In vivo characterization of the optical and hemodynamic properties of the human sternocleidomastoid muscle through ultrasound-guided hybrid near-infrared spectroscopies

Lorenzo Cortese; Pablo Fernández Esteberena; Marta Zanoletti; Giuseppe Lo Presti; Gloria Aranda Velazquez; Sabina Ruiz Janer; Mauro Buttafava; Marco Renna; Laura Di Sieno; Alberto Tosi; Alberto Dalla Mora; Stanislaw Wojtkiewicz; Hamid Dehghani; Sixte de Fraguier; An Nguyen-Dinh; Bogdan Rosinski; Udo M Weigel; Jaume Mesquida; Mattia Squarcia; Felicia A Hanzu; Davide Contini; Mireia Mora Porta; Turgut Durduran

doi:10.1088/1361-6579/ad133a

1. Introduction

The sternocleidomastoid muscle (SCM) is a superficial muscle laying obliquely at both sides of the neck, connecting the manubrium and the clavicle to the mastoid (Gray and Carter 1901). The contraction and the extension of this muscle allow, as a primary function, the rotation of the head and the flexion of the neck. Apart from assisting the movement of neck and head, the SCM has the function of being one of the accessory respiratory muscles to support the respiration in situations of increased respiratory volume and respiratory distress (Roussos and Macklem et al 1982).

Even before the COVID-19 pandemic brought the difficulties of mechanical respiration to worldwide attention, and, inspired by the SCM's role as a supporting muscle in respiration, a series of newer studies have stressed the importance of monitoring the SCM activity in cases of patients with severe respiratory distress. One marker of increased SCM activity, as in other muscles, are the hemodynamic alterations which have been proposed as predictors of ventilatory failure in case of chronic pulmonary diseases, such as chronic obstructive pulmonary disease (COPD) (Guenette et al 2011, Shadgan et al 2011, Katayama et al 2015, Basoudan et al 2016, Reid et al 2016, Tanaka et al 2018, Rodrigues et al 2020). Also, in more acute settings such as acute respiratory failure, SCM activity alterations are hypothesized to provide information to determine the need for initiating mechanical respiratory support, or to decide whether the ventilator support is no longer needed (Reid et al 2016, Istfan et al 2021, Gømez et al 2023). This could impact healthcare given the limitations of current methodologies driving such clinical decisions (Meade et al 2001, Funk et al 2010).

In this framework, near-infrared diffuse optical technologies (Durduran et al 2010) have the potential to play a role in real-time monitoring of the SCM activity as non-invasive methods to quantify quantify the local tissue hemodynamics at the microvascular level, by probing the deep tissue (1–3 cm) using near-infrared (600–1100 nm) light (Istfan et al 2021).

Among the different near-infrared spectroscopic technologies, time-domain near-infrared spectroscopy (TD-NIRS, also known as time-resolved near-infrared spectroscopy, TRS) (Patterson et al 1989, Pifferi et al 2016) is emerging as a reliable and practical tool to measure microvascular tissue/blood oxygenation. TD-NIRS proposes an improvement in accuracy and precision over the continuous-wave near-infrared spectroscopy (CW-NIRS) that is clinically accepted (Ferrari et al 2004, Wolf et al 2007, Murkin and Arango 2009, Torricelli et al 2014, Yamada et al 2019). It works by injecting short laser pulses in the tissue and detecting the diffused signal in a time-resolved manner. Therefore, TD-NIRS is able to measure absolute, wavelength-dependent absorption and scattering coefficients, providing a more robust and reliable determination of absolute oxy-, deoxy- and total hemoglobin concentrations (HbO₂, Hb and THC), and local tissue/blood oxygen saturation (StO₂). TD-NIRS techniques are used since decades in clinical studies, and the reliability of TD-NIRS devices is commonly tested through standardized multi-laboratory accepted protocols, validating device precision, accuracy and other performances under different conditions (Pifferi et al 2005, Wabnitz et al 2014a, 2014b, Pifferi et al 2015, Lanka et al 2022).

Diffuse correlation spectroscopy (DCS) (Boas and Yodh 1997, Yu et al 2007, Durduran et al 2010) on the other hand measures the fluctuations of laser speckle intensity due to light scattering by moving red blood cells after injecting coherent light in the tissue. By utilizing the appropriate physical model, DCS allows the quantification of the tissue microvascular blood flow (i.e. blood flow index, BFi). As a rapidly emerging clinical technique, DCS has been extensively used in the last 10–15 years for studying muscle hemodynamics (Durduran et al 2010, Yu 2012a). The effectiveness of DCS in monitoring blood flow in muscles has been validated in different ways and conditions, and compared to different techniques as ASL-MR and Doppler ultrasound (Yu et al 2007, Li et al 2015, Bangalore-Yogananda et al 2018).

The combination of DCS and NIRS technology such as TD-NIRS, CW-NIRS or frequency domain NIRS (FD-NIRS), allows to retrieve complementary information about tissue hemodynamics, composition and structure, and also, to obtain information about tissue oxygen metabolism, that is, the metabolic rate of oxygen extraction (MRO₂) relating the effective oxygen delivery and consumption by the local tissue (Durduran et al 2010, Durduran and Yodh 2014). During the recent years, the combination of these complementary techniques has been used successfully in several clinical and preclinical studies involving a wide range of situations, from cancer diagnosis and therapy follow-up, to brain monitoring (Cheung et al 2001, Culver et al 2003, Durduran et al 2004, Zhou et al 2007, Roche-Labarbe et al 2010, Choe and Durduran 2011, Yu 2012b, Roche-Labarbe et al 2012, Verdecchia et al 2013, Buckley et al 2014, Lindner et al 2016, He et al 2018, Giovannella et al 2019, Quaresima et al 2019, Milej et al 2020).

Differently to all the previous NIRS studies on the human sternocleidomastoid muscle (Guenette et al 2011, Shadgan et al 2011, Katayama et al 2015, Basoudan et al 2016, Reid et al 2016, Tanaka et al 2018, Rodrigues et al 2020, Istfan et al 2021), here we have employed a unique multi-modal device combining ultrasound (US) imaging with TD-NIRS and DCS (Cortese et al 2021a) to characterize the SCM of a group of healthy subjects and thyroid nodule patients. This multi-modal approach allowed a more reliable, precise and accurate determination of the optical and hemodynamic properties of such muscle, providing simultaneous information about tissue anatomy, oxygenation, perfusion and oxygen metabolism, and enabling also improved precision of the optical measurement due to US guidance.

2. Materials and methods

2.1. Experimental setup: multi-modal US-guided hemodynamic monitor

A multi-modal hybrid platform combining time-domain near-infrared spectroscopy, diffuse correlation spectroscopy and clinical ultrasound has been used for the measurement campaign. A picture of the device, during the measurement procedure, is reported in figure 1(a). The device description and its validation in laboratory and clinical settings have been previously reported in detail in Cortese et al (2021a).

**Figure 1.** (a) Picture of the measurement procedure, with US-guided probe placement. (b) Picture of the multi-modal US-optical probe; center: fiber tips configuration at the probe nose (DCS sources: D-S1 and D-S2; DCS detectors: D-D1 and D-D2, short and long SDSs respectively; TD-NIRS source: T-S1; TD-NIRS detectors: T-D1 and T-D2, short and long SDSs respectively). Adapted with permission from Cortese *et al* (2021a)© The Optical Society. (c) measurement locations. (d) Example of US image of the SCM region acquired simultaneously with the optical data. In the picture, we have highlighted the different tissues, i.e. muscle and superficial (sup.) tissue, composed by skin, adipose tissue and fascia, and the depth of the muscle. Further details and images of the experimental setup are reported in Cortese *et al* (2021a).
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Briefly, the TD-NIRS module (Renna et al 2019) is composed by a custom-made eight wavelength pulsed laser system in the wavelength range 635−1050 nm. The DCS module (Cortese et al 2021b) consists of a long coherence single longitudinal mode continuous-wave laser at 785 nm and sixteen detection channels. The ultrasound system is a customized commercial device (EXAPad, IMV Imaging, France) which is currently commercialized by Quantel Medical (France) under the EvoTouch+ product brand.

