**3. Results**

#### *3.1. Descriptive Statistics, Symmetry and Jaccard Indices (SI and JI)*

The descriptive statistics and symmetry indices for the independent variables (skiing technique and ground reaction forces) and dependent variables (skiing performance) during skiing are presented in Tables 1 and 2, respectively. In most cases, the differences in the independent variables during left and right turns were statistically insignificant (Table 1), the exception being GRF on the entire inside foot (*p* < 0.05). The mean symmetry indices (SI) for the independent variables related to skiing technique ranged from approximately 92 to 98%, with associated Jaccard indices (JI) during the steering phase ranging from approximately 29 to 53%. The corresponding values for the independent variables related to GRF ranged from approximately 85 to 98% and approximately 42 to 71%, respectively.

**Table 1.** The inclination, flexion of the joints and ground reaction forces (GRF) acting on various parts of the legs during the steering phase of left and right turns by elite slalom skiers, together with the corresponding symmetry (SI) and Jaccard (JI) indices (independent variables). All values presented are means ± standard deviations.

BW—body weight; SI—symmetry index; JI—Jaccard index; \* approximated on the basis of the movement of the center of mass.

Moreover, none of the values for the dependent variables reflecting skiing performance differed significantly between the left and the right turns (Table 2). The mean SI for the dependent variables ranged from approximately 71% (in the case of instantaneous performance) to approximately 100% (average velocity). The nature of the parameters involved allowed the JI values to be calculated only for the turning radius and instantaneous performance during the steering phase as approximately 56% and 47%, respectively.

The patterns of the angle of the outside shank of all nine skiers during left and right turns, together with the corresponding JI during the steering phase (ranging from 14% for Skier I to 87% for Skier G), are shown in Figure 4. As depicted in the diagram, the mean angle of the outside shank during left and right turns differed during the entire steering phase for Skiers H and I, during the second half of the steering phase for Skiers B, D and E and during the first half of this phase in the case of Skier A. In contrast, the mean angle of the outside shank of Skier G was largely the same throughout the

entire steering phase. With respect to the mean turning radius of left and right turns, most of the skiers demonstrated visible differences during the second half of the steering phase, with Skier G again being the exception (Figure 5). Moreover, the JI of 81% for the turning radius of Skier G was the largest observed, while the smallest JI of 56% in this regard was demonstrated by Skier C. Visually larger differences were observed between left and right turn instantaneous performance (Figure 6) with the JI ranging from 31% (Skier I) to 78% (Skier G).

**Table 2.** The time, trajectory, velocity and energy dissipation during left and right turns by elite slalom skiers, together with the corresponding symmetry (SI) and Jaccard indices (JI) (dependent variables). All values presented are means ± standard deviations.

*n*/a—not applicable; SI—symmetry index; JI—Jaccard index.

#### *3.2. Multivariable Regression Models*

Altogether, our multivariable linear regression models, each involving no more than two predictor (independent) variables, included a total of 26 predictor and 8 predicted (dependent) variables. Models were discarded if the *p*-value was >0.05, R2 < 0.7 or when the model's predictor coefficients did not differ significantly from 0 (t-statistic, *p* < 0.05). In addition, to restrict our analysis to results that could be meaningful, only the 13 models for which at least one of the predictor coefficient values was >0.1 are shown in Table 3. Of these, all included two independent variables, with the exception of Model #10, which only included one.

The largest predictor coefficients were associated with the SI values for instantaneous (differential specific mechanical energy) and sectional performance (mechanical energy for each specific section/turn normalized to the entrance speed) (Models #10–13, Table 3). The independent variables in Models #10 and 12 were related only to skiing technique, while those in Models #11 and 13 were related to skiing technique in combination with GRF. The remainder of the models had smaller predictive coefficients of 0.46 (Model #5) or lower, among which the coefficients for SI and JI for turning radius were largest (Models #4 and 5). Interestingly, the largest predictive coefficients obtained with Models #6–9, designed to predict the SI for average velocity, all corresponded to the SI for overall GRF.

**Figure 6.** The instantaneous performance during the steering phase of left and right turns by 9 elite slalom skiers (**A**–**I**) and corresponding Jaccard indices (JI). The two vertical lines indicate the beginning and end of the steering phase. Instantaneous performance is defined as energy dissipation per change in altitude normalized relative to the mass of the skier and his equipment.

**Table 3.** Multivariable linear regression analysis of the relationships between the predicted (dependent, columns) and predictor (independent, rows) variables.

insoles; b approximated on the basis of the movements of the center of mass.


*4.2. The Trapped Core and Breaking Stage*

The trapped core is defined as the particle, which was trapped in the wave and carried along at constant propagating speed [29] and occurs when the water velocity exceeds the propagation speed of the wave [30]. It is formed when ISWs shoal from deep to shallow water. As the ISW reaches its breaking limit, it forms a subsurface trapped core [31]. A trapped core was identified in the measured ISW zonal velocity (inside the white line representing the ISW phase speed in Figure 3a). The upper portion of the trapped core was beyond the shipboard ADCP range.

The breaking stage can be defined according to [32] by comparing the peak current velocity *umax* and phase speed *c*. When *umax* > 0.8 *c* in a continuously stratified fluid, the ISW would break. The ISW presented in this paper had values of *umax* = 2.93 m/s and *c* = 1.76 m/s, with peak current velocity much larger. Obviously, the peak current velocity was much larger than the estimated phase speed. The ISW was close to or already in the process of breaking.

The above results are consistent with those in [5], which present 41 ISWs captured in April 1999 and 2000 on the continental slope of the northern South China Sea during the Asian Seas International Acoustics Experiment (ASIAEX) [5]. One ISW among them was similar to our observations, with the largest westward current exceeding 2.4 m/s right near our research area (details shown in Table 1). This suggests that when one ISW approaches the breaking stage, its velocity could be significantly larger than before.

**Table 1.** Observations in this study and in [5].


**Acknowledgement**

244 Apoptosis and Medicine

DR5 and/or DR4 death receptors, thus enhancing TRAIL-induced apoptosis (Haupt S., et al. 2003; Kelley R.F., et al. 2005). Our studies provide evidence for activation of TRAIL-induced apoptosis in pancreatic β-cells by administration of streptozotocin on models of

Mitochondrial-mediated apoptotic pathway plays an important role in the development of pancreatic islet damage in diabetes mellitus (Sakurai K., et al. 2001). In alloxan-induced diabetes intracellular calcium homeostasis is typically impaired. *In vitro* and *in vivo* experiments have shown that cytoplasmic calcium concentrations increase in the cells of pancreatic islets. This effect is due to depolarization of cell and mitochondrial membranes of βendocrine cells which is associated with excessive entry of calcium from the extracellular fluid and intracellular calcium mobilization (Crow M.T., et al. 2004; Jung J.Y., et al. 2004). Thus, considerable gross damage to the intracellular structures by free radicals, oxidation of SHproteins and impairment of intracellular calcium homeostasis typically result in necrosis and

apoptosis, with necrotic processes being more common in alloxan-induced diabetes.

Comparison of morphological data and the dynamics of impairment of β-cell functional activity in experimental models (alloxan-, streptozotocin-, nicotinamide-streptozotocininduced and immune-dependent diabetes) gives insight into the pathogenesis of experimental diabetes. A high apoptotic index and the prevalence of destructive processes, which enable us to assess not only the extent of pancreatic tissue damage but also to evaluate biochemical parameters, such as plasma glucose, insulin, C-peptide, etc., can be used as markers of severity of experimental diabetes (Snigur G.L., Smirnov A.V. 2010).

