Formant Centralization Ratio (FCR): A proposal for a new acoustic measure of dysarthric speech

Abstract

Background and Aims

The vowel space area (VSA) has been used as an acoustic metric of dysarthric speech, but with varying degrees of success. Here we test an alternative metric -- Formant centralization ratio (FCR) -- that is hypothesized to more effectively differentiate dysarthric from healthy speech and register treatment effects.

Methods

Speech recordings of 38 individuals with idiopathic Parkinson disease (IPD) and dysarthria (19 of whom received one month of intensive speech therapy (LSVT® LOUD)) and 14 healthy controls were acoustically analyzed. Vowels were extracted from short phrases. The same vowel-formant elements were used to construct the FCR, expressed as (F2u+F2𝔞+F1i+F1u)/(F2i+F1𝔞), the VSA, expressed as ABS((F1i*(F2𝔞–F2u)+F1𝔞*(F2u–F2i)+F1u*(F2i–F2𝔞))/2), a logarithmically scaled version of the VSA (LnVSA), and the F2i/F2u ratio.

Results

Unlike the VSA and the LnVSA, the FCR and F2i/F2u robustly differentiated dysarthric from healthy speech and were not gender-sensitive. All metrics effectively registered treatment effects and were strongly correlated with each other.

Conclusions

Albeit preliminary, the present findings indicate that the FCR is a sensitive, valid and reliable acoustic metric for distinguishing dysarthric from normal speech and for monitoring treatment effects, probably so because of reduced sensitivity to inter-speaker variability and enhanced sensitivity to vowel centralization.

Introduction

Acoustic analysis has the potential of providing quantitative, objective, and precise means to help depict the presence, severity, and characteristics of motor speech disorders, and to help monitor deterioration or improvement in speech with disease progression, recovery, or treatment effects (e.g., Kent, Weismer, Kent, Vorperian, & Duffy, 1999). The rationale for using acoustic analysis to assess motor speech function is straightforward: the speech signal contains measurable acoustic parameters that are lawfully related to some aspects of speech production and perception (Fant, 1960; Honda & Kusakawa 1997). Thus, by studying speech acoustics, one can make reasonable inferences about motor speech functions, normal and abnormal. Yet, as commented by Kent and Kim (2003), “Acoustic analysis, like any method, carries its own interpretative challenges and limitations, all the more so when it is applied to disordered speech with varying degrees of severity”. (p. 428).

The present study deals primarily with issues and potential alternatives related to acoustic methods of measuring vowel articulation impairment in individuals with dysarthria secondary to idiopathic Parkinson disease (IPD); however, the information gathered from this study may have implications for other types of dysarthria, such as those associated with amyotrophic lateral sclerosis, multiple sclerosis, traumatic brain injury, and cerebral palsy (CP). The most relevant acoustic parameters for the perception and production of vowels are the frequencies of the first two formants, F1 and F2 (Hillenbrand, Getty, Clark, & Wheeler, 1995). These formant frequencies change in a fairly predictable way as a function of the movements of the articulators and as a function of changes in the three dimensional configuration of the vocal tract that result from these articulatory movements. In general, the frequency of F2 increases and that of F1 decreases as the tongue moves forward (e.g., to form the vowel /i/) and the frequency of F2 decreases as the tongue moves backward (e.g., to form the vowels /u/ and /a/). Also, the frequency of F1 decreases when the tongue is elevated (e.g., to form the vowels /i/ and /u/) and increases when the tongue is lowered, alone or in concert with a downward movement of the jaw (e.g., to form the vowel /a/). Furthermore, the frequencies of both F1 and F2 decrease when the lips are rounded (e.g., to form the vowel /u/) and increase when the lips are retracted or become unrounded (e.g., to form the vowels /i/ and /a/) (Kent et al., 1999).

Most types of dysarthria are characterized by articulatory undershoot, i.e., reduced range of articulatory movements, to the extent that the intended place and degree of vocal tract constriction are not fully achieved (Kent & Kim, 2003). This undershoot is likely to result in vowel formant centralization; i.e., formants that normally have high frequencies tend to have lower frequencies, and formants that normally have low frequencies tend to have higher frequencies (Sapir, Spielman, Ramig, Story, & Fox, 2007). One common way to represent this centralization is with the vowel space area (VSA) (Kent & Kim, 2003). Due to articulatory undershoot and consequent centralization of vowels, the VSA in the speech of individuals with dysarthria is expected to be compressed relative to that of normal speech (Kent & Kim, 2003). Improvement in speech due to natural recovery or treatment effects should be reflected in the expansion of the VSA toward normalcy (Sapir et al, 2003). Also, whereas conversational speech is likely to be characterized by some amount of articulatory undershoot, formant centralization, and reduced VSA (cf. Fourakis, 1991), clear speech and hyperarticulated speech are likely to be characterized by increased articulatory precision, VSA expansion, and improvement in speech intelligibility (Ferguson & Kewley-Port, 2007).

In English, the VSA is usually constructed by the Euclidean distances between the F1 and F2 coordinates of the corner vowels /i/, /u/, and /a/ (triangular VSA), or the corner vowels /i/, /u/, /a/, and /ae/ (quadrilateral VSA) in the F1-F2 plane (Kent & Kim, 2003). In the present study we will use the triangular VSA with the vowels /i/, /u/, and /a/. We will also use a logarithmic version of this VSA (henceforth LnVSA), which means that the formant frequencies of the three vowels are logarithmically scaled (with a natural logarithm, or Ln) before the VSA is constructed. Such logarithmic scaling is important for reducing interspeaker variability (see below). The mathematical expressions of the triangular VSA and LnVSA and the explanations for the logarithmic scaling as a means to transform differences in formant frequencies to ratios of formant frequencies are provided in detail in Appendix A.