The different technologies are integrated in a single device through a dedicated control module (custom product, HemoPhotonics S.L., Spain) while the simultaneous acquisition of TD-NIRS, DCS and US signals are allowed by a multi-modal optical/US probe (Cortese et al 2021a). This probe (custom product, Vermon SA, France), reported in figure 1 (b), includes an ultrasound transducer (10.6 MHz center frequency) and source and detector fibers for TD-NIRS and DCS. Both TD-NIRS and DCS have two different source-detector fiber configurations: (i) long source-detector separation (long SDS), where source and detection fiber tips are separated by 2.5 cm, and (ii) short source-detection separation (short SDS), where source and detection fiber tips are separated by 1.9 cm.

The multi-modal method utilized in this study, combining DCS, TD-NIRS and US imaging, has several benefits. DCS and TD-NIRS provide complementary information about different aspects of tissue hemodynamics, and their combination allows to retrieve information about oxygen metabolism. Additionally, simultaneous US imaging better allow the guidance of the optical measurement, assuring a more reliable probe placement, improving the spatial resolution and measurement reproducibility.

2.2. Study population and protocol of measurement

The data reported in this paper consist of a retrospective analysis of measurements acquired in the context of a larger study, with focus on thyroid nodule hemodynamics (LUCA-project, http://www.luca-project.eu). In this framework, the signal from the sternocleidomastoid muscle has been acquired as a reference to establish whether the thyroid hemodynamics differ from the overlaying and surrounding muscle. The in vivo measurement campaign has been conducted according to the guidelines of the Declaration of Helsinki, and following the SAGER (Sex and Gender Equity in Research) guidelines for reporting sex/gender information. The study has been approved by Hospital Clínic Barcelona local Ethic Committee and Agencia Española de Medicamentos y Productos Sanitarios (AEMPS). Before starting the measurement sessions, all the subjects have been asked to provide written informed consent. Various demographic parameters were also acquired such as biological sex (self reported), age, height, weight, and body mass index (BMI).

Two cohorts of subjects, healthy controls and thyroid nodule patients, have been recruited. In order to classify the subjects into these two groups, all subjects have also undergone a blood analysis and a clinical ultrasound examination. Female subjects during their menstrual period have been excluded from both groups because of possible hemodynamic alterations. The healthy controls have been assumed to be without any thyroid pathologies, with a normal thyroid function, with a negative autoimmunity, and with a normal thyroid ultrasound image. The patient group has been recruited from subjects diagnosed with nodular thyroid pathologies who are scheduled to undergo surgery including patients with benign nodules, malignant nodules and multinodular goiter. The particular thyroid conditions are not direct particular interest to this study, and all the nodule patients included in the study have a normal thyroid function. In any case, we have decided to report the results since thyroid pathologies are very common in the general population and if the SCM hemodynamics and optical properties are altered due to the pathology, they should be taken into account.

The measurements have been performed with the subject laying supine, with the neck slightly hyper-extended in straight (not lateralized) position (see figure 1(a)). For eye safety, patients have been asked to wear laser-safety goggles. The multi-modal probe was placed on the subject skin by using an opaque lotion (Polysonic Ultrasound Lotion, Parker, US), which allows ultrasound coupling without affecting the optical acquisitions, as reported in Di Sieno et al (2019). With the guidance of the US real-time images, the correct position over the sternocleidomastoid muscle, just next to the side of the corresponding thyroid lobe, has been found, and lastly, the probe was fixed through a mechanical arm to reduce artifacts due to movements during the data acquisition.

The concurrent US imaging has allowed not only the correct, repeatable placement of the probe but also the determination of the depth of the sternocleidomastoid muscle, i.e. the thickness of the overlaying adipose tissue layer. For all the subjects, two different locations, that is, left and right sternocleidomastoid muscle, have been measured (see figure 1 (c)). The duration of each acquisition (consisting of DCS and TD-NIRS data and simultaneous US images) was approximately 100 s, and two acquisitions per location, separated by approximately 10 min, have been repeated, with a sequence of measurements consisting of location 1—location 2—location 1 (second repetition) - location 2 (second repetition)¹⁷ . The starting location, left versus right has been randomized to avoid possible drifts due to systematic physiological changes during the procedure

2.3. Optical data analysis

The reduced scattering coefficient ${\mu }_{s}^{{\prime} }$ and absorption coefficient μ_a at different wavelengths have been obtained from the TD-NIRS acquisitions by fitting of the solution of the diffusion equation for a semi-infinite homogeneous medium (Haskell et al 1994, Contini et al 1997) after convolving this solution with the instrument response function (IRF). In the fitting procedure, the ${\mu }_{s}^{{\prime} }$ at different wavelengths λ has been constrained by the empirical Mie relation ${\mu }_{s}^{{\prime} }(\lambda )=A\cdot {\left(\lambda /{\lambda }_{0}\right)}^{-b}$ , where λ₀ is the reference wavelength (λ₀ = 785 nm), A is the estimated reduced scattering coefficient at 785 nm, and b is the so-called scattering power (Mourant et al 1997, Pogue et al 2001, Srinivasan et al 2003, DAndrea et al 2006, Cortese et al 2018).

Since it is of interest for other near-infrared spectroscopy modalities, the differential pathlength factors DPF, have been calculated by using the formula DPF(λ) ≅ (1/ρ) · (c/n) · t(λ) (Delpy et al 1988, Pirovano et al 2021), where ρ is the source-detector fiber tip distance, c the speed of light, n the refractive index of the tissue (we set n = 1.4 independently from the wavelength (Bolin et al 1989, Durduran et al 2010, Ciarrocchi and Belcari 2017)), and t(λ) is the photon mean time-of-flight, defined as the first moment of the measured distribution of the time of flights (DTOF).

The retrieved ${\mu }_{s}^{{\prime} }$ and μ_a values have been then used as input parameters to retrieve the blood flow index (BFi) from DCS data by fitting the acquired photon intensity autocorrelation curves with the solution of the electric field correlation diffusion equation for a semi-infinite homogeneous medium (Durduran et al 2010).

The concentrations of oxy- and deoxy-hemoglobin (HbO₂ and Hb, respectively)¹⁸ have been obtained by assuming linearity between the absorption coefficients at different wavelengths and the chromophore concentrations (i.e. HbO₂ and Hb), through the relation μ_a = ∑_i _i(λ) · c_i, where c_i is the concentration of the i-th chromophore and _i its extinction coefficient (Durduran et al 2010). In the inversion procedure, the absorption coefficients at three wavelengths, 669 nm, 722 nm and 825 nm, have been used. Even though additional wavelengths of the device could be used to recover a more quantitative measure, for simplicity and to avoid confounding the results with errors from additional variables, the water concentration was fixed to 78%, and, for the wavelengths used in the analysis, lipid contribution to NIRS signal was considered negligible (Lindner et al 2016). Finally, the total hemoglobin concentration and the tissue oxygen saturation were obtained through the relations THC = HbO₂ + Hb and StO₂ = HbO₂/THC. We note here that a future study could allow to utilize the additional wavelengths in this device, that go beyond the typically utilized range, for the determination of additional chromophores and a better compensation of the myoglobin and hemoglobin signals.

In addition, by combining the hemodynamic parameters obtained from DCS and TD-NIRS data, the local tissue oxygen metabolism, that is, the metabolic rate of oxygen extraction MRO₂ has been quantified, by using the relation MRO₂ = BFi · CaO₂ · OEF. Here the product of BFi with the arterial oxygen concentration CaO₂ represents the availability of oxygenated blood per unit time. The oxygen extraction fraction (OEF) represents the fraction of blood oxygen consumed by the tissue (Durduran et al 2010). Assuming a compartmentalized model, under steady-state balance, the oxygen extraction fraction can be written as OEF = (SaO₂ − StO₂)/(γ · SaO₂), where SaO₂ is the arterial oxygen saturation and γ is the fraction of venous blood volume (including venule and capillary compartments). Thus, ${\mathrm{MRO}}_{2}=\mathrm{BFi}\cdot \tfrac{1}{\gamma }({\mathrm{SaO}}_{2}-{\mathrm{StO}}_{2})\cdot k\cdot {\mathrm{CHb}}_{\mathrm{blood}}$ (Culver et al 2003), where k = 1.36 ml g⁻¹ is the volume of O₂ per unit mass of hemoglobin for mammals (Larimer 1959) and CHb_blood is the total hemoglobin concentration in blood. The value for γ cannot be estimated for each subject, so the variable used for all following statistical analysis is the combination γMRO₂ with units of cm²/s (same as BFi). In turn, CHb_blood values have been measured in blood tests obtained previous to the measurement protocol and, as all subjects were healthy as far SaO₂ is concerned, the mean value over all the population (98% ± 1%) has been considered.