Thus, apoptosis is a complex, multi-step, poorly regulated process. Any regulatory impairment can lead to the development of pathological changes in the endocrine apparatus of pancreatic islets including the development of experimental diabetes (Reed J.C., Green D.R. 2011). Each level and element of this system is a potential drug target. The significance of apoptosis determines the need for the refocusing of biomedical research from theoretical biology to clinical medicine. Investigation of apoptotic mechanisms in various pathological conditions enable us to make more accurate diagnoses and prognoses as well as to adjust therapy. The possibility of deliberate control of apoptotic processes is considered to be the basis for developing new medications used to treat many socially important diseases,

Experimental diabetic rats exhibited significant pathohistological changes in the pancreatic islets caused by cytotoxine (streptozotocin+CFA) at all levels of tissue structure. The development of diabetes mellitus was associated with decreased volume fraction of pancreatic islets and β-cells due to inflammation (insulitis) and pronounced destructive

*Department of Pathologic Anatomy, Volgograd State Medical University, Russia*

streptozotocin-induced and immune-dependent diabetes.

including the development of anti-diabetic drugs.

changes (e.g. necrosis and apoptosis).

A.V. Smirnov and G.L. Snigur

**Author details**

We express our gratitude to the Head of pharmacology department of Volgograd State Medical University, Academician of Russian Academy for Medical Sciences, Honored Scientist of Russia, MD, full professor, Spasov Alexander A., assistant professor of pharmacology department of Volgograd State Medical University, PhD, Cheplyaeva Natalia I., assistant professor of pharmacology department of Volgograd State Medical University, PhD, Chepurnova Mariya V. for their assistance in conducting the present study.


**5. Clinical tables on G6PD deficiency**

Depending on G6PD enzyme deficiency are: Hemolytic Anemia (Drug-induced hemolysis), Diabetes mellitus-induced hemolysis and Infection-induced hemolysis; chronic nonspherocytic anemia, Favism and Neonatal jaundice.


*Article* **Complexity of Frontal Cortex fNIRS Can Support Alzheimer Disease Diagnosis in Memory and Visuo-Spatial Tests**

**David Perpetuini 1,\*, Antonio M. Chiarelli 1, Daniela Cardone 1, Chiara Filippini 1, Roberta Bucco 2, Michele Zito 2 and Arcangelo Merla 1**

Received: 6 December 2018; Accepted: 27 December 2018; Published: 1 January 2019

**Abstract:** Decline in visuo-spatial skills and memory failures are considered symptoms of Alzheimer's Disease (AD) and they can be assessed at early stages employing clinical tests. However, performance in a single test is generally not indicative of AD. Functional neuroimaging, such as functional Near Infrared Spectroscopy (fNIRS), may be employed during these tests in an ecological setting to support diagnosis. Indeed, neuroimaging should not alter clinical practice allowing free doctor-patient interaction. However, block-designed paradigms, necessary for standard functional neuroimaging analysis, require tests adaptation. Novel signal analysis procedures (e.g., signal complexity evaluation) may be useful to establish brain signals differences without altering experimental conditions. In this study, we estimated fNIRS complexity (through Sample Entropy metric) in frontal cortex of early AD and controls during three tests that assess visuo-spatial and short-term-memory abilities (Clock Drawing Test, Digit Span Test, Corsi Block Tapping Test). A channel-based analysis of fNIRS complexity during the tests revealed AD-induced changes. Importantly, a multivariate analysis of fNIRS complexity provided good specificity and sensitivity to AD. This outcome was compared to cognitive tests performances that were predictive of AD in only one test. Our results demonstrated the capabilities of fNIRS and complexity metric to support early AD diagnosis.

**Keywords:** Alzheimer disease; functional near infra-red spectroscopy; signal complexity; clock drawing test; digit span test; corsi block tapping test

#### **1. Introduction**

Early Alzheimer's disease (AD) is characterized by subtle impairments in executive abilities and memory [1,2]. Multiple cognitive test batteries were developed to assess these initial impairments and to allow differential diagnosis between idiopathic dementia and early AD [3,4]. The Clock Drawing Test (CDT) is a functional test that evaluates visuo-constructive and visuo-spatial abilities [5] and it is commonly employed in clinical practice for early dementia screening [6,7]. However, its sensitivity and specificity to early AD is still discussed [8,9]. In fact, novel scoring methods based on CDT outcome were proposed to improve its discrimination capabilities between Mild Cognitive Impairment (MCI) and early AD [5]. The Digit Span Test (DST) and the Corsi Block Tapping Test (CBTT) were developed to assess memory deficits. DST is widely employed in clinics to evaluate short-term memory and verbal working memory abilities [10], whereas the CBTT is employed to estimate visuo-spatial memory skills [11].

Although these tests and associated scorings were developed for sensitive and specific diagnosis of AD, performances in a single test are generally not sufficient for a definitive diagnosis of the disease, often requiring a large set of tests. Functional neuroimaging can be employed during these tests to support diagnosis [12,13]. The importance of using functional neuroimaging during the administration of these tests is widely agreed. In fact, adapted versions of CDT were administrated during a functional Magnetic Resonance Imaging (fMRI) acquisition directly in the MRI scanner [14–16]. DST and CBTT were also adapted for functional neuroimaging acquisition (either through fMRI or functional Near InfraRed Spectroscopy, fNIRS) [15–19]. Adaptation could be related to either environmental constraints (because of the fMRI acquisition) or temporal constraints (because of the need of paced tasks that allow standard functional neuroimaging signal analysis). In fact, when performed with concurrent functional brain imaging, these tests are modified from a non-paced administration of tasks and free doctor-patient interaction to a block or event related paradigm where doctor is replaced by an automated stimulation (e.g., through a screen monitor or a minidisk player) [16–19]. Although these modifications are useful from a neuroimaging standpoint, they indeed alter the ecology of the tests and the interaction between the doctor and the patient. However, these tests characteristics play a primary role in clinical practice and they should be preserved. In this perspective, one of the most suitable neuroimaging techniques is fNIRS that allows functional neuroimaging in outpatient environment.

fNIRS is a scalp-located non-invasive optical methodology able to record oscillation within the brain of oxygenated (O2Hb) and deoxygenated (HHb) hemoglobin related to neuronal activity through the Blood Oxygen Level Dependent (BOLD) effect [20]. This technique is portable, relatively cheap, lightweight and resilient to motion artifacts with a mechanical structure resembling Electroencephalography [EEG] [20] thus being suitable for ecological measurements during the administration of clinical tests. fNIRS was indeed utilized to investigate brain functional alteration in AD during different tasks [21–23]. Studies proved the capabilities of fNIRS to investigate functional alterations between AD patients and healthy controls, as well as between AD and MCI patients. fNIRS was also employed during the administration of CDT and DST, however, it was never performed on AD patients and always through a paradigm adaptation. Shoyama and colleagues [24] employed a 52 fNIRS channels system to investigate brain functional activity of healthy subjects during CDT. Statistically significant activations in the superior temporal cortex and in the frontal cortex were detected [24]. Hoshi et al. [25] compared brain functional activation between DST and a modified DST (backward version) and found significant differences in the dorsolateral prefrontal cortex (dorsolateral PFC) [25]. Tian and colleagues [19] employed fNIRS to investigate difference in the brain activation during the administration of DST between patients with post-traumatic stress disorder and healthy controls [19]. Although both groups showed functional activation in the medium PFC, interesting lateralized differences were found. CBTT was administrated together with fNIRS monitoring to 39 healthy participants to clarify the role of the PFC during the task execution [18].