Several studies have documented centralization of formants and/or compression of VSA in speakers with dysarthria (e.g., Liu, Tsao, & Kuhl, 2005; Weismer, Jeng, Laures, Kent, & Kent, 2001; Zeigler & von Cramon, 1983). Some of these studies have also demonstrated statistically significant positive correlations between VSA and speech intelligibility scores (e.g., Liu et al., 2005; Weismer, et al., 2001, in individuals with ALS). Expansion of vowels and VSA following natural recovery or effective treatment has also been documented (e.g., Sapir et al, 2003; Zeigler & von Cramon, 1983). However, some studies have failed to find statistically significant differences between dysarthric and normal speech on some vowel acoustic measures, including VSA, although an overall trend toward centralization of vowels in the dysarthric speech was evident (e.g., Bunton & Weismer, 2001; Sapir et al, 2007; Weismer et al., 2001, in individuals with IPD). Moreover, in some studies, the VSA accounted for only 6–13% of the variance in measures of speech intelligibility (McRae, Tjaden, & Schoonings, 2002; Tjaden & Wilding, 2004).

The reasons for the inconsistent performance of the VSA are not clear. One likely explanation is that the VSA is highly sensitive to interspeaker variability, and this variability might mask, statistically speaking, true differences between dysarthric and normal speech. Interspeaker variability in vowel formant frequencies and VSA is expected due to anatomical and physiological differences, such as those associated with gender and age (re: size and shape of the vocal tract) (Hashi, Westbury, & Honda, 1998; Yang, 1996), idiosyncratic strategies of posturing the articulators (e.g., habitually speaking with a relatively fronted or retracted tongue posture for all vowels; habitually coupling or decoupling lip rounding with tongue backing in the formation of /u/) (e.g., de Jong, 1997; Hashi et al., 1998), idiosyncratic differences in inter-articulatory coordination or coarticulation (de Jong, 1997), and idiosyncratic differences in vowel perception (e.g., discrimination or prototypic preference), the latter having been shown to affect the vowel production map unique to the individual (Perkell, Guenther, Lane, et al, 2004). Other factors that might also affect interspeaker variability include severity and/or pathophysiology of the dysarthria, idiosyncratic compensatory adjustments to the dysarthria, the nature of the speech task, the phonetic environment in which the vowels in the VSA are measured, and the specific methods of measuring the vowels (Rosen et al., 2008; Yunusova, Weismer, Westbury , Lindstrom, 2008). Given these facts, it is clear that to improve differentiation of dysarthric from normal speech, the acoustic metric must be minimally affected by speaker-related variability and maximally affected by the articulatory impairment, as reflected by vowel formant centralization or other acoustic indices that closely represent the impairment.

In the present study we wanted to test an acoustic metric we have developed that has been designed to maximize sensitivity to vowel centralization and minimize sensitivity to interspeaker variability. We call this metric Formant centralization ratio, or FCR. The FCR is expressed as (F2u+F2𝔞+F1i+F1u)/(F2i+F1𝔞), where F2u is the frequency of the second formant of the vowel /u/, F1i is the frequency of the first formant of the vowel /i/, and so on. The FCR is designed so that the formant frequencies in the numerator are likely to increase, and the formant frequencies in the denominator are likely to decrease with vowel centralization. This arrangement should maximize sensitivity to vowel centralization (i.e., the FCR should increase with centralization and decrease with vowel expansion).

Note also that the FCR is expressed as a ratio. The expression of vowel formants as a ratio is one of the normalization procedures that have been used to reduce speaker-related variability in vowel perception studies (Adank, Smits, & van Hout, 2004). Here we use it not with respect to vowel perception but as a simple way to reduce interspeaker variability in formant frequencies (Yang, 1996). When vowel formants are expressed as a ratio, the value of this ratio is likely to be similar across speakers, even though the formant frequencies of the same vowel across speakers are different. Thus, for example, if a man’s F1i=300 Hz and F2i=2400Hz, a woman’s F1i=350Hz and F2i=2800Hz, and a child's F1i=400Hz and F2i=3200Hz, the ratio F2i/F1i will be the same for all speakers (2400/300=8, 2800/350=8, 3200/400=8), in spite of relatively large differences in F2i and F1i across the speakers. In fact, the coefficient of variation (CV) in this specific example is 0% (CV=SD/mean=0/8=0%). Note also that if we replace the division operator (F2i/F1i) with a subtraction operator (F2i-F1i) the variance across the three speakers is much larger (2400−300=2100, 2800−350=2450, 3200−400=2800, mean difference=2450, SD=350, CV=350/2450=14%). Thus, although the F2i-F1i can also reflect vowel centralization, the interspeaker variability associated with it is much larger than that with the F2i/F1i ratio.

The effects of the FCR on interspeaker variability are considered in Table 1. These are average vowel formant frequencies of men, women, and children obtained from the study by Hillenbrand et al. (1995, Table V, p. 3103). To the right of the formant data are the results of the VSA and FCR metrics applied to these data. Note that the formant frequencies in the children are higher than those of women, and those of women are higher than those of men, as would be expected from the anatomical differences in the vocal tract dimensions associated with gender and age. Note also that when the VSA is applied to the respective formant frequencies in each of the groups, it is highest in children, lowest in men, and in between for women. Thus, the VSA is highly sensitive to these group differences. This sensitivity is also reflected by the relatively large coefficient of variation (CV=26%) shown in Table 1. In contrast, when the FCR is applied to these formant data, there is little difference between the three groups, and the CV value is 1%. Thus, the FCR dramatically reduces interspeaker variability. Note also that the FCR values across men, women, and children in Table 1 are near 1.0. The fact that the FCR has values near 1.0 across these different groups of speakers suggests that it is insensitive, or only minimally sensitive, to gender and age effects. It also suggests that across speakers (at least of the American English language) the sum of the frequencies of the formants in the numerator is very similar to that of the denominator. The FCR also has asymptotic meaning. Specifically, in the extreme case of vowel centralization, the formants of the vowels /i/, /u/, and /a/ should collapse onto one location in the F1-F2 plane, whereby F1i=F1u=F1𝔞 and F2i=F2u=F2𝔞. In terms of the FCR formula, this means that the maximum FCR value should be 2, as indicated below:

