On the complexity matching and multiscale nonlinear perspective of voice restoration via fat injection laryngoplasty in unilateral vocal fold paralysis

Abstract

Voice disorders represent a common medical condition affecting up to 16.9% of the general population, with unilateral vocal fold paralysis (UVFP) being particularly severe. This condition causes breathy dysphonia, maladaptive articulatory behaviours, and cortical alterations in sensory processing. Although injection laryngoplasty (IL) is considered an effective minimally invasive treatment, traditional acoustic analysis often does not provide robust metrics to evaluate its effectiveness. Here, a multiscale nonlinear approach, including the concept of complexity matching computed through the correlation of scaling factors obtained from Multi-Fractal Detrended Fluctuation Analysis, is introduced to better detect improvements in vocal fold vibratory patterns and vocal tract resonance in 69 UVFP patients, treated by autologous fat IL. This method revealed that mildly recovered (MR) patients show stronger similarity of physiological complex characteristics between pre- and post-operative conditions than fully recovered ones. This outcome shows agreement between perceptual and objective evaluations, indicating that the chaotic properties of voice production are still preserved in the MR group. This finding could assist clinicians in recognising patients requiring further treatment, fostering a patient-centred care approach. Moreover, sample entropy (SE) emerged as the most reliable parameter in this study as it could consistently identify vocal recovery at both phonatory and articulatory levels. This result suggests that using multiscale SE could be a unique metric to support and simplify traditional acoustic analysis procedures.

Introduction

Unilateral vocal fold paralysis (UVFP) is a voice disorder characterised by impaired motility of a single vocal fold. In the general population, the incidence of UVFP among voice pathologies is estimated at 1.2%¹. Its etiopathogenesis is wide and includes mechanical trauma to the head and neck, neoplasms, neurological diseases, idiopathic origin and, most commonly, iatrogenic causes (typically represented by injuries occurring in thyroid and cardiothoracic surgery). The most common and perceivable symptom of UVFP is dysphonia, with patients experiencing breathy voices due to the air leakage caused by glottal insufficiency. Such impaired communication may harm the quality of life, possibly leading to stress and isolation, which is particularly worsened for professional voice users (such as teachers, actors, or singers). Moreover, UVFP may cause speech dyspnea, swallowing problems and, in most severe cases, body stabilisation difficulties due to hyperventilation while speaking.

Voice rehabilitation constitutes the initial treatment for glottic insufficiency. Surgery becomes necessary when unsatisfactory results are obtained². There is no clinical consensus regarding the best intervention to close the glottic gap and recover the mucosal wave. A promising technique is injection laryngoplasty (IL), which inserts a mouldable and biocompatible material (e.g., autologous fat and fascia) to medialise the paralysed vocal fold². The main advantages of this approach are that it does not require open surgery, has material-wide availability, is cost-effective and does not hamper spontaneous reinnervation. Moreover, feedback on voice improvements can be collected in real-time: this is an important aspect as it can counteract the main and inevitable disadvantage of IL, fat reabsorption, because it may help the phonosurgeon to regulate the over-injection. With specific preparation procedures, the beneficial effect of IL on voice outcomes can be permanent.

The gold standard for the clinical evaluation of UVFP treatment efficiency and monitoring is the direct visualisation of the vocal fold movements through laryngoscopy. Nonetheless, complementary assessments are advisable as voice production is a multidimensional phenomenon and, thus, a multidimensional approach to study voice changes over time is necessary, especially to demonstrate positive results obtained by any type of treatment. Furthermore, the lack of high-resolution imaging devices in primary care units, or the need to be physically present in hospitals might be overcome by indirect methods of evaluation of voice quality. A well-established method is the perceptual evaluation of voice, which is typically performed along with laryngoscopy, that implements standardised batteries as the commonly used GRBAS scale, that account for the overall degree of dysphonia severity (G), roughness (R), breathiness (B), asthenia (A) and strain (S)³. Nevertheless, auditory assessments may suffer from drawbacks such as inter-rater variability and physicians’ experience. Acoustic analysis has become a widespread technique that automatically provides several parameters that objectively describe multiple aspects of voice production, such as phonation (the fundamental frequency F0), period and amplitude perturbation (jitter and shimmer), and noise (noise-to-harmonics ratio NHR, and normalised noise energy NNE). These measures proved to be sensitive to changes in vocal quality in UVFP patients treated with laryngoplasty. Meta-analyses have highlighted that jitter and MPT significantly improved in both short- and long-term after the injection. In contrast, shimmer was significantly reduced only in the short-term period⁴. Individual studies have also reported significant improvement of F0⁵ and HNR⁶.