Without ad-hoc modifications of the tests structures, the ecological characteristics of these tests definitely do not allow for a standard functional neuroimaging analysis, which requires task-related design matrix to provide statistical inference about brain activity generally based on block averaging or General Linear Model (GLM) [26]. We recently implemented a novel signal analysis approach for functional data acquired through fNIRS that can assess alterations of brain signals in AD overcoming the limitations of standard analysis approaches. In particular, we suggested to estimate the complexity of cortical functional oscillations measured through fNIRS during these tests employing the Sample Entropy (SampEn) metric [27]. SampEn is the negative natural logarithm of the conditional probability that signal subseries of length m (pattern length) that match pointwise within a tolerance r (similarity factor) also match at the m+1 point and it evaluates non-linear predictability of the signal [27]. Moreover, it can be assessed at different time scales using a Multi Scale approach (MSE) [28]. The rationale behind this idea is that AD patients may present a modified structure of functional oscillations during cognitive tests that may reflect in a modified SampEn of the recorded fNIRS signals. SampEn is currently employed for biomedical signal evaluation to assess physiology and pathology. For example,

it was used to investigate nonlinear properties of heart rate time series [29–31]. Moreover, it was applied to evaluate the complexity of fMRI signals in attention deficit hyperactivity disorder patients [32] and in patients affected by schizophrenia [33]. In AD, it was utilized to analyze resting-state brain activity deriving from Magnetoencephalographic [34] and EEG signals [35,36]. Concerning fNIRS, SampEn was used to investigate cortical activation in AD patients during the administration of Free and Cued Selective Reminding Test [37,38].

In the present study, we report evaluation of fNIRS SampEn in frontal cortex of early AD and healthy controls (HC) during CDT, DST and CBTT as they are performed in clinical practice. Statistical differences in signal complexities between AD and HC were assessed and the capability of fNIRS and SampEn to provide good sensitivity and specificity to the disease was investigated through a multivariate analysis.

#### **2. Materials and Methods**

#### *2.1. Participants*

Twenty-two participants were recruited in the study. The sample population was composed of eleven early AD patients (mean age ± SD: 72.2 ± 4.5 years; 7 males/4 females) and eleven HC (mean age ± SD: 67.5 ± 5.0 years; 8 males/3 females). The AD patients had a diagnosis of Mild probable Alzheimer's disease, as defined by the Diagnostic and Statistical Manual of Mental Disorders, 5th edition (DSM-5). Patients with moderate to severe cognitive impairment (Mini Mental State Examination, MMSE < 25/30) [39], vascular dementia, behavioral or psychiatric disorders, hydrocephalus, brain lesions or with a history of stroke or traumatic brain injury were excluded from the study. The study was approved by the Research Ethics Board of the local university, and it was conducted according to the principles described in the Declaration of Helsinki. Informed consent form was signed by all participants before the experiment and they were able to withdraw from it at any time.

#### *2.2. Experimental Design*

Experimental environment and layout are reported in Figure 1. Figure 1a shows the ecological settings of the experiment with the doctor sitting in front of the patient while freely interacting with him during the administration of the tests. Figure 1b shows the experimental paradigm. The different tasks, CDT, DST and CBTT were administered to the participants in a consecutively manner, spaced by 1-min rest periods, as they are usually performed in outpatient environment. Rest periods allowed for avoidance of overlapping effects among tasks. At the start of the experiment, the participants were instructed to relax for 1 min with their eyes closed. Afterward, CDT test started. CDT consisted in presenting to the patients a blank A4-sized paper and in asking to draw a circle with numbers representing a clock. Finally, patients were asked to draw the clock hands at a specific time. After another rest period DST was administered. The patients were asked to repeat a series of digits of increasing length (starting from two) verbally presented by the examiner at a pace of 1 s. If the participants were not able to repeat the sequence, another sequence of the same length was disclosed. The test stopped when the participants could not accurately repeat two series of the same length. After another minute of rest, CBTT was performed. In CBTT, the doctor consecutively tapped an increasing number (starting from two) of cubes located on a wooden tablet (Figure 1a) whose sequence had to be remembered by the patient. The cubes were touched with the index finger at a rate of 1 cube per second. The participants had to tap the cube sequence in the same order immediately after the doctor. The experiment temporal structure resembled that of DST. The overall experiment ended after the administration of CBTT.

**Figure 1.** (**a**) Experimental environment and layout. The doctor was sitting in front of the patient while freely interacting with him during the administration of the tests. (**b**) Experimental paradigm. The different tasks, CDT, DST and CBTT were administered to the participants in a consecutively manner, spaced by 1-min rest periods, as they are usually performed in outpatient environment.

#### *2.3. Functional Near-Infrared Spectroscopy Instrumentation and Measurement*

A frequency-domain near-infrared spectroscopy (NIRS) system (Imagent, ISS Inc., Champaign, IL, USA) was used in this study. The system consisted of 32 laser diodes sources, 16 at 690 nm and 16 at 830 nm of wavelength, and 4 photomultiplier-tube (PMT) detectors. The lasers were modulated at 110 MHz and the PMTs at 110.005 MHz for heterodyne detection of modulated light. A time multiplexing scheme was utilized on the sources to prevent cross-talk. The overall instrument sampling rate (accounting for source time-multiplexing) was set at 10 Hz. The light power was lower than 4 mW/cm2, in respect of the ANSI standard limits allowing safe measurements. NIR light was carried to the scalp using single optic fibers (0.4 mm core) and from the scalp back to the PMTs using fiber bundles (3 mm diameter). The fibers were located on the frontal and prefrontal areas and were held in place by means of an EEG helmet adapted for NIRS (Figure 1a). The fibers were placed according to the international 10–20 electrode placement system [40]. Source and detector locations were digitized with a Polhemus FastTrak 3D digitizer (Colchester, VT, USA; accuracy: 0.8 mm) using a recording stylus and three head-mounted receivers, which allowed for small movements of the head in between measurements. Optodes layout allowed to measure fNIRS signals from 21 channels (source-detector couple) with source-detector distances separation of either 3 cm or 4 cm. These distances inter-optodes bring to a depth of penetration that allow to measure cortical activity [41]. Figure 2a shows the among subjects' average channels locations after warping of the digitized sources and detectors into MNI space (Colin27) using AtlasViewerGUI of Homer2 NIRS analysis package [42]. The logarithmic channels' and subjects' average light sensitivity map (Jacobian), is displayed in Figure 2b, showing the frontal and prefrontal sensitivity of the optical probe. According to a sensitivity analysis performed in NIRS-SPM [43], the brain Brodmann Areas (BAs) investigated were numbers 8, 9, and 46. Notice that fNIRS is known to investigate regions up to ~3 cm from the scalp surface. Thus, it is indeed suited to investigate superficial cortical regions, as the BAs investigated, not being sensitive to deeper brain structures.