$$\text{FCR}=(\mathrm{F}2+\mathrm{F}2+\mathrm{F}1+\mathrm{F}1)/(\mathrm{F}2+\mathrm{F}1)$$ (1)

$$=(2\mathrm{F}2+2\mathrm{F}1)/(\mathrm{F}2+\mathrm{F}1)$$ (2)

$$=2(\mathrm{F}2+\mathrm{F}1)/(\mathrm{F}2+\mathrm{F}1)$$ (3)

$$=2.0$$

The FCR value of ∼ 1.0 calculated with the mean data of Hillenbrand et al. above suggests that this value may closely approximate the normal FCR value, at least for American English speakers. What the asymptote should be at the other end of the FCR scale is not clear; theoretically, it should get infinitesimally close to 0 as the vowel space expands. Empirically, though, it is likely to be close to a value that is associated with clear speech and hyperarticulation of vowels. Ferguson & Kewley-Port (2007) noted that in clear speech the quadrilateral vowel space area increases by up to 10% compared to conversational speech. If this increase is typical of clear or hyperaticulated speech, we should expect the FCR value associated with clear speech to be around 0.90.

Table 1.

Mean formant data of men, women and children from the study by Hillenbrand et al (1995). The results of applying the VSA and FCR to these data are shown in the right columns. Also shown are the mean, standard deviation (SD) and coefficient of variation (CV). VSA = triangular vowel space area. FCR = Formant centralization ratio.

	F1i (Hz)	F2i (Hz)	F1𝔞 (Hz)	F2𝔞 (Hz)	F1u (Hz)	F2u (Hz)	VSA (Hz2)	FCR
Men	342	2322	768	1333	378	997	264423	0.99
Women	437	2761	936	1551	459	1105	399862	0.96
Children	452	3081	1002	1688	494	1345	448147	0.97
Mean	410	2721	902	1524	444	1149	370811	0.97
SD	60	381	121	179	60	178	95245	0.01
CV	15%	14%	13%	12%	13%	16%	26%	1%

Table 5.

Mean formant data of children with dysarthric associated with cerebral palsy, and neurologically normal children from the study by Higgins & Hodge (2002). The results of applying the VSA, LnVSA, F2i/F2u, and FCR to these data are shown in the right columns.

	F1i (Hz)	F2i (Hz)	F1𝔞 (Hz)	F2𝔞 (Hz)	F1u (Hz)	F2u (Hz)	VSA (Hz2)	LnVSA (LnHz2)	FCR	F2i/F2u
Children with normal speech	532	3528	1232	1556	520	1710	648132	0.31	0.91	2.06
Children with dysarthric speech	576	3406	930	1765	592	2029	230601	0.12	1.14	1.68

To test the sensitivity of the FCR to formant centralization and its ability to differentiate dysarthric from normal speech, we elected to study vowel articulation in individuals with idiopathic Parkinson's disease (IPD) and dysarthria and compare it to healthy controls (HC). The dysarthria associated with IPD has been characterized by various voice and speech abnormalities, including articulatory undershoot (Sapir, Ramig, & Fox, 2008). Thus, we expect the FCR to reflect such undershoot, by showing vowel centralization in the IPD speakers relative to the HC speakers. We also expect the FCR to show a decrease in vowel centralization following successful treatment of the dysarthria, such as the Lee Silverman Voice Treatment (LSVT® LOUD) (Sapir et al., 2007). We therefore elected to test the ability of the FCR to register treatment effects in individuals who have been treated with LSVT, by measuring changes from pre- to post-treatment. The LSVT is an intensive regimen that trains individuals to speak in a healthy louder voice and with greater effort than they use in their hypophonic and hypokinetic speech (Ramig, Fox, & Sapir, 2008). The treatment is based on principles of motor learning and neural plasticity and has been proven highly effective in the reduction of speech problems, including hypokinetic vowel articulation in individuals with IPD (Fox, Ramig, Ciucci, Sapir, McFarland, & Farley, 2006; Sapir et al., 2007).

As argued above, the VSA is limited in its ability to differentiate dysarthric from healthy speech due, most likely, to its high sensitivity to interspeaker variability. On the other hand, the VSA should be minimally affected by interspeaker variability when it is used to assess treatment effects, as the comparison is largely within rather than across speakers. Therefore, we expect the VSA to be sensitive to changes associated with treatment. We also expect the FCR to correlate well with the VSA when the correlated variable is the change induced by treatment.

To test the hypothesis that the VSA performs less effectively than the FCR, presumably because of high sensitivity of the VSA to interspeaker variability, we compared the VSA with a logarithmically scaled version of the VSA (henceforth LnVSA). As shown in Appendix A, logarithmic scaling of formant frequencies maps differences between frequencies into a ratio of these frequencies; once these frequencies are in a ratio form, their interspeaker variability is likely to be reduced considerably, as discussed above (see also discussion on gender normalization procedures in Yang, 1996). Thus, we would expect the LnVSA to be less affected by interspeaker variability and to perform better than the VSA in the differentiation of dysarthric from normal speech. The sensitivity of a metric to interspeaker variability is indexed here by gender effects and the magnitude of coefficient of variation (CV). High sensitivity to interspeaker variability should be reflected in significant gender effects and relatively large CV values. Low sensitivity to interspeaker variability should be reflected in the lack of gender effects and relatively small CV values. We also expected that the FCR and LnVSA will show stronger correlations with each other than the correlation between the FCR and VSA, given that both the FCR and LnVSA are designed to reduce interspeaker variability whereas the VSA is not.

