
				 patients with cleft palate often exhibit nasality , which is a distinctive feature and an important target in speech therapy and rehabilitation .
to evaluate velopharyngeal function , the aerodynamic and acoustic aspects of nasalization have been studied .
an aerodynamic exam can diagnose the degree of velopharyngeal closure [ 1 , 2 ] , and acoustic measurements can categorize velopharyngeal insufficiency [ 3 , 4 ] . the abnormal resonance generated by velopharyngeal insufficiency
can be evaluated quantitatively using a nasometer . on the other hand , the voice and speech of patients with cleft palates
have been studied using many techniques including spectral analysis , perturbation analysis , and formant analysis .
zajac and linville   and lewis et al .   reported that cleft palate speakers have larger frequency perturbations ( jitter ) than normal controls .
however , the methods used to calculate perturbations , jitter , and shimmer are only reliable for nearly periodic voice signals and can not reliably analyze strongly aperiodic signals .
recently , nonlinear dynamic methods have enabled the quantification of aperiodic and chaotic phenomena [ 911 ] . in our previous paper , we reported that the lyapunov exponents ( les ) of the vowels /a/ , /e/ and /o/ for adult cleft palate patients are higher than those for normal resonance adults and that there were no correlation coefficients between les and nasalance scores ( nss ) .
these results suggested that vocal fold vibration may be less stable in adult cleft palate patients than in normal resonance subjects and that the le may be a parameter independent of resonance .
subsequently , we investigated the nonlinear dynamic characteristics of cleft palate speech and voice . in the present paper ,
the purpose was to clarify the difference between the les for cleft palate patients with hypernasality versus without hypernasality and to investigate the relationship between their les and nss .
six repaired cleft palate patients with severe hypernasality ( mean age 9.2 years ; range 6 to 13 , 2 boys and 4 girls ) and six repaired cleft palate patients without hypernasality ( mean age 8.0 years ; range 6 to 13 , 4 boys and 2 girls ) were enrolled .
the presence of hypernasality was perceptually judged by two speech therapists from okayama university hospital .
the present study , which was approved by the okayama university institutional ethical board , was carried out after obtaining informed consents from the parents of all participants .
the voices were recorded through a microphone ( shure bg1.1 , niles , ill ) on a portable solid - state recorder ( marantz pmd 640 , itasca , ill ) with a nasometer ii headset ( model 6400 , kay elemetrics corp . , lincoln park , nj ) in a quiet room designated for speech therapy in the okayama university dental hospital .
the voice samples were recorded on the compact flush medium of the recorder at a sampling rate of 44.1 khz , at 16 bits , in a * .wav file format .
the japanese vowels /a/ ; [ a ] , /i/ ; [ i ] , /u/ ; [  ] , /e/ ; [ e ] , and /o/ ; [ o ] were used as voice samples . each vowel was naturally phonated during approximately one - second three times .
the voice data were processed on a personal computer ( nec mate ma30y , tokyo ) with a modified chaos analyzing program ( ver .
1.0.4 , cci corporation , fukuoka ) , which used the algorithm from sano and sawada .
the first lyapunov exponent ( le1 ) was computed for each one second interval , while the interval was being shifted by 100 msec .
the first zero - crossing points of autocorrelation were calculated for each vowel . as a result , the delay time was estimated at 15 , 32 , 27 , 22 , and 21 points ( 1 point = 1/44.1  msec . ) for the vowels /a/ , /i/ , /u/ , /e/ , and /o/ , respectively ( table 1 ) .
the fractal dimensions were computed using the grassberger - procaccia algorithm , and convergent diagrams , in which the embedding dimensions were assumed , were then constructed for each vowel . thus , the embedding dimensions were estimated at 5 for all vowels ( table 1 ) .
the differences of the first zero - crossing points of autocorrelation , estimated the embedding dimensions , and the mle1s between the two groups with versus without hypernasality were analyzed statistically using the mann - whitney u test .