**Figure 2.** (**a**) Among subjects' average channels locations after warping of the digitized sources and detectors into MNI space (Colin27). (**b**) Logarithmic channels' and subjects' average light sensitivity map displayed up to an attenuation of 100 times (40 dB) showing the frontal and prefrontal sensitivity of the optical probe.

#### *2.4. Functional Near-Infrared Spectroscopy Signal Analysis*

fNIRS data were analyzed employing a standard continuous wave based fNIRS analysis by means of Homer2 NIRS Processing package [42]. Raw signal intensities were converted into optical densities (ODs). Motion artifacts were identified and removed relying on a wavelet-based algorithm [44]. Artifact free ODs were band-pass filtered using a 3rd order Butterworth filter (0.01–0.4 Hz) to remove slow drifts and physiological contaminations related to heart and breathing rates. ODs were converted into O2Hb and HHb oscillations employing the modified Beer-Lambert law (MBLL). In order to further increase the signal to noise ratio (SNR) of functional signals, we employed an algorithm that exploit the brain activity-induced anticorrelation between the two hemoglobin forms (correlation-based signal improvement, CBSI) [45]. CBSI allows to obtain an O2Hb signal corrected through HHb. Although this procedure increases O2Hb SNR, it creates statistical dependencies among O2Hb and HHb, allowing to further analyze only O2Hb. Thus, subsequent analysis was performed on O2Hb only.

In order to estimate O2Hb signal complexity, the SampEn metric was evaluated for each fNIRS channel integrated over the different experimental phases.

The SampEn of a time series {x1, ... ,xN} of length N is calculated based on following set of equations [32]:

$$\text{SampleEn}(\mathbf{m}, \mathbf{r}, \mathbf{N}) = \ -\ln\left[\frac{\mathbf{U}^{m+1}(\mathbf{r})}{\mathbf{U}^{m}(\mathbf{r})}\right] \tag{1}$$

$$\mathbf{U}^{\text{m}}(\mathbf{r}) = \ [\mathbf{N} - \mathbf{m}\mathbf{T}]^{-1}\sum\_{i=1}^{\mathbf{N}-\mathbf{m}\mathbf{T}}\mathbf{C}\_{i}^{\text{m}}(\mathbf{r})$$

$$\mathbf{C}\_{i}^{\text{m}}(\mathbf{r}) = \frac{\text{B}\_{i}}{\text{N} - (\mathbf{m} + 1)\mathbf{T}}$$

$$\text{B}\_{i} = \text{number of j where d } |\mathbf{X}\_{i}, \mathbf{X}\_{j}| \le \mathbf{r}$$

$$\text{X}\_{i} = \left(\text{x}\_{i}, \text{x}\_{i+\Gamma}, \dots, \text{x}\_{i+(m-1)\Gamma}\right)$$

$$\text{X}\_{j} = \left(\text{x}\_{j}, \text{x}\_{j+\Gamma}, \dots, \text{x}\_{j+(m-1)\Gamma}\right)$$

$$\text{i } \le j \le \text{N} - \text{m}\mathbf{T}, \text{ j } \ne \text{i}$$

where N is total length of the time-series examined, m is the embedded dimension, r is the tolerance factor (scalar for which two subseries with distance below its value are considered identical) and T is the time delay expressed in samples. In this work, the computation of the SampEn was performed choosing a time delay T = 1, an embedded dimension of m = 2 and a similarity factor of r = 0.2·SD, where SD is the Standard Deviation of the signal evaluated. These parameters are commonly employed for complexity analysis of biological signals and they were chosen in accordance with [27].

In order to investigate signal complexity at multiple time scales we further employed the Multiscale Entropy (MSE) method [28]. MSE relies on computing coarse-grained time-series. The course-graining procedure is described by the following equation [32]:

$$\mathbf{y}\_{\mathbf{j}}^{(\pi)} = \frac{1}{\pi} \sum\_{\mathbf{i} = (\mathbf{j} - 1)\pi + 1}^{\mathbf{j}\pi} \mathbf{x}\_{\mathbf{i}} \mathbf{1} \le \mathbf{j} \le \frac{\mathbf{N}}{\pi} \tag{2}$$

where y(τ) j is the coarse-grained signal for a given sample j and a scaling factor τ which is generated from an average of samples of original signal x. Afterwards, SampEn of each coarse-grained time series is estimated. In the current study only two scale factors of τ = 2, τ = 3 were considered, because of the limited total time of each experimental phase. Moreover, in order to eliminate a possible effect on the SampEn and MSE metric of the time series length, for each experimental phase we cut the last period of each phase for each subject to the shortest one. We obtained homogenized experimental phases lengths for CDT (370 samples), for DST (380 samples) and for CBTT (530 samples).

#### *2.5. Statistical Inference and Multivariate Classification*

Behavioral results were estimated through unpaired t-tests comparing AD with HC with a NULL hypothesis rejection set at *p* < 0.05. Receiver operating characteristics (ROC) [46] curve was evaluated to provide an estimate of the behavioral tests' sensitivity and specificity to the disease.

SampEn and MSE for O2Hb in each channel, for each experimental phase and each subject were estimated. Average significant differences between AD and HC were tested by means of unpaired t-tests (*p* < 0.05). In order to avoid increased chance of false positive for fNIRS, multiple comparison correction, accounting for channels numerosity, was performed through the False Discovery Rate (FDR) algorithm [47]. Estimation of the BA investigated by the statistically activated channels was performed in NIRS-SPM [43].

A multivariate analysis was implemented to provide a classification of disease (AD or HC), starting from the SampEn and MSE of all the 21 channels in each experimental phase. A linear multiple regression [48] was performed on a dependent variable that labelled the presence of the disease (AD = 1, HC = 0). In order to provide an unbiased estimate of the out-of-sample performance of the classifier a leave one out cross-validation procedure was implemented. This cross-validation procedure consisted in leaving one subject out of the regression and estimating the predicted output value (between 0 and 1) on the given subject. The same procedure was iterated for all the subjects. A ROC curve analysis on the 22 out-of-sample predicted outputs provided estimates of fNIRS signal complexity sensitivity and specificity to the disease in each experimental phase.

#### **3. Results**

CDT [48] presented significant differences between AD and HC (t = −4.20, df = 20, *p* = 4.4 × 10−4). However, DST [49] and CBTT [50] could not discriminate between the two groups (t = −0.31, df = 20, p = N.S., t = −1.45, df = 20, p = N.S.).

Figure 3 reports statistical maps (t-scores) of AD vs. HC for signal complexity of fNIRS for the three experimental phases. Figure 3a,b reports results employing the SampEn metric, whereas Figure 3c reports results employing the MSE (τ = 3).

**Figure 3.** Statistical maps (t-scores) of AD vs. HC for signal complexity of fNIRS for the three experimental phases. Dashed black circles shows significant channels (*p* < 0.05), that did not survive FDR correction, whereas continuous black circles show channels that were still significant (*p* < 0.05) after multiple comparison correction. (**a**) t-score maps (AD vs. HC) based on the SampEn metric during CDT. (**b**) t-score maps (AD vs. HC) based on the SampEn metric during DST. (**c**) t-score maps (AD vs. HC) based on the MSE (τ = 3) metric during CBTT.