We also elected to compare the FCR with the F2i/F2u ratio. The F2i/F2u ratio has been shown to effectively differentiate dysarthric speech of individuals with IPD from normal speech of healthy age- and gender-matched controls, and to effectively register treatment effects (Sapir et al, 2007). This metric has also been proven highly effective in differentiating abnormal articulation in children with Down syndrome from normal speech in typical children (Moura et al, 2008). The F2 frequency range formed by the English vowels /i / and /u/ is relatively large (∼1500 Hz, from about 1000 Hz for the vowel /u/ to about 2500 Hz for the vowel /i / (Hillenbrand et al., 1995), and as such, it might serve to index changes in the extent of articulatory movements. This ratio should be especially sensitive to anterior-posterior movements of the tongue, and rounding and un-rounding of the lips, as these movements are most likely to affect F2i and F2u. Thus, the F2i/F2u ratio should decrease with articulatory undershoot and increase with improved articulatory movements. Other researchers have successfully used F2 parameters (e.g., F2u, F2i-F2u, F2 extent, F2 slope) to quantify and measure speech articulation impairment in dysarthric speakers (e.g., Rosen et al., 2008; Yunusova et al., 2005). Thus, the F2i/F2u seems a reasonable metric against which the convergent validity of the FCR might be tested. One might argue that the FCR is superfluous, given that the F2i/F2u in our previous study (Sapir et al., 2007) reliably differentiated dysarthric and normal vowel articulation and effectively registered treatment effects. However, the F2i/F2u is inclusive of only one formant and two vowels, whereas the FCR is inclusive of two formants and three vowels. Thus, the FCR has the advantage of being more effective than the F2i/F2u in the detection of articulatory abnormalities when these abnormalities involve more than just F2i and F2u.

METHODS

Participants

The study included 38 individuals with IPD and dysarthria, of whom 19 received intensive voice/speech therapy (LSVT® LOUD) (henceforth PD-T group, 10 males, 9 females) and 19 received no treatment (henceforth PD-NT group, 9 males, 10 females). These groups were compared to another group of 14 neurologically healthy controls with normal voice and speech (henceforth, HC, 7 males, 7 females), age- and gender-matched to the IPD groups. The acoustic data (mean and SD of the F1 and F2 frequencies of the vowels /i/, /u/, and /a/) and the biomedical data of the majority of these individuals (29 of the IPD individuals and all HC individuals) have already been reported in our previous study (Sapir et al., 2007).

All participants were speakers of American English as their first language. The majority of these individuals were recruited from either Tucson, Arizona or Denver, Colorado. The mean age of the PD-T group was 68.79 (SD = 9.85), the mean stage of disease (Hoehn & Yahr, 1967, disability scale: 0–5, where 5 is most severe) in this group was 2.92 (SD=1.08), and the mean years since diagnosis was 6.97 (SD=6.12). The mean age of the PD-NT group was 68.11 (SD = 10.83), the mean stage of disease was 2.12 (SD=0.65), and the mean years since diagnosis was 7.00 (SD=5.08). The mean age of the HC group was 69.79 (SD=7.51).

In the majority of the participants with IPD, the dysarthria was rated as mild or moderate and characterized by reduced loudness, hoarseness, and monotone speech. In some individuals, there were other speech problems, mostly imprecise articulation. The participants with IPD were taking anti-Parkinson medications at the time of data collection. They were all optimally medicated and stable at the time of the study.

Data Collection

For the Tucson participants, data collection for all three groups took place on 3 different days just before the time of treatment and on 2 different days just after the end of treatment. For the Denver participants, data collection for all three groups took place on a single day before the beginning of treatment and on a single day just after the end of treatment. Those recordings took place within 2–3 days before or after treatment. The terms T1 and T2 will be used to indicate the day of recording before treatment (PRE) and the day of recording after treatment (POST), respectively, with the understanding that only the PD-T group received treatment and that the specific dates of recordings were different across participants, yet the overall time schedule, as described previously, was the same for all participants.

The data in the present study were based on multiple repetitions of three phrases obtained in the Tucson recordings (“The blue spot is on the key,” “The potato stew is in the pot” and “Buy Bobby a puppy”), and on multiple repetitions of one phrase obtained in the Denver recordings (“The stew pot is packed with peas”). Each phrase in the Tucson recordings was repeated by each participant 3 times on each day of recording (i.e., 9 times total before and 6 times total after the time of treatment), and the single phrase in the Denver recordings was repeated by each participant 10 times on each day of recording (i.e., 10 times before and 10 times after time of treatment). The Tucson recordings were obtained in a sound-treated booth using a head mounted condenser microphone (AKG C410) positioned 6 cm from the lips and a DAT 2-channel recorder (Sony PC-208AUC). The data were digitized from the DAT tape to a computer at a sampling rate of 22 kHz using Goldwave® software. Similar recording methods were used in the Denver study, but the acoustic signals were collected directly to a computer using an AKG C420 head-mounted microphone and sampled at 44.1 kHz with Kay Elemetrics Inc. CSL model 4300B hardware and software. All files were down-sampled to 22 kHz for formant analysis.

Acoustic analyses and measurements

The vowels /i/, /u/, and /a/ were extracted from the words “key”, “stew”, and “Bobby” (Tucson recordings), or from the words “peas”, “stew”, and “pot” from the single phrase (Denver recordings), respectively. Regardless of the type and number of phrases uttered and the number of samples used, all vowels were extracted and all F1 and F2 values were measured in the same manner. Formant frequency analysis was done using TF32, a Windows-based version of CSpeech® software (Milenkovic, 2001). Forty percent (40%) of the analyzed data were also analyzed using Matlab® (version 5.3) to assess reliability of the measures. F1 and F2 frequency values for /i/ and /a/ were measured for a 30-ms segment at the temporal midpoint of each vowel. For the vowel /u/, F1 and F2 were measured from a 30 ms segment at the end of the vowel. This segment was chosen to avoid the intrusion of the formant transition immediately preceding the /u/ in “stew”. Tests of the validity and reliability of the acoustic measures have been described in our previous publication (Sapir et al., 2007). These tests indicate high intra- and inter-judge reliability for the F2 measures (Pearson product correlation r=0.96–0.99) and moderate-to-high for the F1 measurements (r=0.83–0.95) across the different vowels (/i/, /u/, /a/) and groups (IPD, HC). Standard error of measurements (SEMs) were relatively small for both F2 (range=20–26 Hz) and F1 measurements (range=19–42 Hz).