For all the optically-derived parameters, we have evaluated and compared the precision of a single acquisition, the reproducibility over probe repositioning on the same location, and the whole population variability, by calculating the coefficient of variation defined as $\mathrm{CV}=100\cdot \sigma (x)/\left\langle x\right\rangle$ , where σ(x) is the standard deviation and $\left\langle x\right\rangle$ the average of the variable under consideration (Cortese et al 2021c).

2.4. Statistical analysis

Experimental, demographic and anatomical parameters have been utilized to explore whether they are associated with the measured optical variables. This includes demographic variables as sex, age and BMI, anatomical considerations like the side of the neck, depth and thickness of the muscle, the thyroid pathologies as nodule presence and side, as well as the source-detector separation.

The statistical analysis has been conducted in R Statistical Software (v4.0.0, R Core Team 2020), using base packages and 'lme4' (v1.1.23) and 'performance' (v0.9.1) packages, and 'raincloud' package for plots (Allen et al 2021). The boxplots reported in section 3.2 detail the minimum and maximum values (excluding outliers), median, and first and third quartiles.

As a first step of the statistical analysis, the normality of the distributions has been checked by using the Shapiro-Wilk test on data averaged sequentially over the duration of the single measurement (approximately 100 s of data acquisition, see section 2.2), over repetitions for probe replacement and the side of the neck. This resulted in one value per patient. Then, correlations between demographic variables and anatomical information from US, have been tested by calculating the Pearson correlation coefficient.

In general, to test for significant effects of the different parameters on optical variables, linear mixed effects (LME) models have been used fitting a random value for each side of the neck and considering as the random-effect structure the probe replacement index nested within the subject id number. For the special case of testing for a difference between sides of the neck (and side relative to the nodule position), the sides have been not considered to have different random intercepts.

The demographic or anatomical parameter to be tested has been considered as a unique fixed effect in a separate model each time. This model was compared to a null model without the fixed effect through a likelihood ratio test with restricted maximum likelihood (REML) procedure. When the test yielded a significant difference between models (p − value < 0.05), it has been refitted without REML to obtain unbiased estimates.

In addition, an exponential dependence of the optical and hemodynamic parameters on age, BMI and muscle depth has been tested with a LME model by considering the logarithm of the measured parameters, and the quality of the fit was compared to that of the linear model.

3. Results

3.1. Study population

The pertinent information about the population is reported in table 1. In total, sixty-five subjects (forty-nine females, sixteen males, average age 46 years, minimum age 18, maximum 70 ) have been included in the study. Among the included sixty-five subjects, seventeen are in the healthy subject group (eleven females, six males), and forty-eight in the thyroid nodule patient group (thirty-eight females, ten males). Statistically significant differences in the demographic variables are highlighted with '*' for differences between healthy subject and nodule patients, and with '⋆' for differences between males and females within the corresponding group. Healthy subjects differ from thyroid nodule patients for age, BMI and average muscle depth. Males show a larger muscle thickness respect to females within all the groups considered. Within the healthy subject group, males show higher BMI. Lastly, the population of this study followed the epidemiological characteristics of thyroid nodules. Nodules are more common with increasing age and in women than in men (Hegedüs 2004, Cooper et al 2009, Kwong et al 2015).

Table 1. Demographic table of the subjects included in the study, including parameters such as sex, the number N of subjects per group, the age, body mass index BMI, and the depth and thickness of the muscle (measured with US). For these parameters, the average value ± the standard deviation is reported, and in parenthesis the minimum and maximum values. Statistically significant differences in the demographic variables are highlighted with '*' for differences between healthy subject and nodule patients, and with '⋆' for differences between males an females within the corresponding group.

	N	Age	BMI	Muscle depth	Muscle thickness
		(years)	(kg m⁻²)	(mm)	(mm)
All	65	46(18, 70) ± 13	25(16.0, 35.5) ± 4	3.1(1.26, 6.06) ± 1.0	6.6(4.55, 11.10) ± 1.5
Males	16	48(27, 67) ± 12	26(20.1, 29.6) ± 3	3.0(1.38, 4.85) ± 0.9	⋆7.7(4.76, 11.10) ± 1.9
Females	49	45(18, 70) ± 14	24(16.0, 35.5) ± 5	3.2(1.26, 6.06) ± 1.0	⋆6.2(4.55, 8.03) ± 1.1

Healthy	17	*36(24, 49) ± 9	*23(17.5, 29.4) ± 3	*2.4(1.26, 4.05) ± 0.8	6.8(5.17, 9.07) ± 1.4
Males	6	38(27, 49) ± 8	⋆25(20.1, 29.4) ± 3	2.4(1.38, 3.75) ± 0.7	⋆7.7(6.18, 9.07) ± 1.3
Females	11	36(24, 49) ± 9	⋆22(17.5, 28.7) ± 3	2.4(1.26, 4.05) ± 0.8	⋆6.3(5.17, 7.36) ± 1.3

Patients	48	*49(18, 70) ± 13	*25(16.0, 35.5) ± 4	*3.4(1.93, 6.06) ± 1.0	6.5(4.55, 11.10) ± 1.5
Males	10	54(37, 67) ± 10	27(24.9, 29.6) ± 2	3.4(2.51, 4.85) ± 0.9	⋆7.8(4.76, 11.10) ± 1.3
Females	38	48(18, 70) ± 14	25(16.0, 35.5) ± 5	3.4(1.93, 6.06) ± 1.0	⋆6.2(4.55, 8.03) ± 1.1

3.2. Distribution of measured parameters and optical properties

In figure 2 we report the distributions of the measured variables, together with the boxplots, for both long and short SDSs, obtained considering one data point per subject (see above)¹⁹ Detailed tables with the average values of the parameters considered are reported in appendix A. In table A3, we furthermore report the comparison between the variability of a single acquisition (precision of a single acquisition of approximately 100 s), between repetitions (due to probe repositioning on the same location), and the whole population variability, for the parameters reported in figure 2.

The normality of the distributions reported in figure 2 has been tested by using the Shapiro-Wilk test. We have found that parameter b is normally distributed for both source-detector separations, while μ_a at 669 nm is normally distributed only for the long SDS. The rest of parameters are not normally distributed. We note that the LME method that as employed for further statistics does not require normality (Schielzeth et al 2020, Knief and Forstmeier 2021). Figure 2 also highlights some possible differences between long and short SDSs acquisitions. The statistical tests applying the LME model shows significant differences between long and short SDSs for all the parameters measured, except for the μ_a at 669 nm. Details of these tests are shown in table B1 in appendix B, where we report the LME model best estimate (and standard error) of the measured value, highlighting the differences between the groups considered. As expected, the values resulting from fitting the LME model, only slightly differ from the mean values obtained considering one average point per subject, reported in appendix A.

In the following section, we will focus on results only related to the longer SDS (2.5 cm) acquisitions, which, as discussed in section 4, is in first approximation more sensitive to the deeper tissue properties, that is, the sternocleidomastoid muscle.

A detailed characterization at different wavelengths of the optical properties, that is ${\mu }_{s}^{{\prime} }$ , μ_a and DPF determined by TD-NIRS acquisitions, is reported in figure 3 and in tables A4, A5 and A6 in appendix A. We note that these plots are for illustration purposes of the overall tendencies and the statistically significant differences should be checked by using the above-mentioned tables in appendix B.

**Figure 3.** (Upper panel) The measured reduced scattering coefficient, (center panel) the absorption coefficient, and, (lower panel) differential pathlength factor of the sternocleidomastoid muscle over different wavelengths at both long and short SDSs is shown. The average over all subjects (solid lines) is shown together with a boxplot. Outliers are marked in red.
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3.3. Effects of measurement location and sex

The dependence of the measured parameters (for the long SDS) on the location (left versus right muscle), and on the subject biological sex, has been studied. In figures 4 and 5, we highlight the differences between the muscle location and the sex. In the figures, the parameters showing statistically significant differences are highlighted by reporting the LME model best estimate in red and by an asterisk, while the estimate of the parameters not showing significant differences are reported in light gray. Detailed results of the statistical tests are reported in tables B2 and B3 in appendix B.