the statistical package spss ( ver.16.0 ) was utilized , and differences with p values of less than 0.05 were considered to be statistically significant .
there were no significant differences between the first zero - crossing points and the estimated embedding dimensions of those patients with or without hypernasality for all vowels ( table 1 ) .
the mle1 for /o/ in the patients with hypernasality was significantly higher than in patients without hypernasality ( p = 0.015 ) ( table 2 ) .
the nss for /i/ , /u/ , /e/ , and /o/ in the patients with hypernasality were significantly higher than in patients without hypernasality ( table 3 ) .
the correlation coefficients between the mle1 and ns for all vowels were not statistically different ( table 4 ) .
although nasality can be evaluated using a spectral analysis of speech signals , voice acoustic measures of nasality are not universally used in clinical or empirical work because of ambiguity in the literature regarding the appropriate acoustic methodology , the amount of labor involved as compared with the nasometer , and so forth .
however , vogel et al .   demonstrated the potential for the wider application of acoustic investigation into nasality .
several authors have described laryngeal disorders , including organic and functional disorders , in cleft palate speakers [ 16 , 17 ] .
zajac and linville   and lewis et al .   reported that cleft palate speakers have higher frequency perturbations ( jitter ) than normal controls .
nicollas et al .   demonstrated that neither jitters nor shimmers significantly differed with age or gender .
van lierde et al .   reported a multiparameter approach to vocal quality but stated that the nature of the vocal quality and the voice range measurement differences can not be explained from their study .
therefore , we concluded that future studies on the voice of cleft palate subjects using nonlinear analysis may be beneficial in gaining further insight into the mechanics of phonation . to our knowledge
, there have been no reports on the application of nonlinear dynamic analysis to cleft palate speech .
our previous study demonstrated that the mle1 for /a/ , in both males and females with cp , is significantly higher than in normal resonance individuals and that the mle1 for /e/ in males with cp and for /o/ in females with cp are significantly higher than in normal resonance individuals . since the mle1 is a measure of the instability of the voice signal , these results suggest that the vocal fold vibration is less stable in cp speakers than in normal resonance subjects . in addition , the correlation coefficients between the mle1 and ns for all vowels were not statistically different in both normal and cp subjects .
the mle1 for /o/ in the patients with hypernasality was significantly higher than in patients without hypernasality ; in other words , the voice signal of /o/ for the patients with hypernasality was more instable than in those without hypernasality .
on the other hand , the correlation coefficients between the mle1 and ns for all vowels were not statistically different in patients both with versus without hypernasality .
this supported the independence of chaotic phenomenon and nasal resonance in cleft palate speech and voice , which was demonstrated in our previous paper .
nicollas et al .   reported that the large le seems to decrease with age from their studies of children between 6 and 12 years of age .
it was also suggested that the large le is lower in boys than in girls overall but varies for each age . in our present study , the boys and girls were not separated because of the small sample size .
the voice signal of /o/ for the patients with hypernasality was more instable than in those without hypernasality .
 
 objectives . to clarify the difference between lyapunov exponents ( les ) for cleft palate ( cp ) patients with hypernasality versus without hypernasality and to investigate the relationship between their les and nasalance scores ( nss ) . 
 material and methods . 
 six cp patients with severe hypernasality ( mean age 9.2 years ) and six cp patients without hypernasality ( mean age 8.0 years ) were enrolled . 
 five japanese vowels were recorded at 44.1  khz , and the nss were measured simultaneously . the mean first le ( mle1 ) from all one - second intervals was computed . 
 results . 
 the mle1 for /o/ in patients with hypernasality was significantly higher than that in patients without hypernasality . 
 the correlation coefficients between the mle1 and ns for all vowels were not statistically different . conclusion . 
 the voice signal of /o/ for the patients with hypernasality was more instable than in those without hypernasality . 
 the chaotic phenomenon was independent of nasal resonance in cp voice . 
1. Introduction
2. Materials and Methods
3. Results
4. Discussion
5. Conclusions