Statistical analyses

The vowel-formant data (e.g., frequency, in Hz, of F1𝔞, F2i, F1u, etc.) were separately averaged for each individual for T1 and T2. The VSA, F2i/F2u and FCR were then constructed from these averages. In the case of the LnVSA, the formant frequencies were first transformed to a logarithmic scale and then used to construct the LnVSA. These data were then subjected to statistical analyses as detailed here. The Kolmogorov-Smirnov test was used to test for normality of the distribution of the data. Differences between the three groups (PD-T, PD-NT, HC) for each of the dependent variables (VSA, F2i/F2u, FCR) were separately evaluated for the T1 (“Pre-treatment”) data using a one-way analysis of variance (ANOVA). A repeated measures multivariate analysis of variance (RM-MANOVA) was run to assess T2 (“Post-treatment”) differences while accounting for T1 variation. The Duncan's Multiple Range test was used for planned comparison analyses of significance, with alpha set at the 0.05 level for significance. Gender effects for the T1-T2 differences in the three groups were tested with a two way ANOVA with interaction. The magnitude of difference between means was assessed with an effect size (ES) measure, using a pooled variance method (Cohen, 1988). By this method, an ES of 0.80 is considered large, 0.50 is considered medium, and 0.20 is considered small. Inter-speaker variability was measured in terms of coefficient of variation (CV).

To assess the strength of the relationship between VSA, LnVSA, F2i/F2u and FCR, the T1-T2 differences of these metrics in the PD-T group were correlated using Pearson Product Moments correlation analysis. We anticipated that if the four acoustic metrics measure similar phenomena, this should be reflected by a strong correlation. Poor correlation between two metrics might imply that these metrics measure different aspects of vowel articulation.

RESULTS

Tests of normality

The Kolmogorov-Smirnov test indicated that, with one exception, the VSA, LnVSA, F2i/F2u and FCR data were normally distributed in each of the three groups (PD-T, PD-NT, HC) and at T1 and T2. The exception was the VSA at T2 in group PD-T, which deviated from normality (kurtosis=−1.1138). Nevertheless, given that the majority of the data showed normal distribution, given that the majority of the analyses were done with the T1 data, and given the highly significant differences in the VSA from T1 to T2 in the PD-T group (see below), we elected to use parametric statistics for the data.

Differences between groups at T1

The mean and standard deviation (SD) of the vowel-formant elements at T1 and T2 are shown in Table 2 and Table 3. The mean and standard deviation of the VSA, F2i/F2u, LnVSA and FCR data at T1 and T2 are shown in Table 4. The mean and standard deviation (error bar) of the VSA, LnVSA, F2i/F2u and FCR data at T1 and T2 for the three groups (PD-T, PD-NT, and HC) are shown graphically in Figure 1.

Table 2.

Mean (in Hz) and standard deviation (SD) of the F1 of the vowels /i/, /u/, and /a/ at T1 (“PRE”) and T2 (“POST”) in the three groups of participants (PD-T, PD-NT, and HC). For explanation of the abbreviations, see Figure 1 caption.

		F1i (Hz)	F1i (Hz)	F1u (Hz)	F1u (Hz)	F1𝔞 (Hz)	F1𝔞 (Hz)
		T1	T2	T1	T2	T1	T2
	mean	330	328	361	369	756	803
PD-T	SD	67	62	60	61	114	105
	CV	20.3%	18.9%	16.6%	16.7%	15.1%	13.1%
	mean	338	331	363	370	786	781
PD-NT	SD	30	26	45	47	103	104
	CV	8.8%	7.8%	12.4%	12.6%	13.0%	13.3%
	mean	318	320	384	380	788	775
HC	SD	41	46	35	43	89	94
	CV	13.0%	14.4%	9.2%	11.4%	11.3%	12.1%

Table 3.

Mean (in Hz) and standard deviation (SD) of the F2 of the vowels /i/, /u/, and /a/ at T1 (“PRE”) and T2 (“POST”) in the three groups of participants (PD-T, PD-NT, and HC). For explanation of the abbreviations, see Figure 1 caption.

		F2i (Hz)	F2i (Hz)	F2u (Hz)	F2u (Hz)	F2𝔞 (Hz)	F2𝔞 (Hz)
		T1	T2	T1	T2	T1	T2
	mean	2417	2490	1364	1252	1326	1315
PD-T	SD	303	328	193	213	182	137
	CV	12.5%	13.2%	14.1%	17.0%	13.7%	10.4%
	mean	2480	2481	1323	1330	1335	1330
PD-NT	SD	335	329	216	217	135	134
	CV	13.5%	13.3%	16.3%	16.3%	10.1%	10.1%
	mean	2565	2563	1189	1212	1307	1315
HC	SD	222	232	163	145	102	125
	CV	8.7%	9.1%	13.7%	11.9%	7.8%	9.5%

Table 4.

Mean, standard deviation (SD), and coefficient of variation (CV) of the FCR, VSA, LnVSA, and F2i/F2u data at times T1 and T2 and in the three groups (PD-T, PD-NT, and HC). For explanation of the abbreviations, see Figure 1 caption. The VSA is expressed in Hz² (rounded off to 1 Hz accuracy).

		FCR	FCR	VSA (Hz2)	VSA (Hz2)	LnVSA (LnHz2)	LnVSA (LnHz2)	F2i/F2u	F2u/F2u
		T1	T2	T1	T2	T1	T2	T1	T2
	Mean	1.07	1.00	217551	281724	0.21	0.28	1.79	2.02
PD-T	(SD)	(0.08)	(0.10)	(99982)	(121441)	(0.08)	(0.10)	(0.24)	(0.27)
	CV	7.5%	10.0%	46.0%	43.1%	37.7%	36.4%	13.5%	13.6%
	Mean	1.03	1.04	233508	234683	0.24	0.24	1.90	1.89
PD-NT	(SD)	(0.09)	(0.09)	(83369)	(92646)	(0.07)	(0.08)	(0.24)	(0.26)
	CV	8.3%	9.0%	35.7%	39.5%	28.7%	35.2%	12.9%	13.8%
	Mean	0.96	0.97	280420	272430	0.28	0.27	2.18	2.13
HC	(SD)	(0.07)	(0.07)	(77579)	(77184)	(0.07)	(0.06)	(0.27)	(0.22)
	CV	7.6%	6.0%	27.7%	28.3%	24.0%	21.5%	12.5%	10.1%

Figure 1.