However, the computation of perturbation measures, which directly depend on the estimation of the F0, can become extremely challenging and unreliable, especially in UVFP patients for their highly irregular, breathy, and partially aphonic utterances^2,7. Moreover, recent works demonstrated the existence of several nonlinear phenomena in voice production that the algorithms embedded in common tools used for acoustic characterisation are insensitive to. Therefore, the mismatch between the mathematical framework and the biosignals attributes can lead to ambiguous results in acoustic analysis, hindering its advantages and applicability^4,7, as well as impeding a clear, robust evaluation of treatment efficiency. For instance, subglottic airflow properties, rheological characteristics of the vocal fold tissue, as well as their mechanical collision, and asymmetry in left and right vocal fold movements may generate unique properties that require novel and alternative techniques to extract and investigate them from audio recordings^8,9. To address the literature gap, an emerging body of research proposed nonlinear dynamical systems theory as a promising candidate to investigate dysphonic voices with a broader perspective^7,10. As the complete dynamics of a system is often complex and not directly observable, this approach typically relies on reconstructing a given biosignal in the so-called state space, an alternative representation achieved by considering multiple delayed copies of the original time series, to reveal its hidden internal states and compute metrics capable of describing its full evolution even when little information (i.e., a single time series, in this study, the voice recording) is available.

Background on nonlinear acoustic analysis

The characterisation of acoustic samples can be divided into three types of feature sets: perturbation, cepstrum, and complexity measures. A multidimensional approach is typically advised to describe the phonatory system functioning efficiently, as some properties related to vocal diseases (e.g., aperiodicity) are also inherent to non-pathological states⁹. Moreover, when analysing dysphonic voices, perturbation parameters such as jitter and shimmer can become unreliable for detecting alterations from normophonic subjects and, above all, when comparing them across other pathologies and in pre- and post-operative conditions¹¹. Therefore, parameters that can be extracted from audio recordings without relying on the computation of the F0 and that can account for well-known nonlinearities in speech production have become more popular in the last two decades. Among complexity parameters, three categories may be identified: measures describing the state space geometrical properties and trajectories, information theory and self-similarity measures.

In the first group, the correlation dimension (D2) is a particular type of fractal dimension that estimates the geometric shape of the state space occupied by the attractor (or a set of points). It specifies the degrees of freedom needed to describe and generate the corresponding physiological process¹². A more complex system has a higher dimension, meaning more independent variables may be needed to describe its dynamic state. In voice analysis, D2 was found significantly higher in dysphonic patients than normophonic subjects^12–15, presenting also high recognition rates and accuracies in distinguishing the two populations^12,15. On the other hand, the Largest Lyapunov Exponent (LLE) quantifies the sensitivity of the attractor to the initial conditions. It has been introduced in acoustic analysis as the larynx can be considered a dissipative system where oscillations are both attenuated and emphasised¹⁶. Lyapunov exponents describe the evolution of trajectories in each dimension of the attractor, and its largest value (i.e., the LLE) represents a simple measure of how two initial nearby trajectories rapidly diverge or converge in the phase space. A LLE represents divergence, and vice versa.

The main disadvantage of these types of metrics is that it requires speech dynamics to be purely deterministic. Such an assumption can be proven only under specific circumstances, and this modelling approach does not account for randomness, which characterises voice, especially in the presence of specific physiological phenomena such as airflow turbulence¹⁵. Therefore, information theory measures have been introduced in acoustic analysis to overcome this issue, since they do not consider the deterministic or non-deterministic nature of the signal. One of the most used features is represented by the Approximate Entropy (AE), which reflects the unpredictability of the fluctuations in a time series. Sample entropy (SE) was proposed as an improved version of AE as the latter intrinsically produces a bias toward regularity: SE eliminates self-matching, leads to more consistent results, and presents a good independence from signal length¹⁷. SE allowed to separate the vocal phenotypes of four genetic syndromes¹⁸, proved to be higher in dysphonic patients¹⁹, and was successfully used as a feature in machine learning paradigms^20,21. Research has also investigated voice parametrisation with other variants of entropy, e.g., correlation, Shannon, Kolmogorov, Renyi, Fuzzy ones⁹.

Regarding self-similarity measures, detrended fluctuation analysis (DFA) has been implemented in voice analysis as an alternative to entropy measures to study chaotic vibration. DFA represents a method for determining the self-affinity of a signal²² through a scaling exponent . It has been used to detect the presence of turbulence noise in audio samples. Such value was found significantly higher in disordered voice⁷ and in Parkinson’s disease²³.

Nevertheless, DFA (as well as entropy) assumes that the scale invariance does not depend on time and space. However, such variations often occur in biomedical signals, including voice and speech^24,25, and consequently indicate a multifractal, rather than monofractal, structure. Hence, multifractal DFA (MFDFA) could be a more adequate and promising technique to analyse and characterise the multiple components, interactions, and scales that the voice production system involves over time^26,27. A few works conducted MFDFA to investigate affective speech and newborn cries to develop more efficient automatic recognition tools^28,29. Still, more research is needed to understand its capabilities when considered disordered voices.

Notably, MFDFA has been implemented to study the so-called complexity matching (CM) between interacting systems³⁰. CM refers to a maximised flow of information between systems when they share similar complexity, and its occurrence has been demonstrated in participants engaged in joint activities, as well as two different effectors (i.e., lower limbs) of the same individual³⁰. In speech analysis, acoustic onsets occurring during dyadic conversation that reflect turn-taking proved to follow a power law distribution (similarly to critical events of complex networks) and a CM effect was found in the temporal structure of language when comparing participants talking about topics where they do not and do share common opinions and beliefs³¹.