In the figure we report results where we obtained statistical significance after FDR algorithm. Dashed black circles shows significant channels (*p* < 0.05), that did not survive FDR correction, whereas continuous black circles show channels that were still significant (*p* < 0.05) after multiple comparison correction. A NIRS-SPM-based evaluation of the BA investigated by the significantly activated channels (surviving multiple comparison correction) reported in Figure 3, highlighted higher SampEn for AD in BA 10 for the CDT (Channel 10, t = 3.44, df = 20, *p* = 2.6 × 10−3). Significant lower SampEn during the DST was found instead in a channel investigating BA 9 (Channel 20, t = −3.48, df = 20, *p* = 2.4 × 10−3). Higher MSE (τ = 3) was finally found in two channels encompassing BA 10 and 46 during CBTT (Channel 4, t = 3.12, df = 20, *p* = 5.4 × 10−3, Channel 6, t = 2.63, df = 20, *p* = 0.01). Notice that MSE was estimated for all the different tests. However, CBTT was the only one providing statistically significant results.

ROC analysis performed on the behavioral results and the fNIRS complexity-based multiple regression analysis, described in the method section, are reported in Figure 4. We obtained significant classification outcome when behavioral tests were analyzed only for the CDT (AUC = 0.90) with a best performance sensitivity of 0.82 and specificity of 0.72. DST and CBTT were not able to provide a significant classification (AUC = 0.54 and AUC = 0.60). On the contrary, although less sensitive than CDT test, we obtained above chance classification when relying on fNIRS complexity metric for all the three tests performed with an AUC = 0.75 for CDT, AUC = 0.65 for DST and AUC = 0.71 for CBTT with a best performance sensitivity of 0.73 for all three tests and specificity of 0.82 for CDT and 0.73 for DST and CBTT. Whereas CDT and DST were evaluated on the SampEn metric, CBTT was evaluated on the MSE, which provided channels based significant average differences between AD and HC.

**Figure 4.** ROC analysis performed on the tests outcome (**a**) and on the fNIRS complexity-based multiple regression analysis (**b**).

#### **4. Discussion**

The aim of this study was to assess the capabilities of employing fNIRS during clinical tests that are commonly utilized for AD diagnosis. fNIRS could in fact support these tests by improving sensitivity and specificity to the disease.

Based on our sample population, we found that CDT scores were on average significantly different between AD and HC however DST and CBT were not, further justifying the need of a neuroimaging supporting tool.

In order to preserve the ecological conditions of the tests without altering the standard clinical protocol, we investigated whether a phase-integrated metric of complexity of hemoglobin oscillations could highlight differences between AD and HC. The complexity of the signals was evaluated by means of the SampEn and MSE algorithms.

We found fNIRS channels-based significant AD vs HC differences in SampEn and MSE of O2Hb oscillations during CDT, DST and CBTT in brain regions (BAs) involved in visuo-spatial and mnemonic tasks [49]. As demonstrated by Vaillancourt and Newell, these results seem to support the hypothesis that disease can cause a dysregulation of brain physiology that can result in altered functional patterns identifiable through a complexity analysis of time-dependent physiological signals [50]. However, our results do not provide a definitive answer on the direction of the complexity variations due to the disease. Although an increase complexity in some channels was the dominant effect among the different tasks, we indeed had a significant complexity decrease during DST in one fNIRS channel. Previous studies evaluating complexity on electrophysiological brain recordings (EEG [51] and Magnetoencephalography, MEG [34]) showed a decrease in signal complexity with AD, however these studies were performed at rest. On the contrary, signal complexity of fNIRS was here evaluated during the execution of a visuo-spatial and working-memory tests hence strictly evaluating task-related changes induced by AD. Vaillancourt and Newell [50] showed that a pathological state can alter the complexity of an output of a biological system as a function of the input. This input dependent

modulation of the alteration makes particularly unpredictable the direction of changes in fNIRS complexity as a function of channel location. In fact, the direction of change might intrinsically depend on the original task-induced activation pattern. This originally unknown activation pattern may indeed justify the variable direction of the complexity changes induced by AD during these clinical tests. In fact, because of the heterogeneous response of different brain region to a given stimulus, fNIRS signals may vary both in space and time. Due to the spatial distribution of fNIRS optodes on the frontal cortex, it is indeed plausible that different channels show a different statistic, generating a peculiar statistical map.

Inferring about the underlying causes of the found fNIRS signal complexity variations induced by AD, early findings by Hock et al. [52] identified reduced oxygenation and cerebral blood flow in AD during the execution of verbal fluency tasks. The authors justified the found alterations in oxygenation and CBF based on an impaired neurovascular coupling. In fact, neurovascular coupling is regulated by means of neurons, glia and vascular cells [51,53,54]. AD patients exhibit a deposition of amyloid β-peptide in neuropil and vessels that could impair such mechanism [55]. Moreover, an altered brain electrical activity and a loss of functional neural connectivity is observed in AD patients [55–57], that could further impact a complexity analysis of functional brain modulations.

A ROC curve analysis of clinical tests scores showed above chance classification capabilities only for CDT (AUC = 0.90) which evaluates visuo-spatial skills and apraxia [58]. On the contrary, fNIRS complexity-based multiple regression analysis showed good classification capabilities for all the three tests performed (AUC = 0.75. for CDT, AUC = 0.65 for DST and AUC = 0.71 for CBTT). These results clearly suggest that the use of fNIRS during the administration of cognitive tests may help AD diagnosis.

In fact, in clinical practice it is a common procedure to diagnose AD after long battery of tests, thus intrinsically assuming a high variability in a single test performance and across tests. The group of patients analyzed in this study had in fact a determined diagnosis based on this long battery. Although in our sample CDT seemed particularly suited for a single-test diagnosis, fNIRS entropy-based outcome seemed to provide more stable results among tests compared to cognitive performances. This means that fNIRS seems to be a good supporting tool for a standard multi-test diagnosis.

However, further studies should be performed increasing population sample size. In fact, our study was constituted by a limited number of participants and the fNIRS-based classification outcome, since it relies on a multivariate analysis of all the channels employed, might dramatically increase its performance with a large sample numerosity. In fact, although the study can be considered rather small in sample size, the investigation was conducted employing a leave-one-out cross-validation procedure (eliminating one subject at a time and testing the classifier outcome on that subject), thus intrinsically evaluating the out-of-sample performance. Thus, the results obtained are indeed generalizable. Increasing the sample size may allow further increase of the performance by decreasing a possible in-sample overfitting effect of the classifier.

Further advancement in classification procedure should employ non-linear classifiers, that were not utilizable in this work because of the small sample size and a possible over-fitting effect. Furthermore, it could be of great interest to decouple the contributions of altered brain electrical activity and impaired neurovascular coupling by combining the hemodynamic information provided by fNIRS with electrophysiological signals acquired, for example, by means of synchronous EEG measurements [59] through wearable technology [60]. These brain activity measurements could be further compared with recordings of peripheral autonomic activity (e.g., heart-rate and galvanic skin response monitoring systems) that can be themselves altered by the presence of the disease. Indeed, this study cannot provide an alternative diagnostic tool for early AD, but at least it opens the possibility of utilizing fNIRS as a supporting clinical procedure and it suggests to further explore its diagnostic potentialities.