Shown from top left, in a clockwise direction, the mean FCR, VSA, LnVSA, and F2i/F2u (error bar represent 1 standard deviation) at T1 and T2 for the PD-T, PD-NT, and HC groups. FCR=Formant Centralization Ratio; VSA=Vowel Space Area. LnVSA=Logarithmically scaled VSA; PD-T: Individuals with dysarthria secondary to Parkinson's disease who received treatment with LSVT®; PD-NT: Individuals with Parkinson's disease who did not receive treatment for their dysarthria; HC=Healthy Controls. T1 and T2 correspond to the times before and the time after treatment, respectively.

As can be seen in Table 4 and Figure 1, at T1, the means of the VSA, LnVSA, and F2i/F2u are smaller, and the mean of the FCR is larger, in the PD-T and PD-NT groups relative to the corresponding means in the HC group. These findings are consistent with vowel centralization in the PD groups. One-way ANOVA of the T1 data indicates significant differences between the three groups for the FCR [F(2,49)=8.01, p=.001], F2i/F2u [F(2,49)=10.36, p=0.0002], and LnVSA [F(2,49)=3.80, p=0.0292], but not for the VSA [F(2,49)=2.12, p=0.1303]. For the FCR, Duncan's paired comparison tests indicate a significant difference between the PD-T and HC groups, and between the PD-NT and HC groups, and no significant difference between the PD-T and PD-NT groups. The significant differences are associated with large effects sizes (1.47 and 0.97, respectively). For the F2i/F2u, the Duncan's tests indicates a significant difference between the PD-T and HC groups, and between the PD-NT and HC groups, but not between the PD-T and PD-NT groups. The significant differences are associated with large effects sizes (1.54 and 1.11, respectively). For the LnVSA, Duncan's indicates a significant difference between the PD-T and HC groups, but not between the PD-NT and HC groups, or between the PD-T and PD-NT groups. The significant difference is associated with a large effect size (0.96). Thus, at T1, the FCR and F2i/F2u significantly and robustly differentiate dysarthric from normal groups, the LnVSA differentiates only partially between the groups, and the VSA fails to differentiate between dysarthric and nondysarthric groups

Gender effects at T1

For the FCR data at T1, a two way ANOVA with interaction indicates a significant main effect for Group [F(2,46)=8.66, p=.0006], but not for Gender [F(1, 46)=1.11, p=.2975] or Gender by Group interaction [F(2,46)=3.010, p=.0590]. For the F2i/F2u, there is a main effect for Group [F(1,46)=10.23 , p=0.0002 ], but not for Gender [F(2,46)= 2.42, p=0.1266] or Gender by Group interaction [F(2,46)=0.48 , p=0.6246]. For the VSA, there is a main effect for Gender [F(1,46)=8.43, p=.0056], but not for Group [F(2,46)=2.47, p=.0956] or Gender by Group interaction [F(2,46)=0.070, p=.9325]. For the LnVSA, there are main effects for Gender [F(1,46)=7.50, p=.0087] and Group [F(2,46)=3.98, p=.0254] and not for Gender by Group interaction [F(2,46)=0.24, p=.7849]. Thus, only the VSA and LnVSA were gender-sensitive at T1.

Detecting treatment effects (changes from T1 to T2)

RM-MANOVA for between-participants tests indicates significant between group differences for the FCR [F(2,49)=4.79, p=0.0126] and F2i/F2u [F(2,49)=7.83, p=0.0011] but not for the VSA [F(2,49)=0.53, p=0.5943] and LnVSA [F(2,49)=1.30, p=0.2821]. RM-ANOVA with univariate within subjects tests indicate no main effect for Time for the FCR [F(1,49)=3.34, p=0.0738], F2i/F2u [F(1,49)=2.00, p=0.1635], VSA [F(1,49)=3.92, p=0.0534], and LnVSA [F(1,49)=3.25, p=0.0765], but significant Time by Group effects for the FCR [F(2,49)=6.44, p=0.0033], F2i/F2u [F(2,49)=5.02, p=0.0104], VSA [F(2,49)=10.64, p=0.0001], and LnVSA [F(2,49)=7.77, p=0.0012]. Effect size measures of the T1-T2 difference in the PD-T group were large for the FCR (0.84) and the F2i/F2u (0.88), medium-to-large for the LnVSA (0.74), and medium for the VSA (0.58). Effect size measures of the T1-T2 differences in the PD-NT and HC groups are small in all metrics (absolute effect size <0.25). Thus, all metrics register significant treatment effects in the PD-T group, but the FCR and F2i/F2u register a more robust effect than the VSA and LnVSA, as reflected by the effect size measures.

Gender effects for the T1-T2 difference

For the FCR, a two way ANOVAs with interaction indicate a main effect for Group [F(2,46)=6.43, p=.0034], but not for Gender [F(1,46)=1.15, p=.2289] or Gender by Group interaction [F(2,46)=1.21, p=.3068]. For the F2i/F2u, there is a main effect for Group [F(2,46)=4.75 , p<0.0134], but not for Gender [F(1,46)=0.26 , p=0.611 ] or Gender by Group interaction [F(2,46)=0.22 p=0.8029]. For the VSA, there is a main effect for Group [F(2,46)=10.723, p<.0001], but not for Gender [F(1,46)=0.13, p=.7180] or Gender by Group interaction [F(2,46)= 1.05, p=.3598]. For the LnVSA, there is a main effect for Group [F(2,46)=7.53, p=.0015], but not for Gender [F(1,46)=1.37, p=.2483] or Gender by Group interaction [F(2,46)= 0.56, p=.5756]. Thus, none of the metrics shows a gender effect when measuring treatment changes.