**Figure 4.** Differences between left (circle) and righ (triangle) is shown. The data points from the same subject are connected by the gray lines. LME model best estimates with error bars (standard error) are overlapped to data points, and are reported in red (and together with an asterisk) when differences between groups are statistically significant.
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**Figure 5.** Differences between sexes is shown. The model best estimates with error bars are overlapped to data points, and are reported in red and highlighted with an asterisk when differences between groups are statistically significant.
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3.4. Effect of age, BMI, muscle depth and thickness

In this study we have considered a population with age ranging from 18 to 70 years, with an average value of 46 . Considering such a wide range, we have analyzed the effects of this variable as confounding factor on the measured parameters. The correlations are shown in figure 6, where we report the data points of each subject, for the long SDS, together with the fitted lines in red where we have found statistically significant correlations. Detailed data of the statistical tests are reported in appendix B, table B4.

**Figure 6.** Effect of the subject age on the measured parameters. One data point per each subject, result of the average over repetitions and locations, is reported, together with the statistical model fitted lines. When the correlation is statistically significant, the fitted line are reported in red and highlighted with an asterisk.
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Moreover, as reported in section 2.4, we have tested whether an exponential relation better describes the dependence between the measured parameters on subject age, finding no improvements for any of the analyzed variables with respect to the linear model.

We also have studied the effects of body mass index, depth and thickness of the muscle (measured through simultaneous US imaging), on the measured parameters (for the long SDS). Such correlations have been represented in figures 7 and 8 (plots not reported for muscle thickness), and the results of statistical tests reported in tables B5, B6 and B7. In case the exponential model better explains such correlations, such tables also report the logarithm of the parameter under consideration as independent variable.

**Figure 7.** Effect of the subject body mass index BMI on the measured parameters. One data point per each subject, result of the average over repetitions and locations, is reported, together with the statistical model fitted lines. When the correlation is statistically significant, the fitted line are reported in red and highlighted with an asterisk.
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**Figure 8.** Effect of muscle depth on the measured parameters. One point per repetition (two repetitions and two sides per patient) is reported. Points related to the left side are shown as circles, while to the right side as triangles. Points corresponding to the same subject are connected with gray lines. Data points are reported together with the statistical model fitted lines. When the correlation is statistically significant, the fitted lines are reported in red and highlighted with an asterisk.
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3.5. Effect of the presence of thyroid nodules

As the last part, we have investigated whether the presence of a thyroid nodule on the subject's thyroid affects the measured parameters on the sternocleidomastoid muscle, for the long SDS. With this aim, we first have analyzed possible differences between the group of healthy controls and thyroid nodule subjects. The plots highlighting the statistically significant differences between these two groups are reported in figure 9, and results of statistical tests are detailed in table B8.

**Figure 9.** Differences between healthy control and thyroid nodule patient groups. One data point per each subject, result of the average over repetitions and locations, is reported. Model best estimates with error bars are overlapped to data points, and are reported in red and highlighted with an asterisk when differences between groups are statistically significant.
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Second, we have studied the differences within the group of thyroid nodule subjects, looking at the possible differences between the parameters measured on the muscle at the same side of the neck as the nodule (nodule side), and what measured on the muscle at the opposite side (nodule-free side). The plots are reported in figure 10, and the detailed results of the statistical analysis are reported in table B9, in appendix B.

**Figure 10.** Differences between muscles at the nodule side of the neck and at the 'nodule-free' side, within the group of thyroid nodule patients. One data point per side per each subject, result of the average over repetitions, is reported. Data points corresponding to the left side are represented with circles, and to the right side with triangles. Points correspondent to the same subject are connected by a gray line. Model best estimates with error bars are overlapped to data points, and are reported in red and highlighted with an asterisk when differences between groups are statistically significant.
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4. Discussion

Our study represents the first characterization of the sternocleidomastoid muscle performed using a multi-modal device simultaneously combining TD-NIRS, DCS and is guided by US imaging (Cortese et al 2021a). The results reported in section 3 and discussed here represent a comprehensive reference for future studies utilizing near-infrared diffuse optical methods to measure the SCM hemodynamics and oxygen metabolism. By utilizing a state-of-the-art system with concurrent ultrasound guidance and a large number of wavelengths, we have provided not only parameters for designing new system but also for avoiding confounding effects such as the demographic variables and common pathologies such as the presence of thyroid nodules (Haugen et al 2016, Bray et al 2018). Figures 2 and 3 and tables in appendix A report the measured physiological and optical parameters. Apart from the preliminary characterization on a small group of subjects performed using a hybrid TD-NIRS/DCS system (Lindner et al 2016), the only SCM diffuse optical characterizations reported up to now have been performed by using FD-NIRS or CW-NIRS (Katayama et al 2015, Yang et al 2020a, Istfan et al 2021, Van Hollebeke et al 2022), which have shown to be less reliable in measuring absolute values. Most studies report trends in blood oxygenation instead. Albeit the values retrieved in this study show important differences from the literature. For example, respect to the recent study of Istfan et al (2021) performed with a FD-NIRS device, we report a systematic overestimation of approximately 10%–30% for variables as scattering coefficient, DPF, and StO₂, and a similar underestimation for absorption coefficient, THC, HbO₂ and Hb.

We explain these trends by considering that the main differences arise from the different technologies and data analysis models used to characterize the muscle. Several studies indeed have highlighted systematic differences between optical measurements obtained with different technologies and, within the same technology, with different devices and/or different analysis methods (Hyttel-Sorensen et al 2011, Kleiser et al 2016, 2018, Istfan et al 2021, Lanka et al 2022).

Demographic differences between the two studies can also explain such trends. Istfan et al 2021 have considered a reduced group of ten healthy subjects, much younger than the whole population considered in our study. When we limit our analysis only to the younger group of subjects without thyroid nodules (see table B8), these systematic differences tend to be smaller.

Lastly, slightly different position of the probe over the sternocleidomastoid muscle and different body orientation of the subject, can also explain the differences reported in the measured values. Respect to the study of Istfan et al (2021), we have indeed considered a less lateral position over the SCM, just at the side of the thyroid lobe, and the subject laying supine instead of seated in upright position as in the study of Istfan et al (2021).

Figures 2 and 3 and the statistical results reported in sections 3.2 and appendix B highlight differences in the measured parameters due to the source-detector separation used for the measurements as expected since the muscle has significant overlaying tissue.

As well known by light transport theory (Martelli 2009), longer SDS acquisitions are in first approximation more sensitive to photons probing deeper tissue. Shorter source-detector acquisitions, on the other hand, results more affected by photons probing the superficial tissue (in this case skin and fat layer covering the sternocleidomastoid muscle), showing different optical and hemodynamic properties respect to the deeper tissue (Nasseri et al 2016, Istfan et al 2021, Pirovano et al 2021).

The recorded differences between long and short SDS results (table B1) are remarkable for perfusion and scattering related parameters (∼10%−20%) and smaller for absorption related parameters, such as hemoglobin content and saturation (<4%).

We explain such small differences by considering that short SDS channel can be sensitive to muscle properties too, since the average muscle depth is 3.1 mm and the long and short SDS channels only differ of 6 mm (long SDS: 2.5 cm, short SDS: 1.9 cm) (Istfan et al 2021). In this respect, future studies with the aim of improve the depth sensitivity applying multi-distance detection and layered analytical/numerical models, should consider a smaller source-detector separation for the short SDS channel, in order to better take care of the superficial tissue properties.

A well-known challenge of diffuse optical NIRS technologies is the limited spatial resolution, that can lead to large variability in the measured parameters. We have tried to address this point by analyzing the precision of our measurements in details. The data reported in table A3, comparing the precision of single and multiple acquisitions to the group variability, underline the high quality of the measurements performed. Such precision result in line with the laboratory characterization of the device used (Cortese et al 2021a), and well allow the detection of physiological changes due to SCM and other muscle activation due to exercise training or pathological situation (Yu et al 2005, Guenette et al 2011, Shadgan et al 2011, Gurley et al 2012, Shang et al 2013, Katayama et al 2015, Basoudan et al 2016, Reid et al 2016, Perrey and Ferrari 2018, Tanaka et al 2018, Quaresima et al 2019, Rodrigues et al 2020, Giovannella et al 2021, Istfan et al 2021).