The current study

This paper proposes a novel approach to studying voice quality recovery. It is applied on a specific sample, i.e., UVFP patients after autologous fat IL.

Firstly, to account for voice scale invariance dependence from time and space, several complexity metrics will be computed following a multiscale strategy to describe vocal properties comprehensively. This will allow for investigating the latter on multiple levels simultaneously, possibly underlining specific aspects of voice production related to phonation and articulation.

Then, it aims to introduce and highlight a potential complexity-matching effect when comparing audio recordings from pre- and post-operative conditions, which is calculated through MFDFA. In our context, even if it is not possible to allude to a concurrent interaction since audio recordings are acquired in two different instances (see Sect. “Patients”), this innovative perspective may highlight how much information, i.e., the irregular, chaotic voice behaviour, of the pre-operative condition remains in the post-treatment one. Here, it is hypothesised that if patients improve voice quality, the similarity between pre- and post-surgery voice will be low, and vice versa for patients with unsatisfactory voice recovery after intervention.

Additionally, it will analyse how confounding factors may affect the rehabilitation process. By considering the degree of recovery obtained through voice perceptual assessment, the UVFP population will be divided into two subgroups, and age, aetiology, disease time, and post-measurement time will be investigated to uncover possible statistical differences. This could be useful in clinical practice to guide otolaryngologists in planning and monitoring patients’ follow-ups.

Methods

Patients

A total of 69 participants were included in the study, of which 40 are females (mean age = years old) and 29 are males (mean age = years old). They were diagnosed with UVFP through videolaryngostroboscopy with a flexible endoscope or a rigid fiberoptic endoscope, supported by voice perceptual assessment performed with the GRB scale, a variation from the original GRBAS one³ proposed in³². Patients affected by UVFP who did not fully recover voice quality with voice therapy were considered eligible for AFIL. Inclusion criteria were: age >18 years, UVFP lasting since at least 6 months, persistent dysphonia and voice fatigue. Exclusion criteria were: age <18 years, high anaesthesiology risk due to general health conditions, degenerative neurological conditions. Patients underwent surgical treatment with injection laryngoplasty (that is described in detail in Sect. “Surgical procedure”). To evaluate the efficiency of this procedure, voice quality was measured pre- and post-operatively with aerodynamic, auditory and acoustic analyses. In both conditions, recordings were acquired using a C1000S microphone (AKG Acoustics GmbH, Vienna, Austria) with a sampling frequency of 44.1 kHz at a fixed distance of 5 cm from the patient’s mouth during phonation. Participants were asked to utter a sustained vowel /a/ for at least 3 s at comfortable pitch and loudness. The mean postoperative time was  months. The study was conducted in accordance with the Declaration of Helsinki, all data were recorded anonymously, and informed consent was obtained from each subject. The human data analysis procedure was approved by the Ethics Commission (n. 275-04/09/2023).

Surgical procedure

The procedure is performed under general anaesthesia by direct microlaryngoscopy. Autologous fat is harvested from the lower abdomen by liposuction under low negative pressure with a 10-cc Luer-lock syringe connected to a 3-mm blunt aspiration cannula. The obtained lipoaspirate is centrifuged at 1200 g for 3 min according to the lipostructure Coleman technique³³. Three layers are obtained: the upper layer formed mainly by blood, the intermediate layer of fatty parcels, and the lower layer of liquid fat deriving from ruptured fat cells. The top and bottom layers are discarded. The intermediate layer is transferred to a 3.0-cc Luer-lock syringe and then is injected into the vocal folds using a lipoinjection handle (Medicon Instrumente, Tüttlingen, Germany) with a 21-gauge, 22-cm-long bayonet needle. Multiple injections are performed in the paralyzed vocal fold in several layers, both in the muscle layer and the paraglottic space, to facilitate contact between the injected fat parcels and the recipient tissue. This technical aspect is critical to enhance the revascularization and ensure the survival of the injected fat as only the adipocytes, being at less than 300 microns from the recipient tissue, will survive after injection³⁴. The total injected amount varies from case to case, from 0.5 to 2 cc, depending on the severity of vocal fold atrophy, and is generally higher in males due to bigger vocal folds. A smaller amount (0.2–0.4 cc) is also injected into the contralateral mobile vocal fold. At the end of the injection procedure, a massage of both vocal folds is performed with cotton soaked in diluted epinephrine. This step is fundamental to favour an even distribution of the injected fat parcels in the body of the vocal fold and to allow drainage of the liquid and oily components through the multiple puncture sites. Patients are hospitalized for 24 h after surgery.

Perceptual measurements

The perceptual evaluation was performed according to the GRB scale³² blindly by a speech therapist with long experience in voice disorders. A single rater assessed all recordings once and randomly to reduce bias. The GRB scale is composed of three items:

• G (global grade of dysphonia): the judgement is based on the overall impression of voice quality deterioration.

• R (Roughness): the impression of irregular vocal fold vibration and noise.

• B (Breathiness): turbulent noise related to air escape through the vocal folds.