#### **5. Conclusions**

In this study, we estimated fNIRS complexity (through SampEn and MSE) in the frontal cortex of early AD and controls during three tests that assess visuo-spatial and short-term-memory abilities (CDT, DST, CBTT). A channel-based analysis of fNIRS complexity revealed AD-induced changes in BAs 9,10 and 46 that where inhomogeneous in direction. A multivariate analysis of fNIRS task-related complexities based on multiple linear regression provided decent specificity and sensitivity to AD. This outcome was compared to test performances that were predictive of AD in one of the three tests (CDT). These findings, although preliminary, seem to confirm the hypothesis that AD may produce a dysregulation of brain electrical activity and neurovascular coupling that may present earlier than clear behavioral impairment. Our results demonstrated the capabilities of fNIRS and complexity metric to support early AD diagnosis.

**Author Contributions:** Conceptualization, D.P., R.B., M.Z. and A.M.; methodology, D.P.; software, D.P. and A.M.C.; validation, D.P., D.C. and C.F.; formal analysis, D.P. and A.M.C.; investigation, D.P. and R.B.; resources, M.Z. and A.M.; data curation, D.P., D.C. and C.F.; writing—original draft preparation, D.P. and A.M.C.; writing—review and editing, D.P.; visualization, D.P.; supervision, A.M.; project administration, A.M.; funding acquisition, A.M.

**Funding:** This research was partially funded by grant H2020, ECSEL-04-2015-Smart Health, grant n. 692470, Advancing Smart Optical Imaging and Sensing for Health (ASTONISH).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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*3.4. Increased Phosphorylation of Hippocampal IRS1 at Ser Residues in Young Amyloid Precursor Protein (APP) Knock-In (APP KINL-G-F) Mice Occurs Prior to the Onset of Memory Decline*

To investigate whether AD-related activation of Ser residues on neural IRS1 emerges before or after the onset of memory decline, we employed a novel AD mouse model, APPKINL-G-F mice carrying a humanized Aβ sequence and three AD mutations, i.e., Swedish, Beyreuther/Iberian, and Arctic mutations, in the endogenous *App* gene [19]. First, we measured body weight and glucose metabolism in 12-week-old (young) APPKINL-G-F mice. There were no differences in terms of body weight, blood glucose level, and plasma insulin concentration between WT and APPKINL-G-F mice at 12 weeks of age (Figure 4A, Figure S2B). Next, we confirmed memory function as well as Aβ40 and Aβ42 levels in the hippocampi of young APPKINL-G-F mice. At 12 weeks of age, APPKINL-G-F mice exhibited normal memory function (Figure 4B).

Using monoclonal antibody (BNT77/BC05)-based sandwich ELISA for human/rat/mouse Aβ42, we successfully confirmed that T-PER-extractable Aβ42 level had already increased in young APP KINL-G-F mice (Figure 4C, right). A conspicuous increase in T-PER-extractable Aβ42 level in these mice was detected by human Aβ42 sandwich ELISA using monoclonal antibodies (BAN50/BC05) (Figure 4D, right). However, T-PER-extractable Aβ42 levels in both ELISA were comparable to the range of Tris-buffered saline (TBS)-extractable Aβ42 level in the brain and cortex of APPKINL-G-F mice reported by Saito et al. (2019) and Saito et al. (2014). Similarly, human/rat/mouse Aβ40 and human Aβ40 sandwich ELISA revealed the same range for Aβ40 level in the T-PER fractions of the hippocampi of young APPKINL-G-F mice (black bar on the left in Figure 4C,D and Figure 5C,D). Meanwhile, regardless of age, human/rat/mouse Aβ40 or human Aβ40 sandwich ELISA showed almost the same levels (white bar on the left in Figures 1D, 2C, 3C, 4C and 5C) or range (white bar on the left in Figures 4D and 5D) of T-PER-extractable Aβ40 in WT mice, respectively.

**Figure 4.** Activation of multiple Ser residues on hippocampal IRS1 unrelated to memory decline in young amyloid precursor protein (APP) knock-in (APPKINL-G-F) mice. (**A**) The graphs of body weight and blood glucose levels in young wild-type (WT) and APPKINL-G-F mice (12 weeks of age, n = 6 mice per group). (**B**) Evaluation of learning memory function in young WT (n = 5 mice per group) and APP KINL-G-F mice (n = 5 mice per group) using the water T-maze test. (**C**) Quantitative analysis of T-PER-extractable Aβ40 and Aβ42 levels in the hippocampi of young WT and APPKINL-G-F mice using the human/rat/mouse β amyloid (1–40 and 1–42) ELISA (12 weeks of age, n = 5 biologically independent samples per group). (**D**) Quantitative analysis of T-PER-extractable Aβ40 and Aβ42 levels in the hippocampi of young WT and APPKINL-G-F mice using the human β amyloid (1–40 and 1–42) ELISA (12 weeks of age, n = 5 biologically independent samples per group). (**E**) Western blot analysis of phosphorylated insulin receptor substrates 1 mouse Ser307 [p-IRS1 (mSer307)], p-IRS1 (mSer612), p-IRS1 (mSer632/635), p-IRS1 (mSer1097), IRS1, and ß-tubulin in the hippocampi of young WT and APP KINL-G-F mice (12 weeks of age, n = 6 biologically independent samples per group). Arrows indicate the p-IRS1 mSer612-corresponding band (lower band) and p-IRS1 mSer632/635-corresponding band (lower band) in (**E**). Quantitative analysis of the phosphorylation of IRS1 at mSer307, mSer612, mSer632/635, and mSer1097 normalized to the respective total protein contents. (**F**)Western blot analysis of phosphorylation levels of Akt Ser473, p70S6K Thr389, AMPK Thr172, and GSK3β Ser9 as well as total protein levels of Akt, p70S6K, AMPK, GSK3β, and ß-tubulin in the hippocampi of young WT and APPKINL-G-F mice (12 weeks of age, n = 6 biologically independent samples per group). Quantitative analysis of phosphorylation of Akt Ser473, p70S6K Thr389, AMPK Thr172, and GSK3β Ser9 normalized to the respective total protein contents. Results are presented as mean ± SEM, \* *p* < 0.05; \*\* *p* < 0.01.

**Figure 5.** Memory decline accompanied by sustained phosphorylation of IRS1 Ser residues in the hippocampus of middle-aged APPKINL-G-F mice. (**A**) The graphs of body weight and blood glucose levels in middle-aged wild-type (WT) and APPKINL-G-F mice (34–36 weeks of age, n = 5 mice per group). (**B**) Evaluation of learning memory function in middle-aged WT (n = 14) and APPKINL-G-F mice (n = 15 mice per group) using the water T-maze test. (**C**) Quantitative analysis of T-PER-extractable Aβ40 and Aβ42 levels in the hippocampi of middle-aged WT and APPKINL-G-F mice using the human/rat/mouse β amyloid (1–40 and 1–42) ELISA (34–36 weeks of age, n = 4 biologically independent samples per group). (**D**) Quantitative analysis of T-PER-extractable Aβ40 and Aβ42 levels in the hippocampi of middle-aged WT and APPKINL-G-F mice using the human β amyloid (1–40 and 1–42) ELISA (34–36 weeks of age, n = 4 biologically independent samples per group). (**E**) Western blot analysis of phosphorylated insulin receptor substrates 1 mouse Ser307 [p-IRS1 (mSer307)], p-IRS1 (mSer612), p-IRS1 (mSer632/635), p-IRS1 (mSer1097), IRS1, and ß-tubulin in the hippocampi of middle-aged WT and APPKINL-G-F mice (34–36 weeks of age, n = 6 biologically independent samples per group). Arrow indicates the p-IRS1 mSer612 -corresponding band (lower band) in (**E**). Quantitative analysis of the phosphorylation of IRS1 at mSer307, mSer612, mSer632/635, and mSer1097 normalized to total protein. (**F**) Western blot analysis of phosphorylation levels of Akt Ser473, p70S6K Thr389, AMPK Thr172, and GSK3β Ser9 as well as total protein levels of Akt, p70S6K, AMPK, GSK3β, and ß-tubulin in the hippocampi of middle-aged WT and APPKINL-G-F mice (34–36 weeks of age, n = 6 biologically independent samples per group). Quantitative analysis of the phosphorylation of Akt Ser473, p70S6K Thr389, AMPK Thr172, and GSK3β Ser9 normalized to the respective total protein contents. Results are presented as mean ± SEM, \* *p* < 0.05; \*\* *p* < 0.01.