In particular, we do not reveal differences between precision of short SDS and long SDS acquisitions, the last characterized by a much lower detection count-rate (data not shown). This point demonstrates that the main contribution to the variability of a single acquisition comes from physiological changes during the acquisition time (∼100 s). This is promising in light of the possibility of drastically reducing the measurement integration time to improve the device temporal resolution without affecting the precision (Cortese et al 2021b).

The variability over probe repositioning on the same location, is both affected by physiological changes in the tissue between the two different repetitions, and by errors in finding the exact same position of the probe in the neck. This point is also strengthened by the differences measured in muscle depth and thickness between the first and second repetition on the same location, CV rep. ∼ 9 %. In this respect, the proposed multi-modal approach combining optical measurements guided by simultaneous US imaging helps to reduce the impact of probe position errors in the measurement precision.

With regard to the differences between muscle location, reported in figure 4 and table B2, we note that all the optical and hemodynamic variables show significant differences. Small hemodynamic differences between sides of the neck have already been observed (Lindner et al 2016, Lindner 2017). In these references, Lindner et al explained such differences with muscle activation due to neck hyperextended position, inducing hemodynamics changes during the measurement protocol. In that case, for all the subjects, the first location to be measured was the right side, and last the left side. In the present study, we also have noted statistical differences between the first side of the neck measured in each patient and the second side (significant differences in A, b, BFi and γMRO₂—data not shown). However, due to randomization of the starting measurement side (see section 2.2), this does not effect the previous results comparing left and right sides as a group.

Figure 5 and table B3 highlight differences on the measured parameters between sexes. The contrast of hemodynamic and optical variables between sexes have been also noticed previously (Farzam et al 2014, Istfan et al 2021). Such variations can be linked to BMI differences between the two groups, since, as reported in table 1, they are statistically significant. As reported in section 3.4 and discussed later on, it is indeed well known that BMI affects NIRS acquisitions (Durduran et al 2002, Spinelli et al 2004, Pirovano et al 2021). Additionally, different muscle mass (i.e. thickness) between sexes (see table 1) may be responsible of the differences detected between the two groups. Lastly, such variations can be explained by different hemoglobin content between sexes (Murphy 2014), also detected with blood analysis test among the population of this study (data not presented).

In figures 6, 7 and 8 we have reported the correlations between the measured parameters and age, BMI and muscle depth respectively. These three parameters are linearly positively correlated (see table B10): BMI and muscle depth are a measure of the presence of a thicker fat superficial layer, which is prominent in older population. As BMI and muscle depth increase, our measurement will be indeed more sensitive to the thicker superficial layer of adipose tissue, which has a different hemodynamics and composition than muscle (Nasseri et al 2016, Istfan et al 2021, Pirovano et al 2021).

Considering the muscle depth dependence of the optically measured parameters is of key importance, due to its large variability (>30%) between subjects, as reported in table A3. By the means of the multi-modal optical-US device used, and by the statistical analysis reported, we aim to reduce the effect of such variability in the optically derived parameters, setting the path for being more sensitive to the specific tissue under investigation. The simultaneous acquisition of US images indeed allows to re-normalize the optical parameters by taking into account the muscle depth as reported in section 3. In the future, the anatomical information carried by US, should come together with advanced computational analysis methods, such as Monte Carlo and finite element methods (Fang 2010, Jermyn et al 2013), capable of modelling light propagation using segmented US images. Such methods should be furthermore integrated with novel systems allowing multiple source detector distance acquisitions for a better separation between superficial and deep tissue properties (Wang et al 2022).

In addition, we would like to make a last comment on the dependence of the measured parameters on muscle depth, reported in figure 8. We note that, we have acquired one US depth measurement for every repetition and location (so, four depth values measured per subject, two repetitions per side). The average variability between repetitions is ∼9 %, as reported in table A3. This variability can in principle hide the dependencies of the measured hemodynamic parameters on the thickness of the fat layer tissue. Differences on measured depth among repetitions on the same subject could indeed reflect differences of probe pressure on subject neck more than anatomical differences (i.e. thicker fat layer), that can significantly impact on the local hemodynamics (Mesquita et al 2013, Farzam et al 2014, Baker et al 2015).

With regard to the differences between healthy control and thyroid patient groups reported in section 3.5, they possibly mainly reflect the age, BMI and muscle depth differences between the two groups. Healthy subjects are indeed in average younger, and with lower BMI and muscle depth than patients (table 1). Lastly, the slight differences reported among the patient group between the nodule side and nodule-free side of the neck, could supposedly reflect small anatomical differences between the two neck regions, with and without nodule.

As last point, we would like to comment on the clinical relevance of the present study. Our work, together with the previously-mentioned studies (Guenette et al 2011, Shadgan et al 2011, Katayama et al 2015, Basoudan et al 2016, Reid et al 2016, Tanaka et al 2018, Rodrigues et al 2020, Istfan et al 2021, Gømez et al 2023) using different near-infrared diffuse optical devices, have shown that diffuse optical technologies are among the new technologies capable of non-invasively monitoring the SCM activity. Additionally to NIRS studies, we also mention here promising results of photoacoustic imaging in monitoring skeletal muscle activity (Yang et al 2020b, Karlas et al 2020, Wagner et al 2021). In this respect, albeit photoacoustic imaging spatial resolution is better than diffuse optical technology resolution, such technology is unable to provide a direct measure of blood perfusion, which is made available by the device used in this study.

Monitoring the activity of the SCM muscle can be of great importance in cases of patients with severe respiratory distress such as COPD. Since the SCM muscle acts as an accessory respiratory muscle, it is indeed recruited to aid in respiration in such cases, when primary respiratory muscle effort, such as diaphragm, is not sufficient. By monitoring SCM activity, information can be obtained on the degree of the patient's respiratory effort that is required to maintain an optimal minute ventilation (Guenette et al 2011, Shadgan et al 2011, Katayama et al 2015, Basoudan et al 2016, Reid et al 2016, Tanaka et al 2018, Rodrigues et al 2020).

In particular, SCM monitoring would be relevant in more acute settings in the intensive care unit (ICU), such as acute respiratory failure, in order to establish the necessity of mechanical respiratory support, or to decide whether the ventilator support is no longer needed. On that behalf, SCM monitoring may be of special interest to determine the readiness of an intubated patient for weaning from ventilation (Reid et al 2016, Istfan et al 2021). In this context, only few physiological parameters have demonstrated predictive power, and new tools for improving weaning success are urgently needed (Meade et al 2001, Funk et al 2010). When failure from weaning from ventilation occurs, the cardiovascular system is unable to meet the increased oxygen cost of breathing (Field et al 1982, Vassilakopoulos et al 1996). Usually, the increased oxygen cost of breathing during extubation and/or spontaneous breathing trial (SBT) process, is met by redirecting blood flow from the periphery towards the primary respiratory muscles, such as the diaphragm, and accessory respiratory muscles as the SCM (Gruartmoner et al 2014, Mesquida et al 2020). Anyway, long ICU stay and prolonged invasive mechanical ventilation, can cause dysfunction and atrophy to respiratory muscles, which, during the extubation or SBT phase, are not able to cope with the increased oxygen cost of breathing. In this respect, no activation or, on the other hand, early and elevated activation of the SCM during the SBT have been associated to weaning failures, reflecting the inability of primary respiratory muscles to resume autonomous respiration (Parthasarathy et al 2007, Dres et al 2017, Dres and Demoule 2018, Dres et al 2020, Van Hollebeke et al 2022).

In such framework, non-invasive monitoring of SCM hemodynamics through near-infrared spectroscopies before and during the spontaneous breathing trial and within the early extubation phases, may add important additional biomarkers for determining the right moment for extubation, drastically reducing the failure rate, or for early detecting extubation failure and the need for rapid re-institution of mechanical ventilation (Reid et al 2016, Istfan et al 2021).