The scores range from 0 to 3, where 0 is the rating for the best voice condition and 3 for the worst one.

Signal preprocessing & nonlinear analysis

Audio recordings were downsampled at 22.05 kHz for computational efficiency and automatically segmented, selecting a central section of about 743 ms (precisely 2¹⁴ samples, i.e., the power of two number of samples that is closest to 1000 ms, to guarantee equal window size when scaling) to remove the unstable parts concerning vocal onset and offset.

Multi-Fractal Detrended Fluctuation Analysis, introduced in³⁵, can be divided into 5 steps that roughly follow the same procedure developed in³⁶ for Detrended Fluctuation Analysis.

It starts by centering and integrating the time series x(i) of length N according to Eq. 1. Figure 1 displays this operation applied on a pre-treatment acoustic signal from our dataset.

1

Fig. 1.

The original time series is centred and integrated, obtaining the orange signal.

In the second step, the time series X(k) is divided into non-overlapping segments of length n, with according to predefined scale sizes. In each window, a (typically linear) trend is computed with Eq.  2.

2

where the constants and are obtained after a linear fit. Figure 2 shows this operation using three scales (s = 128, s = 256, s = 512) used in this study.

Fig. 2.

Trend computation in each segment across three different scales. (A) s = 128, (B) s = 256, (C) s = 512.

After detrending, step 3 provides the calculation of the Root Mean Square (RMS) of the residuals (i.e., the deviation from the trend), obtaining the fluctuation function for each scale s according to Eq. 3. Figure 3 shows the for the same above-mentioned scales.

3

Fig. 3.

Fluctuation functions for three different scales. The red horizontal line represents the mean of F(n, s).

At step 4, MFDFA deviates from the original DFA method to account for the multifractal structure of a signal. Indeed, the fluctuation functions are computed for different orders than q = 2, then averaged to derive the q-order fluctuation functions as in Eq. 4. This allows highlighting the segments where extremely small or large RMS occurs, as Fig. 4 illustrates.

4

Fig. 4.

Fluctuation functions obtained considering a single scale (s = 256) and three different q-order moments (q = 1, q = 2 for reference to the B. panel of Fig. 3 and q = 3). Since positive q are selected, only the largest variations are emphasised.

Finally, MFDFA step 5 can be subdivided into three smaller passages. Firstly, the are plotted against the corresponding scale size n in a loglog graph (see Fig. 5) and, if a long-term relationships exist, then should increase with n following a power law:

5

where h(q) is the scaling exponent computed as the slope of the linear regression of log against log n.

Fig. 5.

Hurst Exponent visualisation on a loglog graph for a set of different orders q and scales s.

Then, scaling exponents are converted into Renyi exponents by Eq. 6:

6

from which the Lipschitz–Hölder exponents are obtained with:

7

Therefore, MFDFA requires setting three parameters: the scale range, the q-order that weights local variations and the polynomial order for the detrending.

According to Ihlen et al.²⁷, we have considered a mean fundamental frequency of 200 Hz and the sampling frequency of 22.05 kHz; the minimum segment size should be greater than 110.25 samples, which was later approximated to the closest power of two number, i.e., 128 samples. Furthermore, as suggested in³⁰, since physiological time series often present different scaling regimes over the short and long term, it is advisable to estimate the multifractal exponents firstly over the entire set of available ranges (in our context, from 2⁷ to N/2, i.e., 2¹³), then considering more limited sets, progressively excluding the shortest intervals. This strategy should better highlight a true CM effect between interacting systems and discard local corrections. Therefore, four scale ranges were implemented: the longest range (LLR, from 2⁷ to 2¹³), the long range (LR, 2⁸–2¹³), the short range (SR, 2⁹–2¹³) and the shortest range (SSR, 2¹⁰–2¹³).

The q-order decides the weighting of the local fluctuations. In a monofractal signal, the absence of both large and small magnitude fluctuations allows for the variation of the time series itself to be fully described by its variance, i.e., its second-order statistical moment. This is not the case for a signal exhibiting a multifractal structure; therefore, multiple q-order statistical moments should be considered. To account for periods with both small and large variations, the set of q-order should encompass both negative and positive values; additionally, to perform a more precise computation, large (in absolute value) orders should be avoided. This paper investigated the multifractality in the from −15 to 15 range, according to³⁰.

Finally, as an exploratory analysis, the polynomial order implemented for detrending the signal was set to 1.

After calculating the individual q-order singularity exponents , the CM was obtained by computing the correlation coefficient of and , where refers to pre- and post-surgical treatment conditions, respectively. Since this study is interested in analysing how much information is retained after medical intervention in voice signals (which might reflect treatment inefficacy), the UVFP cohort was arbitrarily split into two populations based on the change of grade G of the GRB scale. Patients presenting a decrease of magnitude two or higher and a passage from G = 1 to G = 0 were considered as the fully recovered group (FR), whereas lower decrease values represented the mild recovery (MR) group. Moreover, to understand whether a common pattern of the disease recovery process exists or, rather, it is characterised by variations that are specifically related to each subject, the order of data for the MR group was randomised in the sets of exponents from both pre- and post-operative conditions. It was hypothesised that in the case of patient-specific variations, the correlation coefficient value would drop.