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Subsequently, we investigated the phosphorylation levels of hippocampal IRS1 at Ser residues in young APPKINL-G-F mice. Importantly, the phosphorylation of hippocampal IRS1 at mSer307, mSer612, and mSer1097, but not at mSer632/635, significantly increased in 12-week-old APPKINL-G-F mice (Figure 4E, Figure S4G) displaying normal memory function (Figure 4B). In parallel to these increases, a concomitant elevation in the basal phosphorylation of AMPK, a metabolic energy sensor, with p70S6K activation and a slight decrease in basal JNK phosphorylation were observed in these mice, along with monotonous Akt, GSK3β, and aPKC ζ/λ activity (Figure 4F, Figure S3D, S4H and S5D). Thus, in young APPKINL-G-F mice exhibiting normal memory function, the increased phosphorylation of hippocampal IRS1 at multiple Ser sites accompanied by AMPK-related low energy conditions had already occurred in the presence of increased Aβ42 level, suggesting that the elevation of Aβ42 level and/or AMPK activation provokes the activation of Ser sites on IRS1 in brains of patients with AD prior to the onset of memory decline.


5. Remarks

Thus, we were able to obtain three sets of nonlinear functions which are solutions to the Gross-Pitaevskii equation. With these functions, we have the nonlinear versions of the trigonometric, real, and complex exponential functions and their linear combinations, and a complete set of functions as in the linear counterpart.

Due to the method of solution, which makes use of elliptic functions, these functions will expand the set of solutions that can be given to polynomial nonlinear equations, in general [8, 12–25].

For instance, a well-known optical phenomenon is the nonlinear dispersion in parabolic law medium with Kerr law nonlinearity [24]. This system is described by a nonlinear Schrödinger equation:

$$a\Psi\_t + a\Psi\_{\text{xx}} + b\left|\Psi\right|^2\Psi + c\left|\Psi\right|^4\Psi + d\left(\left|\Psi\right|^2\right)\_{\text{xx}}\Psi = \mathbf{0},\tag{142}$$

where a subindex indicates a derivative with respect to that index. The second term of the above equation represents the group velocity dispersion, the third and fourth terms are the parabolic law nonlinearity, and the last term is the nonlinear dispersion. Some solutions of Eq. (142) were found in Ref. [24]. A solution is the traveling wave, with Jacobi's sn function profile, given by

$$\Psi(\varkappa, t) = A \operatorname{sn} [B(\varkappa - \nu t), m] e^{i\phi},\tag{143}$$

$$B = \left(\frac{-bA^2}{am(1+m) - 2d(m^2+m+2)A^2}\right)^{1/2},\tag{144}$$

$$
\omega = B^2 \left( 2dA^2 - a(1+m) \right). \tag{145}
$$

Three Solutions to the Nonlinear Schrödinger Equation for a Constant Potential DOI: http://dx.doi.org/10.5772/intechopen.80938

where v ¼ �2ak is the velocity, k is the soliton frequency, ω is the soliton wave number, θ is the phase constant, and 0 < m < 1 is the modulus of Jacobi's elliptic function.

A second solution was given as

u ¼ ffiffiffiffiffiffiffi 2ab p ðx

> ¼ 1 ffiffiffiffiffiffiffi 2ab p ab

> > � e

�

with complex argument:

functions.

5. Remarks

counterpart.

48

equations, in general [8, 12–25].

a nonlinear Schrödinger equation:

iΨt þ aΨxx þ bj j Ψ 2

traveling wave, with Jacobi's sn function profile, given by

B ¼ �bA2

0

p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 þ b2 p

p

dt ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2e2t þ b2

Nonlinear Optics ‐ Novel Results in Theory and Applications

�2x ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2

where 2F1 is the hypergeometric function.

where F is elliptic integral of the first kind.

u ¼ ðx 0

e�2x þ a2e2x

b2 � a2 þ b2 � �

e�2t

b2 � e

2F1 3 4 ; 1; 1 4 ; � a2 b2

1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4m sin h2

� � ���

When a ¼ b ¼ 1, the nonlinear functions reduce to Jacobi's elliptic functions

ð Þt

This is the minimum set of properties of the exponential-type nonlinear

Thus, we were able to obtain three sets of nonlinear functions which are solutions to the Gross-Pitaevskii equation. With these functions, we have the nonlinear versions of the trigonometric, real, and complex exponential functions and their linear combinations, and a complete set of functions as in the linear

Due to the method of solution, which makes use of elliptic functions, these functions will expand the set of solutions that can be given to polynomial nonlinear

For instance, a well-known optical phenomenon is the nonlinear dispersion in parabolic law medium with Kerr law nonlinearity [24]. This system is described by

Ψ þ cj j Ψ 4

Ψð Þ¼ x; t A sn½ � B xð Þ � vt ; m e

amð Þ� 1 þ m 2d mð Þ 2 þ m þ 2 A2

!1=2

where a subindex indicates a derivative with respect to that index. The second term of the above equation represents the group velocity dispersion, the third and fourth terms are the parabolic law nonlinearity, and the last term is the nonlinear dispersion. Some solutions of Eq. (142) were found in Ref. [24]. A solution is the

Ψ þ d j j Ψ 2 � �

ω ¼ B2 2dA2 � að Þ 1 þ m � �: (145)

q dt ¼ �iF ix ð Þ j4m , (141)

2x b2 e �2x þ a2 e 2x � �

� � � � �

2F1 3 4 ; 1; 1 4 ; � a2e4x b2

, (140)

xxΨ ¼ 0, (142)

iϕ, (143)

, (144)

$$\Psi(\varkappa, t) = A \operatorname{cn} [B(\varkappa - \nu t), l] e^{i\phi}, \tag{146}$$

$$B = \left(\frac{b}{4d}\right)^{1/2},\tag{147}$$

$$
\rho = B^2 \left( 2dA^2 - a \right) - ak^2. \tag{148}
$$

Since the functions that we have introduced in these chapters comply with differential and algebraic equations similar to the ones for Jacobi's elliptic functions, we can give additional solutions in terms of these new functions, giving rise to new sets of soliton waves.