5. Conclusion

In this paper we have reported a detailed in vivo optical and hemodynamic characterization of the human sternocleidomastoid muscle. The characterization has been performed by using a state-of-the-art multi-modal optical-ultrasound integrated device, combining in a single system a clinical ultrasound, and two cutting edge diffuse optical systems, TD-NIRS and DCS, capable of simultaneously providing hemodynamic and anatomical information of the tissue.

Here, we have reported detailed plots and tables, related to the sternocleidomastoid muscle of sixty-five subjects including healthy population and thyroid nodule patients, with the average values and variabilities of hemodynamic and optical parameters. In addition, we have evaluated, by a rigorous statistical analysis, the dependencies of all the measured parameters on the location of the muscle (left or right side of the neck), on sex, on age, body mass index and depth of the muscle (obtained through simultaneous US acquisitions). Lastly, we have evaluated whether the measured muscle hemodynamics is affected by the presence of a thyroid nodule on the same side of the neck, being this situation very common among the adult population.

Concluding, we posit that the unique platform together with the rigorous analysis reported allows these results to pave the way for future near-infrared spectroscopic studies and clinical applications on SCM hemodynamic monitoring. Lastly, the systematic analysis of the correlations between the retrieved hemodynamic and optical parameters and variables such as side of the neck, sex, age, body mass index and depth of the muscle, will allow future studies to take into account such dependencies.

Acknowledgments

This work has received funding from: the European Union's Horizon 2020 research and innovation programme under grant agreements No. 688303 (LUCA), No. 101016087 (VASCOVID), No. 101017113 (TINYBRAINS), No. 675332 (BITMAP), No. 871124 (LASERLAB-EUROPE V), Fundació CELLEX Barcelona, Fundació Mir-Puig, Agencia Estatal de Investigación (PHOTOMETABO, PID2019-106481RB-C31/10.13039/501100011033), the 'Severo Ochoa' Programme for Centres of Excellence in R&D (CEX2019-000910-S), LUX4MED special program, the Obra social 'la Caixa' Foundation (LlumMedBcn), Generalitat de Catalunya (CERCA, AGAUR-2022-SGR-01457, RIS3CAT-001-P-001682 CECH). Additionally, this project has received funding from the Secretaria d'Universitats i Recerca del Departament d'Empresa i Coneixement de la Generalitat de Catalunya, as well as the European Social Fund (L'FSE inverteix en el teu futur)FEDER. The author's have confirmed that any identifiable participants in this study have given their consent for publication. Finally, we sincerely thank the subjects involved in this study for their enthusiastic participation.

Data availability statement

The data that support the findings of this study are openly available at the following URL/DOI:https://doi.org/10.5281/zenodo.7741369 (Cortese et al 2023).

Disclosure

The role in the project of all the companies (HemoPhotonics S.L., Vermon SA, IMV Imaging) and their employees involved has been defined by the project objectives, tasks, and work packages and has been reviewed by the European Commission (European Union's Horizon 2020 research and innovation programme, LUCA project, grant agreement No. 688303).

ICFO has equity ownership in the spin-off company HemoPhotonics S.L. and UMW is the CEO. TD and UMW are inventors on relevant patents.

MB, DC, ADM, AT are co-founders of PIONIRS s.r.l., spin off company from Politecnico di Milano (Italy), and MB is the CEO of the company. Their involvement in the study was mainly prior to the company foundation.

All the potential financial conflicts of interest and objectivity of research have been monitored by ICFO's Knowledge and Technology Transfer Department.

Appendix A.: Tables of optical and physiological parameters

Table A1. Table of the optically derived physiological parameters (mean ± standard error of the mean) for long and short SDSs. Long SDS: 2.5 cm; short SDS: 1.9 cm.

Sex	SDS	StO₂	THC	HbO₂	Hb	BFi	γMRO₂
		(%)	(μM)	(μM)	(μM)	(10⁻⁹ cm² s⁻¹)	(10⁻¹⁰ cm² s⁻¹)
All	Long	70.6 ± 0.4	135 ± 3	96 ± 2	39.1 ± 0.7	4.8 ± 0.2	2.4 ± 0.1
Male	Long	71.2 ± 0.7	138 ± 7	99 ± 5	38.7 ± 1.8	5.4 ± 0.5	2.9 ± 0.3
Female	Long	70.4 ± 0.4	134 ± 3	95 ± 2	39.3 ± 0.8	4.6 ± 0.2	2.2 ± 0.1

All	Short	72.1 ± 0.4	139 ± 3	100 ± 2	38.1 ± 0.7	4.0 ± 0.2	1.9 ± 0.1
Male	Short	71.4 ± 0.8	140 ± 8	101 ± 6	38.9 ± 1.9	4.6 ± 0.3	2.6 ± 0.3
Female	Short	72.3 ± 0.4	138 ± 3	100 ± 2	37.9 ± 0.8	3.8 ± 0.2	1.7 ± 0.1

Table A2. Table of the retrieved Mie scattering coefficients A and b (mean ± standard error of the mean), from the relation ${\mu }_{s}^{{\prime} }(\lambda )=A\cdot {\left(\lambda /{\lambda }_{0}\right)}^{-b}$ .

Sex	SDS	λ₀	A	b
		(nm)	(cm⁻¹)	(adim.)
All	Long	785	8.0 ± 0.1	0.66 ± 0.01
Male	Long	785	7.2 ± 0.2	0.68 ± 0.02
Female	Long	785	8.2 ± 0.1	0.65 ± 0.02

All	Short	785	9.6 ± 0.2	0.70 ± 0.02
Male	Short	785	8.4 ± 0.2	0.76 ± 0.03
Female	Short	785	9.9 ± 0.2	0.69 ± 0.02

Table A3. Table of the variability of the principal physiological and optical parameters for long and short SDSs. Variability due to single acquisition (CV single) fluctuations, due to probe repositioning between two repetitions on the same location (CV rep. ) and variability within the whole study population (CV group) are reported.

	SDS	Depth	Thickness	A	b	μ_a−669	μ_a−825	THC	StO₂	BFi	γMRO₂
CV single	Long	−	−	0.4%	3.0%	2.0%	1.2%	1.0%	0.9%	5.3%	6.0%
CV rep.	Long	8.5%	8.7%	4.1%	7.1%	6.5%	6.6%	6.8%	2.2%	13.0%	15.0%
CV group	Long	32.2%	22.8%	13.2%	22.3%	21.4%	19.6%	21.7%	6.0%	46.1%	47.6%

CV single	Short	−	−	0.4%	3.1%	2.5%	1.5%	0.8 %	0.8%	5.5%	5.9%
CV rep.	Short	8.5%	8.7%	4.7%	7.3%	6.2%	6.2%	6.0 %	2.0%	12.2%	14.3%
CV group	Short	32.2%	22.8%	21.7%	27.4%	21.3%	20.5%	21.6%	5.6%	47.5%	45.5%

Table A4. Table of the measured reduced scattering coefficients ${\mu }_{s}^{\prime}$ (mean ± standard error of the mean).

Sex	SDS	${\mu }_{s-637}^{\prime}$	${\mu }_{s-669}^{\prime}$	${\mu }_{s-722}^{\prime}$	${\mu }_{s-825}^{\prime}$	${\mu }_{s-841}^{\prime}$	${\mu }_{s-905}^{\prime}$	${\mu }_{s-971}^{\prime}$	${\mu }_{s-1050}^{\prime}$
		(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)
All	Long	9.1 ± 0.1	8.9 ± 0.1	8.4 ± 0.1	7.7 ± 0.1	7.6 ± 0.1	7.3 ± 0.1	7.0 ± 0.1	6.6 ± 0.1
Male	Long	8.2 ± 0.2	7.9 ± 0.2	7.6 ± 0.2	6.9 ± 0.2	6.8 ± 0.2	6.5 ± 0.1	6.2 ± 0.1	5.9 ± 0.1
Female	Long	9.5 ± 0.1	9.2 ± 0.1	8.7 ± 0.1	8.0 ± 0.1	7.9 ± 0.1	7.6 ± 0.1	7.2 ± 0.1	6.9 ± 0.1

All	Short	10.8 ± 0.2	10.5 ± 0.2	9.9 ± 0.2	9.0 ± 0.2	8.9 ± 0.2	8.5 ± 0.2	8.1 ± 0.2	7.7 ± 0.2
Male	Short	9.5 ± 0.2	9.2 ± 0.2	8.7 ± 0.2	7.9 ± 0.2	7.8 ± 0.2	7.3 ± 0.2	7.0 ± 0.2	6.6 ± 0.2
Female	Short	11.3 ± 0.2	10.9 ± 0.2	10.3 ± 0.2	9.5 ± 0.2	9.3 ± 0.2	8.9 ± 0.2	8.5 ± 0.2	8.1 ± 0.2

Table A5. Table of the measured absorption coefficients μ_a (mean ± standard error of the mean).