The multiscale analysis included the following parameters: correlation and fractal dimension (calculated as in³⁷), the largest Lyapunov exponent, Sample Entropy (SE), and Hurst Exponent. Excluding the latter, each of them requires the reconstruction of the state space. This operation was performed at each scale and individually for each recording, considering the first minimum of the mutual information function for computing the time delay tau and the false nearest neighbour method to calculate the embedding dimension, which was also retained as an additional feature to describe the physical properties of the state space. Moreover, regarding sample entropy, the tolerance was set at 20% of the signal standard deviation. A coarse-grained approach was employed to generate the scaled signals, according to Eq. 8³⁸.

8

where x(i) is the i-th sample of the original time series of length N, s is the power of two scale factors (varied from 0, the original signal, to 7), and the symbol denotes the integer part of its argument.

Statistical analysis

A first statistical analysis was conducted to understand whether the voice quality of the whole sample, as measured with the GRB perceptual assessment, improved after IL with a Wilcoxon signed test (setting the -level of significance at 0.05). Then, after dividing the population in two subgroups (FR and MR) according to the degree of the recovery, age, disease time and post-treatment time were compared either with a t-test or a Mann–Whitney U test (), according to the results of a Shapiro–Wilk test for data normality (). On the other hand, to evaluate the role of UVFP aetiology, a cross-tabulation was built and a chi-square test of association () was performed to understand whether the frequency of occurrence of a specific diagnosis impacts on the rehabilitation process.

As explained in Sect. “Signal preprocessing & nonlinear analysis”, after computing the scaling factors for each scale range and q-order moments, a Spearman correlation analysis was performed to discover possible relationships between pre- and post-treatment recordings. Correlation coefficients were computed separately for the FR and MR groups. Moreover, another correlation analysis was performed within the MR group only by randomly assigning patients to highlight individual or common variations. Finally, the same correlation coefficients were averaged within the four scale ranges (SSR, SR, LR, LLR) and separate t-tests were performed to underline different CM effects in each ().

A preliminary multiscale analysis was conducted by considering the whole sample. As counterintuitive results were obtained, it was decided to separate the population into the same FR and MR groups. After such a division, each nonlinear metric underwent either a paired sample t-test or a Wilcoxon signed test () for all scales individually. No comparison between scales for individual features was performed (e.g., correlation dimension across all scales), as the interest was in finding statistical differences between the pre- and post-treatment groups at single scales that could better identify articulation or phonation alterations.

All analyses were performed using MATLAB 2023b (The MathWorks, Inc., Natick, MS, USA).

Results

The perceptual assessment of voice highlighted an overall improvement in vocal quality. All grades of the GRB scale presented a statistically significant decrease from the pre- to the post-operative condition ( and Cliff’s , and Cliff’s , and Cliff’s ), as shown in Fig. 6. Considering the G index as explained in Sect. “Signal preprocessing & nonlinear analysis”, it was obtained that 44 subjects belong to the FR group, whereas 25 participants belong to the MR one. Figure 6 also displays their distribution, where green and purple circles refer to FR and MR cohorts, respectively.

Fig. 6.

Boxplots for GRB perceptual scale indices. In green and purple, superimposed circles represent fully and mildly recovered patients, respectively.

Considering such separation, it was investigated whether the degree of recovery depended on age, aetiology, disease time, and post-measurement time. Age did not present a significant difference between FR and MR (p = 0.55). Aetiology diversity is represented in Fig. 7 and includes idiopathic origin, neck iatrogenic injury, thoracic iatrogenic injury, and base of the skull (cranial base/cranial floor) injury.

Fig. 7.

Histogram for patients’ UVFP aetiology.

The chi-square association test did not highlight a significant difference for this factor (p = 0.41). Disease time is the interval between the voice pathology diagnosis and the medical intervention. After outlier removal, such an anamnestic parameter presented a significant difference (p = 0.0131), underlining a longer disease duration for patients who experienced a mild recovery. Post-measurement time represents the occurrence of the follow-up visit after medical intervention. IL is considered a regenerative procedure because it allows reinnervation and revascularisation of the vocal fold tissues. However, these benefits are affected by a large inter-subject variability and may relate to disease chronicity or age. Nevertheless, statistical analysis showed that the degree of recovery did not depend on post-measurement time (p = 0.81).

Figure 8 represents the MFDFA analysis: solid lines concern the FR group, whereas broken lines concern the MR group. Colours relate to the different scale ranges. All correlation coefficients of the FR group computed between pre- and post-operative scaling factors are not significant, whereas, for positive q, the coefficients of the MR group are significant. Moreover, Fig. 9 shows the distribution of the correlation coefficients for the four scale ranges, highlighting significant differences between the FR and MR cohorts for each of them (p values ). Effect size was calculated with Cohen’s d and it is depicted in Fig. 9. This suggests a stronger CM in patients with poor voice quality after treatment.

Fig. 8.