Pearson correlations between the FCR, F2i/F2u, LnVSA and VSA for the T1-T2 difference in the PD-T group

The T2-T1 difference in the PD-T group was used to correlate pairs of metrics. There are high correlations between the metrics: FCR vs. F2i/F2u (r=−0.90, p<0.0001), FCR vs. VSA (−0.85, p<0.0001), FCR vs. LnVSA (−0.81, p<0.0001), F2i/F2u vs. VSA (r=0.85, p<0.0001), F2i/F2u vs. LnVSA (r=0.81, p<0.0001), and VSA vs. LnVSA (r=0.89).

Finally, as can be seen in Table 4, the CV values are in general largest in the VSA, smaller in the LnVSA, still smaller in the F2i/F2u, and smallest in the FCR. Thus, if we consider the CV an index of interspeaker variability, this variability is largest in the VSA and smallest in the FCR. Note also that the CV values are in general larger in the PD groups than in the HC group.

Discussion

In this study, the FCR, like the F2i/F2u, and unlike the VSA and LnVSA, effectively and robustly differentiated the groups with dysarthria (PD-T and PD-NT) from the HC group. Like the F2i/F2u, VSA, and LnVSA, the FCR effectively registered treatment effects. Unlike the VSA and LnVSA, these treatment effects were registered by the FCR and F2i/F2u with large effects sizes. Also, unlike the VSA and LnVSA, the FCR and F2i/F2u were insensitive to gender effects, and were associated with relatively small CV values. The LnVSA was more effective than the VSA in differentiating dysarthric from normal vowel articulation, but this was true for only the PD-T group. Finally, the FCR correlated highly with the other three metrics when the correlated variable was the change induced by treatment. Collectively, these findings, albeit preliminary, suggest that the FCR is a valid and highly sensitive metric of vowel articulation, normal and abnormal, and that its performance is superior to that of the VSA and the LnVSA in differentiating dysarthric from healthy speech. The presence of gender effects in only in the VSA and LnVSA, and the larger CV associated with their measurements, suggest that these two metrics were much more sensitive to interspeaker variability than the FCR and F2i/F2u. This difference in sensitivity may account for the inability of the VSA, and the partial ability of the LnVSA, to differentiate between the dysarthric and nondysarthric groups. The fact that the LnVSA was associated with smaller CV values than the VSA and that the LnVSA was more successful than the VSA in differentiating between the dysarthric and nondysarthric groups also support the idea that the failure of the VSA to differentiate between dysarthric and nondysarthric speakers has to do, at least in part, with the high sensitivity of the VSA to interspeaker variability. Moreover, the fact that the VSA and LnVSA performed well in registering changes induced by treatment (a within subject comparison) also speaks to the role of interspeaker variability in the performance of these acoustic metrics.

More evidence for the validity of the FCR comes from the studies of Hillenbrand et al (1995) and Higgins and Hodge (2002). As can be seen in Table 1, the calculated values of the FCR from the formant frequencies in the men, women, and children in the study by Hillenbrand et al (0.99, 0.96, 0.97, respectively) are close to the mean FCR values of the HC group in the present study (0.96 at T1, 0.97 at T2). The formant data from the study by Higgins & Hodge (2002) are shown in Table 5, along with the FCR, VSA, LnVSA, and F2i/F2u values calculated from these data. The data are from young children with dysarthria secondary to cerebral palsy and from healthy controls. Note that the formant frequencies of the different vowels are centralized in the children with dysarthria relative to the controls, and this centralization is also reflected in the FCR, VSA, LnVSA, and F2i/F2i. Note also that the FCR value for the typical children is 0.91 and for the children with dysarthria it is 1.14. These values are fairly similar to those in the present study for the normal and dysarthric speakers, respectively. The somewhat smaller FCR value for the typical children and larger FCR value for the dysarthric children relative to the data in the present study might be related to the fact that the children in the Higgins & Hodge study were Canadian and very young (5–6 year old), and the possibility that the dysarthria in the Higgins and Hodge study may have been more severe than the dysarthria in the present study.

In the present study, the F2i/F2u and the FCR were highly correlated (r=−0.90) (when the correlated variable was the treatment induced change) and equally effective in differentiating the dysarthric and nondysarthric speakers and in registering treatment effects. The close performance of these two metrics suggests that, to a large extent, they reflected the same articulatory abnormalities, namely, restricted movements of the tongue in the anterior-posterior direction and restricted movements of the lips (rounding for /u/ and retraction for /i/). Given that the FCR and F2i/F2u performed so much the same and showed a high correlation, one might argue that the FCR is superfluous, as the F2i/F2u seems sufficient to capture the nature of articulatory abnormality. However, there might be individuals with dysarthria whose speech impairment may involve more vowels than the /i/ and /u/ and more than one formant. Thus, to capture such impairment, the FCR is likely to offer additional information and thus be more appropriate than the F2i/F2u.

The FCR, VSA, and LnVSA are all based on the construct of vowel centralization. By this construct, one would expect that all the vowel formants will show centralization. However, such symmetry is unlikely to occur, as most studies of dysarthric vowel articulation indicate (see for example Sapir et al., 2007; Weismer et al., 2001; Yunusova et al., 2008). Also, in some cases the acoustic measures of abnormal vowel articulation might be in the opposite direction of that expected from formant centralization. For example, in the present study, and in the study by Weismer and colleagues (2001), the frequency of F1u in the speech of dysarthric individuals with idiopathic PD tended to be lower than normal, yet by the centralization construct the frequency of F1u should have been higher than normal. Yunusova et al (2008) noted in their kinematic study that whereas the majority of individuals with dysarthria secondary to amyotrophic lateral sclerosis (ALS) had smaller than normal jaw or tongue movements, some individuals with dysarthria and ALS had jaw movements that were considerably larger than normal. Thus, the FCR, VSA, and LnVSA may not fully or faithfully capture the nature of the articulatory impairment in all speakers and all types of dysarthria. In future studies, it would be important to accommodate for such asymmetry, especially if the asymmetry is very characteristic of a particular dysarthria.