Sex	SDS	μ_a−637	μ_a−669	μ_a−722	μ_a−825	μ_a−841	μ_a−905	μ_a−971	μ_a−1050
		(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)	(cm⁻¹)
All	Long	0.39 ± 0.01	0.31 ± 0.01	0.24 ± 0.01	0.29 ± 0.01	0.30 ± 0.01	0.38 ± 0.01	0.56 ± 0.01	0.37 ± 0.01
Male	Long	0.40 ± 0.02	0.31 ± 0.01	0.25 ± 0.01	0.29 ± 0.01	0.31 ± 0.01	0.39 ± 0.02	0.58 ± 0.02	0.37 ± 0.01
Female	Long	0.39 ± 0.01	0.31 ± 0.01	0.24 ± 0.01	0.28 ± 0.01	0.30 ± 0.01	0.38 ± 0.01	0.55 ± 0.01	0.37 ± 0.01

All	Short	0.39 ± 0.01	0.32 ± 0.01	0.25 ± 0.01	0.30 ± 0.01	0.31 ± 0.01	0.38 ± 0.01	0.57 ± 0.01	0.37 ± 0.01
Male	Short	0.41 ± 0.02	0.32 ± 0.01	0.25 ± 0.01	0.30 ± 0.01	0.32 ± 0.01	0.40 ± 0.02	0.60 ± 0.02	0.38 ± 0.02
Female	Short	0.39 ± 0.01	0.32 ± 0.01	0.25 ± 0.01	0.29 ± 0.01	0.31 ± 0.01	0.38 ± 0.01	0.56 ± 0.01	0.37 ± 0.01

Table A6. Table of the measured differential pathlength factors DPF (mean ± standard error of the mean).

Sex	SDS	DPF₆₃₇	DPF₆₆₉	DPF₇₂₂	DPF₈₂₅	DPF₈₄₁	DPF₉₀₅	DPF₉₇₁	DPF₁₀₅₀
		$({adim}.)$	$({adim}.)$	$({adim}.)$	$({adim}.)$	$({adim}.)$	$({adim}.)$	$({adim}.)$	$({adim}.)$
All	Long	3.82 ± 0.04	4.20 ± 0.04	4.72 ± 0.06	4.32 ± 0.04	4.21 ± 0.05	3.80 ± 0.04	3.16 ± 0.04	4.08 ± 0.05
Male	Long	3.61 ± 0.09	4.00 ± 0.10	4.44 ± 0.12	4.12 ± 0.12	4.01 ± 0.12	3.61 ± 0.09	2.99 ± 0.10	3.93 ± 0.12
Female	Long	3.90 ± 0.04	4.26 ± 0.04	4.81 ± 0.07	4.38 ± 0.05	4.28 ± 0.05	3.87 ± 0.04	3.21 ± 0.04	4.13 ± 0.05

All	Short	4.05 ± 0.05	4.38 ± 0.05	4.87 ± 0.05	4.39 ± 0.05	4.32 ± 0.05	3.90 ± 0.04	3.24 ± 0.04	4.10 ± 0.05
Male	Short	3.75 ± 0.09	4.10 ± 0.09	4.52 ± 0.10	4.13 ± 0.11	4.05 ± 0.10	3.64 ± 0.09	3.00 ± 0.08	3.90 ± 0.10
Female	Short	4.16 ± 0.05	4.48 ± 0.06	4.98 ± 0.06	4.48 ± 0.05	4.41 ± 0.05	3.99 ± 0.05	3.32 ± 0.05	4.17 ± 0.05

Appendix B.: Tables of statistical tests

Table B1. Table of LME estimates, standard errors and statistical tests. Source-detector separation differences.

	Long SDS	Short SDS	Absolute difference	Relative difference (%)	p − value
A (cm⁻¹)	8.1 ± 0.1	9.5 ± 0.1	1.46 ± 0.04	16.6 ± 0.5	<10⁻³
$b({adim}.)$	0.65 ± 0.02	0.72 ± 0.02	0.070 ± 0.004	10.2 ± 0.6	<10⁻³
μ_a−669 (cm⁻¹)	0.321 ± 0.007	0.324 ± 0.007	0.003 ± 0.002	0.8 ± 0.6	0.12
μ_a−825 (cm⁻¹)	0.295 ± 0.007	0.307 ± 0.007	0.011 ± 0.002	3.8 ± 0.7	<10⁻³
THC (μ M)	141 ± 3	145 ± 3	4.2 ± 0.4	2.9 ± 0.3	<10⁻³
StO₂(%)	70.6 ± 0.5	71.7 ± 0.5	1.07 ± 0.07	1.5 ± 0.1	<10⁻³
BFi (10⁻⁹ cm² s⁻¹)	4.7 ± 0.2	4.0 ± 0.2	0.71 ± 0.03	16.3 ± 0.8	<10⁻³
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.3 ± 0.1	1.9 ± 0.1	0.40 ± 0.03	19 ± 1	<10⁻³

Table B2. Table of LME estimates, standard errors and statistical tests. Location differences.

	Left	Right	Absolute difference	Relative difference (%)	p − value
A (cm⁻¹)	7.9 ± 0.1	8.1 ± 0.1	0.20 ± 0.03	2.5 ± 0.4	<10⁻³
$b({adim}.)$	0.67 ± 0.02	0.64 ± 0.02	0.033 ± 0.005	5.1 ± 0.7	<10⁻³
μ_a−669 (cm⁻¹)	0.301 ± 0.008	0.323 ± 0.008	0.022 ± 0.003	7.0 ± 0.9	<10⁻³
μ_a−825 (cm⁻¹)	0.274 ± 0.007	0.295 ± 0.008	0.021 ± 0.003	7 ± 1	<10⁻³
THC (μM)	130 ± 3	140 ± 4	10 ± 1	7.5 ± 0.7	<10⁻³
StO₂ (%)	70.4 ± 0.5	70.8 ± 0.5	0.4 ± 0.2	0.6 ± 0.3	0.01
BFi (10⁻⁹ cm² s⁻¹)	4.4 ± 0.2	5.1 ± 0.3	0.63 ± 0.07	13 ± 1	<10⁻³
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.2 ± 0.1	2.5 ± 0.1	0.27 ± 0.05	12 ± 2	<10⁻³

Table B3. Table of LME estimates, standard errors and statistical tests. Sex differences.

	Female	Male	Absolute difference	Relative difference (%)	p − value
A (cm⁻¹)	8.3 ± 0.1	7.4 ± 0.3	0.9 ± 0.3	12 ± 3	<10⁻³
$b({adim}.)$	0.65 ± 0.02	0.67 ± 0.04	0.03 ± 0.04	4 ± 6	0.51
μ_a−669 (cm⁻¹)	0.319 ± 0.008	0.33 ± 0.02	0.01 ± 0.02	4 ± 6	0.40
μ_a−825 (cm⁻¹)	0.291 ± 0.008	0.31 ± 0.02	0.02 ± 0.02	6 ± 6	0.28
THC (μM)	140 ± 4	151 ± 8	11 ± 7	8 ± 5	0.13
StO₂(%)	70.4 ± 0.6	71 ± 1	0.8 ± 1	1 ± 1	0.48
BFi (10⁻⁹ cm² s⁻⁾	4.5 ± 0.3	5.2 ± 0.6	0.7 ± 0.6	20 ± 10	0.20
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.2 ± 0.1	2.9 ± 0.3	0.7 ± 0.3	30 ± 10	0.02

Table B4. Table of LME estimates, standard errors and statistical tests. Age dependence.