Complexity Matching between pre- and post-operative audio recordings in FR (solid) and MR (broken) patient groups. LLR = longest range 2⁷–2¹³, LR = long range 2⁸–2¹³, SR = short range 2⁹–2¹³, SSR = shortest range 2¹⁰–2¹³.

Fig. 9.

Averaged correlation coefficient for each scale range between FR and MR groups. A (***) refers to a significant difference . A () represents a Cohen’s .

On the contrary, Fig. 10 represents the MFDFA results that investigated whether specific variations exist or a general pattern can be found in the MR group: in this case, solid lines refer to the pairwise correlation coefficients and broken lines to the coefficients obtained after randomising patients order, whereas colours still relate to the scale ranges. The coefficients for the randomised correlation analysis are not significant. On one side, this outcome indicates that voice quality variations are subject-specific. On the other one, it shows that correlation coefficients between scaling factors of pre- and post-operative conditions of Fig. 8 are not due to chance, but they reflect a true matching between acoustic signal complexities, hence, an agreement between the perceptual and objective evaluation of voice quality.

Fig. 10.

Complexity Matching between pre- and post-operative audio recordings in MR patients (solid) and randomised order MR patients (broken). LLR = longest range 2⁷–2¹³, LR = long range 2⁸–2¹³, SR = short range 2⁹–2¹³, SSR = shortest range 2¹⁰–2¹³. The abbreviation “rnd” stands for “randomized”.

The outcome of the multiscale nonlinear analysis produced some unexpected results, e.g., the LLE for the third scale () was significantly higher in the post-operative condition than in the pre-operative one (central empty boxplots of Fig. 11). Therefore, it was decided to carry out two additional statistical analyses accounting for the degree of recovery. This suggested that the significance of was determined by the MR population (p = 0.002), whereas, for the FR group, the parameters were not significant (p = 0.92), as also Fig. 11 shows.

Fig. 11.

Boxplots for LLE at scale = 3. Empty boxes refer to all data, whereas filled boxes refer to separated data according to the degree of recovery (orange for FR, blue for MR). A (**) indicates a significant difference below .

Figure 12 displays the trends of the means of nonlinear measures against the varying scales, along with standard error bars for pre- and post-operative conditions; furthermore, on the left, the FR group is represented, whereas the right side shows the results of the MR group. Effect size was calculated with Cohen’s d and it is depicted in Fig. 12.

Fig. 12.

Trends with standard error bars of nonlinear parameters for FR patients (left) and MR patients (right). Blue and orange lines refer to pre- and post-operative conditions, respectively. A (*) refers to a significant difference between before and after treatment, computed separately for FR and MR groups, , (**) to , and (***) to . A () represents a Cohen’s , () , () .

Discussion

Autologous fat IL is a minimally invasive and regenerative surgical procedure used to reduce the glottic gap in several voice pathologies, including UVFP. Treatment efficacy is typically assessed with perceptual evaluation, which may suffer from high inter-rater variability, and linear acoustic parameters (e.g., F0, jitter), which might not be appropriate for studying the complex, nonlinear dynamics of disordered vocal folds’ vibration. This study proposes a multivariate multiscale nonlinear approach that for the first time implements the concept of complexity matching in acoustic analysis. Moreover, to account for the maladaptive behaviour that UVFP patients are known to adopt to achieve better communication, a multiscale analysis was performed to evaluate the effect of IL on articulation dynamics. Indeed, hyperfunctional characteristics such as anterior-posterior or lateral compression of the false vocal folds and the glottis, excessive activation of the cricothyroid muscles, and general tightening of neck muscles, hyperadduction of the healthy contralateral vocal fold are typically observed^39–41. By progressively filtering out specific frequency components from audio recordings, it is possible to highlight better the contribution of vocal tract resonance phenomena to voice timbre, therefore obtaining relevant information that might reflect the coordination and arrangement of the articulators (e.g., the constriction degree of the pharynx, the positioning of the tongue and the rounding of the lips). Moreover, by removing the fundamental frequency, the role of the paralysed vocal fold to voice quality can be investigated: indeed, a slack and compact vocal fold and a partial glottic insufficiency during phonation may produce an acoustic effect in the lowest vocal register, ranging between 50 and 80 Hz, conferring a rattling or popping sound to the produced voice⁴². This phenomenon, called vocal fry, is a particular laryngeal mechanism generated by a loose glottal gap where arytenoid cartilages are drawn together to tightly compress the vocal folds, allowing the production of air bubbles that contribute to a perceptually defined voice as creaky. Therefore, providing a wider insight into phonatory and articulatory capabilities with nonlinear features from audio recordings could help otolaryngologists evaluate and monitor treatment efficiency with a cost-effective and contactless automatic tool.

