Medicine,Kyoto University,Japan (Received26 February 1976;revised6 July 1976) A dynamic model of the vocal cords, namely, a bilaterally symmetric two-mass model, is extended to a bilaterally asymmetrictwo-massmodel to simulatepathologicalconditionsof the vocal cords. Asymmetric behaviorof the computermodel is investigatedfor variousconditionsof imbalancein bilateral tension.The computer model is found to behave in three basic vibratory modes that are similar to those observedin physiologicalexperimentson larynges under tension imbalance. The three distinctive modes are (1) a vibratory pattern with differencesin phase and amplitude of cord vibration; (2) a nearly periodic motion without glottal closure;and (3) an unsteady,dicrotic or tricrotic motion. The three modesare found to be a strong function of the subglottalpressureand the glottal rest area, as well as the imbalanceconditionsof the cord parameters. The asymmetric vocal-cord model is incorporated into a dynamic vocal-tract synthesizerto simulatespeechwith a hoarsevoice. SubjectClassification:[43]70.20, [43]70.50. INTRODUCTION
Isshiki has developed a new laryngeal surgery, which was devised to modify the vocal cord position and ten-
sion by reforming the thyroid cartilage (Isshiki et al., 1974; Isshiki, 1975). This techniquerequires understanding the imbalances
in the vocal cords and the re-
suiting effects on their vibration and voice quality. Toward this end, systematic physiological experiments
were performed with canine larynges (Tanabe, Isshiki, and Kitajima, 1972). Along with the medical study, a computer simulation
of pathologicalvocal-dord vibration and pathological voice production was undertaken. istic
behavior
of a two-mass
model
Specifically, this coupled lumped-constant representation in the thickness (vertical) direction is a first-order approximation of the distributed system of the vocal cords, which vibrate with a vertical phase difference. The glottis is approximated by thin rectangular crosssections and the masses are permitted lateral motion
only.z For direct extension to the asymmetric cord model, we restrict the asymmetric configuration of the pathological vocal cords such that both vocal cords are still on the same level, and the upper and lower masses--in the sense of the two-mass representationmwill col-
Because of the i•eal of the vocal
cords
ml2
(Ishizaka and Flanagan, 1972), and the naturalhess of the syntheticsoundutterances (Flanagan, Ishizaka, and Shipley, 1975), we expandedthe symmetric two-mass model to a bilaterally asymmetric two-mass model for the pathological vocal cords. This permitted a study of the behavior of the computer model under tension imbalance, and a comparison of the model with the physiological results. In this report, we describe the asymmetric two-mass model, some typical behavior of the computer model under tension imbalance, and a computer synthesis of hoarse voices. The physiological and clinical significance of both the medical study and the computer simulation is beyond the scope of the
present paper and is discussedelsewhere (Isshiki et al.,
VOCAL TRACT I •
z22
/
•76). I. ASYMMETRIC
MODEL
OF THE
VOCAL
CORDS
In the two-mass model (Ishizaka and Matsudaira, 1968), a vocal cord is represented by two mechanical resonators coupled by a spring as seen in Fig. 1, and the vocal cords are assumed to be bilaterally symmetric. This is a functionally equivalent representation of the vocal cords on which the intraglottal air pressure acts. This model does not necessarily imply such a distinct inner structure of the cords, corresponding one-to-one to the spring-coupled resonators. 1193
J. Acoust. Soc. Am., Vol. 60, No. 5, November 1976
/
/
Z12
/ /
Ps
TRACHEA
AND
FIG. 1. Schematic diagram of the asymmetric two-mass approximation
of the vocal cords.
Copyright ¸ 1976 by the AcousticalSociety of America
1193
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 131.111.164.128 On: Wed, 24 Dec 2014 01:29:20
1194
K. Ishizakaand N. Isshiki' Simulation of phatologicvocal cord vibrations
Z21 F21
F22
Z22
were obtained from high-speed motion pictures of live
X22
canine larynges (Tanabe, Isshiki, and Kitajima, 1972), andexcisedlarynges(Isshikiet al., 1976).4 The wave-
_LIL,
forms show the motions of the left and right vocal cords
as functionsof time. In the two waveforms of Fig. 3(a),
Zh21 zh22
! '""' -J
o
X21
x**-x,,