The present findings are a first effort at evaluating the FCR. We wish to stress that the FCR is not necessarily the best metric to differentiate dysarthric from healthy vowel articulation, nor necessarily the preferred metric for all types of dysarthria and patient populations. Thus, without comparing the FCR to other metrics (other than those tested here), it is not possible to tell which of these metrics, or a combination of them, are most effective and reliable in measuring dysarthric vowel articulation. Also, there are numerous factors (e.g., speech task, phonetic environment, type and severity of dysarthria, etc.) that can affect vowel production and its acoustic manifestations. Thus, future studies should examine how the FCR performs under these conditions. Furthermore, in this study we tested the VSA and FCR with the vowels /i/, /u/, and /a/. Thus, it would be important to assess how well these metrics might perform with more or different vowels. Finally, at this point it is not clear what specific articulatory abnormalities are represented by the FCR, and how those might be related to perceived speech abnormality. It would therefore be important to correlate the FCR with physiologic and perceptual measurements of vowel articulation, normal and abnormal.

Appendix A

The triangular vowel space area (VSA), constructed with the corner vowels /i/, /u/, and /a/, may be expressed mathematically as

$$\text{VSA}={\text{ABS}((\mathrm{F}1\mathrm{i}}^{\ast }(\mathrm{F}2𝔞-\mathrm{F}2\mathrm{u})+\mathrm{F}1{𝔞}^{\ast }(\mathrm{F}2\mathrm{u}-\mathrm{F}2\mathrm{i})+{\mathrm{F}1\mathrm{u}}^{\ast }(\mathrm{F}2\mathrm{i}-\mathrm{F}2𝔞))/2)$$ (1)

Where ABS is absolute value. This VSA can also be expressed as

$$\text{VSA}={\text{sqrt}(\mathrm{S}}^{\ast }(\mathrm{S}-\text{EDiu})(\mathrm{S}-\text{EDi}𝔞)(\mathrm{S}-\text{ED}𝔞\mathrm{u}))$$ (2)

Where sqrt is square root and

$$\text{EDiu}=\text{sqrt}((\mathrm{F}1\mathrm{i}-{\mathrm{F}1\mathrm{u})}^2+{(\mathrm{F}2\mathrm{i}-\mathrm{F}2\mathrm{u})}^2)$$ (3)

$$\text{EDi}𝔞=\text{sqrt}((\mathrm{F}1\mathrm{i}-\mathrm{F}1𝔞{)}^2+{(\mathrm{F}2\mathrm{i}-\mathrm{F}2𝔞)}^2)$$ (4)

$$\text{ED}𝔞\mathrm{u}=\text{sqrt}((\mathrm{F}1𝔞-\mathrm{F}1{\mathrm{u})}^2+{(\mathrm{F}2𝔞-\mathrm{F}2\mathrm{u})}^2)$$ (5)

$$\mathrm{S}=(\text{EDiu}+\text{EDi}𝔞+\text{ED}𝔞\mathrm{u})/2$$ (6)

Where EDiu is the Euclidean distance between the vowels /i/ and /u/, EDia is the Euclidean distance between the vowels /i/ and /a/, and EDau is the Euclidean distance between the vowels /a/ and /u/ in the F1-F2 plane. The VSA formula in expression (1) is adopted from Liu, Tsao, & Kuhl (2005) and the VSA formula in expression (2) is adopted from Blomgren, Robb, & Chen (1998).

The logarithmic version of the triangular VSA (LnVSA) is expressed mathematically as:

$$\text{LnVSA}={\text{sqrt}(\text{LnS}}^{\ast }(\text{LnS}-\text{LnEDiu})(\text{LnS}-\text{LnEDi}𝔞)(\text{LnS}-\text{LnED}𝔞\mathrm{u}))$$ (7)

Where

$$\text{LnEDiu}=\text{sqrt}((\text{LnF1i}-{\text{LnF}1\mathrm{u})}^2+{(\text{LnF}2\mathrm{i}-\text{LnF}2\mathrm{u})}^2)$$ (8)

$$\text{LnEDi}𝔞=\text{sqrt}((\text{LnF}1\mathrm{i}-\text{LnF}1𝔞{)}^2+{(\text{LnF}2\mathrm{i}-\text{LnF}2𝔞)}^2)$$ (9)

$$\text{LnED}𝔞\mathrm{u}=\text{sqrt}((\text{LnF}1𝔞-{\text{LnF}1\mathrm{u})}^2+{(\text{LnF}2𝔞-\text{LnF}2\mathrm{u})}^2)$$ (10)

$$\text{LnS}=(\text{LnEDiu}+\text{LnEDi}𝔞+\text{LnED}𝔞\mathrm{u})/2$$ (11)

Note that by the mathematical equivalence Ln(A/B)=Ln(A)-Ln(B) we can express the Euclidean distances in equations (8), (9), and (10) as formant ratios:

$$\text{LnEDiu}={\text{sqrt}(\text{Ln}(\mathrm{F}1\mathrm{i}/\mathrm{F}1\mathrm{u})}^2+{\text{Ln}(\mathrm{F}2\mathrm{i}/\mathrm{F}2\mathrm{u})}^2)$$ (12)

$$\text{LnEDi}𝔞=\text{sqrt}(\text{Ln}(\mathrm{F}1\mathrm{i}/\mathrm{F}1𝔞{)}^2+\text{Ln}(\mathrm{F}2\mathrm{i}/\mathrm{F}2𝔞{)}^2)$$ (13)

$$\begin{array}{l}\text{LnED}𝔞\mathrm{u}=\text{sqrt}(\text{Ln}(\mathrm{F}1𝔞/{\mathrm{F}1\mathrm{u})}^2+\text{Ln}(\mathrm{F}2𝔞/{\mathrm{F}2\mathrm{u})}^2)\\ \end{array}$$ (14)