Indeed, MFDFA demonstrated that UVFP patients who present a mild perceptual voice quality recovery have the strongest correlation between scaling coefficients of the pre- and post-conditions, from the shortest to the longest ranges, and for each q-order statistical moment. However, as Fig. 8 shows, the highest correlation values are below 0.5 and, excluding the ones concerning positive q-order LR to SSR scale ranges of the MR group, not significant, as opposed to the results of³⁰. This could suggest that a complexity-matching effect never occurs. Nevertheless, these weaker relationships could be caused by the specific experimental protocol, which did not investigate simultaneously interacting physiological systems but the same system at two different time points. Therefore, what Fig. 8 displays could be interpreted as the fact that nonlinear phenomena of voice production, which a multifractal approach is better suited to describe in case of pathology due to turbulences and chaotic behaviours, present the strongest similarity when, perceptually, vocal quality is not fully restored. Interestingly, this could mean that a larger degree of information (e.g., frequency components, noise, irregular vibratory patterns) from the pre-operative condition is still present in the phonation after surgery, which indicates an agreement between the auditory and objective voice evaluation. Moreover, the boxplots shown in Fig. 9 highlight that, for each scale range, the correlation coefficients between the scaling exponents are significantly higher for the MR group than the FR one. Hence, at all levels of voice production, patients with poorer surgical outcome present similar vocal alterations to those assessed in the pre-treatment condition, especially the degree of breathiness and, more marginally, of roughness, as Fig. 6 supports. Therefore, the complexity similarity obtained through the MFDFA efficiently distinguishes between two populations, and it may help clinicians to detect post-operative patients that need further medical care, e.g., more frequent follow-up visits or additional logopaedic therapy, to complete the rehabilitation process better and guarantee a proper recovery of both vocal and life quality. The results from Fig. 10 suggest that complex interactions within the multifractal structure of voice are subject-specific. It was first hypothesised that a randomized order to compute the correlation would not affect the coefficient values if the MR group was characterised by an underlying common property of voice nonlinearities. However, the relevant drop in the strength of the relationships recommends planning precision medicine procedures to follow the rehabilitation of UVFP patients individually. Such an outcome is partially supported by the chi-square tests of associations that underlined that the degree of the recovery did not depend on aetiology (as well as age and post-time measurement) but simply on disease time, even if it has been observed that patients with thoracic surgery usually undergo a more difficult recovery. This may be a result of clinical relevance as it advises the healthcare system to organise medical intervention more quickly, and, on the other hand, it suggests people with dysphonia to seek medical treatment more actively, as the beneficial effects of IL seem to relate mostly to the vocal pathology chronicity. In future studies with more data, artificial intelligence-based frameworks could be tested to understand whether scaling exponents, correlation coefficients or their combination represent novel biomarkers of treatment efficiency.

For the multivariate and multiscale analysis, three significant differences were found in the FR group at the original signal level (scale = 1). Unexpectedly, the embedding dimension proved to be smaller in the pre-operative condition. This could result from greater sensitivity to the richer content of higher frequency harmonics that characterise normophonic voices, in contrast with dysphonic ones where that range is mostly dominated by noise; although not significant, this outcome could also be supported by the higher correlation dimension. On the other hand, both the LLE and Fractal Dimension have a significantly larger value in the pre-operative condition. The LLE highlights that IL surgery may decrease the divergence rate of close trajectories, making the attractor more compact and requiring fewer independent variables to describe it, as the significantly lower fractal dimension would also suggest. Such an ambiguous result might indicate that, according to¹⁵, the D2 and LLE parameters are not adequate for studying dysphonic voices, or at least the ones characterised by glottal insufficiency and, consequently, airflow turbulence phenomena, since they assume deterministic speech dynamics. Moreover, Fig. 12 shows that pre- and post-operative trends intersect frequently, especially for LLE, making these parameters seemingly less robust to evaluate voice quality improvements as their behaviour changes repeatedly across the different scales. Analogously, for the Hurst Exponent, no significant difference was discovered.

Sample entropy presents instead a coherent pattern, with the pre-operative condition values being constantly larger than the post-operative ones. At scale 2, where the habitual speaking range stands after removing higher frequency components (above 11.025 kHz), a more physiological periodicity of the acoustic signal seems to be restored. Since a conversational sustained phonation of /a/ does not contain much more information beyond the threshold of the third formant (usually below 4 kHz⁴³), as opposed to a sung /a/ phonation, a similar result to the one previously described should be found. SE proved to be significantly higher in the pre-operative condition also at scale three and, additionally, scale four, where the contribution of the third formant is filtered out. Unsurprisingly, this can indicate that UVFP, and its potential inappropriate articulatory adjustments, do not affect lip rounding capabilities. Thus, evaluating the motility of two articulators instead of three could be sufficient to assess a patient’s articulation. This result also advises otolaryngologists to consider such an aspect when evaluating treatment efficiency to ensure that compensatory behaviours are progressively deserted. This can guarantee UVFP patients better vocal and life quality since such behaviours are also known to determine brain adaptation mechanisms, e.g., alterations to the processing and integration of sensory and sensorimotor activity, that should be avoided^44,45. However, SE at scales 5 and 6 seems to reveal that articulatory differences are mostly due to tongue movements and not the pharyngeal tract, as the contribution related to its frequency components does not lead to a significant difference between pre- and post-treatment. Interestingly, endoscopy evaluation demonstrated that after IL, patients presented a more relaxed pharynx musculature. This may suggest that the consequent change in pharyngeal degree of constriction is not sufficient to affect the first formant, but, since the pharyngeal wall is tightly linked with the tongue base, such relaxation may be reflected in tongue motility. Therefore, non-invasive diagnostic tools, e.g., ultrasonography, may highlight additional aspects clinicians could use to better understand the post-treatment rehabilitation process and plan more personalised care. At scales 7 and 8, where the vibration of vocal folds is more evident, pre-operative SE remains larger than the post-operative ones, even if significance was achieved for the last scale only. This result could mean both a regularisation of male voices and a diminishment of vocal fry occurrence in female voices, possibly aligning with the lower G and R indices obtained with the perceptual evaluation. In any case, such an outcome underlines beneficial effects on the vocal quality of the IL procedure at both phonatory and articulatory levels. Notably, SE seems to be a reliable nonlinear parameter for studying the MR group, as the trend remains lower for each scale in the post-operative condition. Moreover, significant differences were obtained at scales 1, 2, and 7, pointing to the improvements in vocal quality even in the mild recovery case, as both noise (supported by Fig. 6b purple circles as well) is reduced and vocal folds’ vibration is regularised. Even if no statistically significant difference was found, the fourth row of Fig. 12 further demonstrates an agreement between perceptual and objective measures, as SE measures are higher in the MR group than the FR one, especially at smaller scales (e.g., 1–3). This may mean that, even if the glottic gap closure helps relieve stress in the voice production system at the phonatory level when vocal quality is evaluated with a wider perspective, SE can be more sensitive to the degree of treatment effectiveness. Moreover, since breathy vocal quality is not solely associable with UVFP, this strategy may be applied to other voice pathologies, encouraging a broad usability.