	Intercept	Slope (unit/year)	p−value
A (cm⁻¹)	8.2 ± 0.4	−0.003 ± 0.009	0.72
$b({adim}.)$	0.80 ± 0.06	−0.003 ± 0.001	0.01
μ_a−669 (cm⁻¹)	0.41 ± 0.02	−0.0019 ± 0.0005	<10⁻³
μ_a−825 (cm⁻¹)	0.41 ± 0.02	−0.0025 ± 0.0004	<10⁻³
THC (μM)	192 ± 9	−1.1 ± 0.2	<10⁻³
StO₂(%)	77 ± 2	−0.14 ± 0.03	<10⁻³
BFi (10⁻⁹ cm² s⁻¹)	6.1 ± 0.9	−0.03 ± 0.02	0.08
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.3 ± 0.5	−0.0004 ± 0.01	0.97

Table B5. Table of LME estimates, standard errors and statistical tests. BMI dependence. We also report the logarithm of μ_a−669, μ_a−825, BFi and γMRO₂ as independent variables, since we have found that an exponential model better describe the relation between these variables and BMI.

	Intercept	Slope (unit/(kg m⁻²))	p−value
A (cm⁻¹)	7.8 ± 0.7	0.01 ± 0.03	0.71
$b({adim}.)$	1.21 ± 0.08	−0.023 ± 0.003	<10⁻³
μ_a−669 (cm⁻¹)	0.52 ± 0.04	−0.008 ± 0.002	<10⁻³
μ_a−825 (cm⁻¹)	0.46 ± 0.04	−0.007 ± 0.001	<10⁻³
THC (μM)	220 ± 20	−3.3 ± 0.7	<10⁻³
StO₂ (%)	71 ± 3	−0.006 ± 0.1	0.96
BFi (10⁻⁹ cm² s⁻¹)	9 ± 1	−0.17 ± 0.06	0.004
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	3.8 ± 0.7	−0.06 ± 0.03	0.046
$\mathrm{log}({\mu }_{a-669}/({\mathrm{cm}}^{-1}))$	−0.6 ± 0.1	−0.023 ± 0.005	<10⁻³
$\mathrm{log}({\mu }_{a-825}/({\mathrm{cm}}^{-1}))$	−0.8 ± 0.1	−0.018 ± 0.006	0.004
$\mathrm{log}(\mathrm{BFi}/({10}^{-9}{\mathrm{cm}}^{2}{{\rm{s}}}^{-1}))$	2.4 ± 0.3	−0.04 ± 0.01	<10⁻³
$\mathrm{log}(\gamma {\mathrm{MRO}}_{2}/({10}^{-10}{\mathrm{cm}}^{2}{{\rm{s}}}^{-1}))$	1.6 ± 0.3	−0.03 ± 0.01	0.004

Table B6. Table of LME estimates, standard errors and statistical tests. Muscle depth dependence. We also report the logarithm of γMRO₂ as independent variable, since we have found that an exponential model better describe the relation between this variable and muscle depth.

	Intercept	Slope (unit/mm)	p−value
A(cm⁻¹)	7.1 ± 0.2	0.31 ± 0.04	<10⁻³
$b({adim}.)$	0.80 ± 0.02	−0.048 ± 0.006	<10⁻³
μ_a−669 (cm⁻¹)	0.36 ± 0.01	−0.014 ± 0.003	<10⁻³
μ_a−825 (cm⁻¹)	0.30 ± 0.01	−0.002 ± 0.003	0.48
THC (μM)	144 ± 5	−0.8 ± 1	0.52
StO₂ (%)	67.9 ± 0.8	0.9 ± 0.2	<10⁻³
BFi (10⁻⁹ cm² s⁻¹)	4.3 ± 0.4	0.08 ± 0.09	0.39
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.6 ± 0.2	−0.10 ± 0.06	0.09
$\mathrm{log}(\gamma {\mathrm{MRO}}_{2}/({10}^{-10}{\mathrm{cm}}^{2}{{\rm{s}}}^{-1}))$	0.97 ± 0.08	−0.07 ± 0.02	<10⁻³

Table B7. Table of LME estimates, standard errors and statistical tests. Muscle thickness dependence.

	Intercept	Slope (unit/mm)	p−value
A (cm⁻¹)	7.6 ± 0.2	0.08 ± 0.02	<10⁻³
$b({adim}.)$	0.74 ± 0.03	−0.012 ± 0.003	<10⁻³
μ_a−669 (cm⁻¹)	0.30 ± 0.01	0.004 ± 0.002	0.02
μ_a−825 (cm⁻¹)	0.25 ± 0.01	0.008 ± 0.001	<10⁻³
THC (μM)	121 ± 5	3.0 ± 0.6	<10⁻³
StO₂ (%)	67.0 ± 0.8	0.54 ± 0.09	<10⁻³
BFi (10⁻⁹ cm² s⁻¹)	4.7 ± 0.4	−0.02 ± 0.04	0.69
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.9 ± 0.2	−0.09 ± 0.03	0.001

Table B8. Table of LME estimates, standard errors and statistical tests. Patients Vs. healthy subjects.

	Control	Patient	Absolute difference	Relative difference (%)	p−value
A (cm⁻¹)	7.6 ± 0.2	8.2 ± 0.4	0.6 ± 0.3	7 ± 4	0.03
$b({adim}.)$	0.76 ± 0.03	0.61 ± 0.05	0.15 ± 0.03	22 ± 3	<10⁻³
μ_a−669 (cm⁻¹)	0.36 ± 0.01	0.31 ± 0.02	0.05 ± 0.02	16 ± 5	<10⁻³
μ_a−825 (cm⁻¹)	0.33 ± 0.01	0.28 ± 0.02	0.05 ± 0.01	15 ± 3	0.002
THC (μM)	159 ± 6	136 ± 8	23 ± 6	16 ± 3	<10⁻³
StO₂(%)	71 ± 1	70 ± 1	0.5 ± 1	0.8 ± 1	0.63
BFi (10⁻⁹ cm² s⁻¹)	5.0 ± 0.5	4.5 ± 0.7	0.5 ± 0.6	10 ± 10	0.36
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.4 ± 0.3	2.3 ± 0.4	0.06 ± 0.3	3 ± 10	0.85

Table B9. Table of LME estimates, standard errors and statistical tests. Nodule versus Nodule-free sides (only thyroid nodule patients).

	Nodule-free side	Nodule side	Absolute difference	Relative difference (%)	p−value
A (cm⁻¹)	8.2 ± 0.2	8.2 ± 0.2	0.02 ± 0.05	0.2 ± 0.6	0.76
$b({adim}.)$	0.62 ± 0.02	0.62 ± 0.02	0.003 ± 0.007	0.5 ± 1	0.67
μ_a−669 (cm⁻¹)	0.299 ± 0.009	0.30 ± 0.01	0.003 ± 0.004	0.9 ± 1	0.53
μ_a−825 (cm⁻¹)	0.274 ± 0.009	0.271 ± 0.009	0.003 ± 0.004	1 ± 1	0.48
THC (μM)	132 ± 4	128 ± 4	4 ± 2	3 ± 1	0.02
StO₂ (%)	70.5 ± 0.6	70.4 ± 0.6	0.2 ± 0.2	0.2 ± 0.3	0.45
BFi (10⁻⁹ cm² s⁻¹)	5.2 ± 0.3	4.4 ± 0.3	0.7 ± 0.1	16 ± 2	<10⁻³
γMRO₂ (10⁻¹⁰ cm² s⁻¹)	2.6 ± 0.2	2.3 ± 0.2	0.35 ± 0.08	14 ± 3	<10⁻³

Table B10. Table of the Pearson correlation coefficients for demographic and anatomical continuous variables. Statistically significant linear correlations are highlighted in bold.

	Age	BMI	Depth	Thickness
Age	−	0.32	0.38	−0.086
BMI	0.32	−	0.69	0.14
Depth	0.38	0.69	−	0.13
Thickness	−0.086	0.14	0.13	−

In vivo characterization of the optical and hemodynamic properties of the human sternocleidomastoid muscle through ultrasound-guided hybrid near-infrared spectroscopies

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Abstract

1. Introduction

2. Materials and methods

2.1. Experimental setup: multi-modal US-guided hemodynamic monitor