Despite offering novel insights, some limitations of the study must be acknowledged. First, the relatively small sample size may limit the statistical power of the analyses and the robustness of the conclusions, particularly within the MR group. Moreover, this same issue did not allow a proper separation between female and male patients, which could have highlighted gender-specific potential improvements, especially when considering the contributions at the higher scales, where the fundamental frequency lies. As such, caution should be exercised at that range and when extrapolating these results to larger or more diverse populations. Second, this study focused only on a UVFP cohort, even if glottic insufficiency is a sign for other voice disorders, such as sulcus vocalis and, more in general, larynx soft tissues defects, hindering the study’s generalisability. Therefore, future research should recruit patients also diagnosed with such pathologies. However, the sustained phonation of /a/ may allow us to apply this approach to languages different from Italian, as it has been proven that such a vocal task is relatively language-independent⁹. Third, other tasks (e.g., cardinal vowels /i/ and /u/, counting, or standardised passages) should be required for a better overview of articulation capabilities.

Conclusion

Traditional acoustic features may not be accurate and reliable when assessing treatment efficiency for highly disordered voices, as the ones of UVFP patients, because they do not account for well-known nonlinear phenomena.

On the one hand, the complexity matching analysis, obtained through MFDFA, highlighted a stronger similarity in voice production complex behaviour between pre- and post-operative conditions for patients whose vocal quality was not fully recovered. Therefore, this novel approach could support clinicians in identifying cases that require further treatment automatically and without relying on perceptual assessment. Moreover, the altered vocal properties seem patient-specific: such an outcome suggests continuing to promote the development of more personalised healthcare services. Hence, an approach based on the CM phenomenon could provide a robust, cost-effective, contactless device to support otolaryngologists in evaluating the different vocal quality improvement paths of UVFP patients after IL.

On the other hand, the multiscale sample entropy may represent the best parameter to investigate the post-operative beneficial effects of IL at multiple levels, from phonation to articulation. Indeed, this single metric highlighted lower noise at higher frequencies, more regular vibration of the vocal folds, and the importance of the frequency components related to the second formant to objective voice quality. It suggests clinicians should include the assessment of tongue motility to achieve a complete overview of the rehabilitation process. Furthermore, SE may be implemented as a promising supportive tool for the evaluation of fat reabsorption or other minor collateral effects (e.g., partial reopening of the glottis) of IL during follow-up visits and potentially in real-time during the medical intervention due to its low computational load.

Author contributions

Conceptualization: F.C., G.C., A.L., Methodology: F.C., L.F., G.C., A.L., Software: F.C., Formal analysis: F.C., Investigation: F.C., G.C., A.L., Resources: G.C., G.B., L.B., Data curation: F.C., G.C., G.B., L.B., writing—original draft: F.C., writing—review & editing: G.C., A.L., Visualization: F.C., Supervision: G.C., L.F., A.L., Project administration: G.C., A.L.

Funding

The research leading to these results has received funding from the project PE8-AGE-IT “A novel publicprivate alliance to generate socioeconomic, biomedical and technological solutions for an inclusive Italian ageing society”, Codice MIUR: PE 00000015, CUP: B83C22004800006.

Data availability

Data will be made available from the corresponding author upon reasonable request.

Declarations

Competing interests

None to declare.

Ethics approval and consent to participate

All data was recorded anonymously, and informed consent was obtained from each participant. The study data analysis was conducted according to ethical guidelines, and approval was obtained from the Ethics Commission of the University of Florence (n. 275-04/09/2023).

Consent for publication

Not applicable.