*3.3. Online Detection*

Once the DTDA is trained, the common temporal feature representation can be obtained. The source domain label classifier *Gy*(·) can then be used well to recognize the fault in the data of the target domain. Therefore, in the online stage, the sequentially collected data batch is directly fed into *Gy*(·) to determine if a fault has occurred. This process does no need to re-train the DTDA, while the main computational cost is the linear calculation in *Gy*(·). As a result, the detection speed is very fast.


2.2.4. Growth Dynamics

Growth of the individual organs was fitted to the beta-function and parameters for the third phytomer showed significant differences for internode and petiole, but not for the leaf lamina. The absolute differences of the parameters for all three organs were relatively small and did not show any tendency to change with decreased BPFD (Table 4).

**Table 4.** Least square means of estimated parameters of the beta-function. Time of elongation (te) and time of maximum elongation (tm) for internode, petiole and leaf at the third phytomer under different blue photosynthetic flux densities (BPFD). Letters indicate significant differences between treatments (*p* < 0.05).


**Simultaneous LC**/**MS Analysis of Carotenoids and Fat-Soluble Vitamins in Costa Rican Avocados (***Persea americana* **Mill.)**

#### **Carolina Cortés-Herrera 1,\*, Andrea Chacón 1 , Graciela Artavia 1 and Fabio Granados-Chinchilla 2**

#### Academic Editor: Severina Pacifico

Received: 26 August 2019; Accepted: 5 October 2019; Published: 10 December 2019

**Abstract:** Avocado (a fruit that represents a billion-dollar industry) has become a relevant crop in global trade. The benefits of eating avocados have also been thoroughly described as they contain important nutrients needed to ensure biological functions. For example, avocados contain considerable amounts of vitamins and other phytonutrients, such as carotenoids (e.g., β-carotene), which are fat-soluble. Hence, there is a need to assess accurately these types of compounds. Herein we describe a method that chromatographically separates commercial standard solutions containing both fat-soluble vitamins (vitamin A acetate and palmitate, Vitamin D2 and D3, vitamin K1, α-, δ-, and γ-vitamin E isomers) and carotenoids (β-cryptoxanthin, zeaxanthin, lutein, β-carotene, and lycopene) effectively (i.e., analytical recoveries ranging from 80.43% to 117.02%, for vitamins, and from 43.80% to 108.63%). We optimized saponification conditions and settled at 80 ◦C using 1 mmol KOH L−1 ethanol during 1 h. We used a non-aqueous gradient that included methanol and methyl *tert*-butyl ether (starting at an 80:20 ratio) and a C30 chromatographic column to achieve analyte separation (in less than 40 min) and applied this method to avocado, a fruit that characteristically contains both types of compounds. We obtained a method with good linearity at the mid to low range of the mg L−1 (determination coefficients 0.9006–0.9964). To determine both types of compounds in avocado, we developed and validated for the simultaneous analysis of carotenoids and fat-soluble vitamins based on liquid chromatography and single quadrupole mass detection (LC/MS). From actual avocado samples, we found relevant concentrations for cholecalciferol (ranging from 103.5 to 119.5), δ-tocopherol (ranging from 6.16 to 42.48), and lutein (ranging from 6.41 to 15.13 mg/100 g dry weight basis). Simmonds cultivar demonstrated the higher values for all analytes (ranging from 0.03 (zeaxanthin) to 119.5 (cholecalciferol) mg/100 g dry weight basis).

**Keywords:** avocado; LC/MS; fat-soluble vitamins; carotenoids

### **1. Introduction**

Avocado represents a billion-dollar industry, the projection of the apparent *per capita* consumption of avocado sets the top six world importers of avocado to be US, Netherlands, France, United Kingdom, Spain, and Canada with 3.64, 1.62, 2.10, 2.21, 2.30, and 2.55 kg in a given year, respectively [1]. Avocado exports have made some countries like Mexico, Dominican Republic, Peru, Chile, Colombia, and Costa Rica increase their cultivated area [1].

The topmost exporter countries have directed their offer to destinations such as the US, Europe, and Asia, especially China [2], where import growth is in the order of 250%, from 154 tons in 2012, to 25,000 tons in 2016 [3,4]. For example, Costa Rican avocado harvested area was estimated at 1 888 ha in 2014 and increased to 3092 ha in 2017, which represents 845 tons of Costa Rican avocado (or 448900 USD) [5].

As a complex matrix, performing chemical analysis on the avocado flesh presents an additional difficulty. The ripe avocado fruit has a firm, oily, and yellow to light green colored mesocarp that contains both fat-soluble vitamins and carotenoids associated with other lipids [6]. Usually, both types of analysis have to be performed separately using different chromatographic conditions altogether, which represents an additional expense, both economic and in terms of labor. Analyzing both types of fat-soluble compounds is relevant, especially in fruits such as avocado in which there is evidence that carotenoid absorption might be improved by the addition of avocado and avocado oil [7–9].

Interestingly, the Association of Official Analytical Chemists (AOAC) Official Methods of Analysis (OMASM) does not have any method established for neither fat-soluble vitamins nor carotenoids in fruits. Several papers have already annotated the relevance of including avocado in the diet as it has been related to health benefits [10–19]. Previously, another report analyzed carotenoid content in avocado using spectrophotometry [20]. A later report has used a similar approach to measure total carotenoid content [21]. On another hand, a research group has analyzed avocado pigments in oil [22] and tissue [22,23] using HPLC coupled with a photodiode array detector using a triphasic organic solvent gradient. Carotenoids in avocado seed have also been described [24,25].

The application of chromatography and mass spectrometry to carotenoid analysis in fruits is not new [23,26,27]. However, few papers have been dedicated solely to the study of both fat-soluble and carotenoid content in avocado fruits. For example, research assayed both types of compounds (i.e., carotenoids and tocopherol) using two independent chromatographic techniques [28].

Among the papers dedicated to assessing specifically carotenoids or vitamins in avocado, the most relevant include advantages such as that most researchers use acetone (a versatile and low boiling point solvent) during primary extraction [22,23,28,29] and ethyl ether or hexane after saponification [22,23,29]. For saponification at room temperature, the use of 2,6-di-*tert*-butyl-4-methylphenol, and nitrogen flushing seems to be a norm [28,29], thus protecting the target analytes. Diversity of carotenoids studies is ample (including epoxides [28], isomers of carotene [20], chlorophylls [22], phytoene [23]). Mobile phases are usually simple and environmentally friendly [22,23,29], which include methanol, water, methyl *tert*-butyl ether, and ethyl acetate. Yano and coworkers were able to apply their method to 75 and 15 different fresh and processed fruits, respectively [23]. Solid-phase extraction has been used to reduce interferences [22]. Mass spectrometry has been used to recognize unidentified compounds [20,28].

Disadvantages of these methods include the presence of water in the mobile phase (which increases mobile phase polarity), several approaches exhibit some issues with chromatographic resolution for some of the signals [28,29] and in some cases saponification time [29], base concentration [29], and chromatographic run [23] are excessive or the identification of compounds is based on light absorption [20,22,29]. Finally, vitamin analysis of the fruit is scarce at best [11,28].

Lastly, very little information has been gathered regarding varieties of Costa Rican avocados, proximate analysis, mineral content, and some vitamins have been explored [30]. Some papers have also focused on standing out differences between avocado varieties [21,28], including varieties of Guatemalan race (e.g., Hass [11] and Nabal [20]), as avocadoes originated from New Zealand [22], California [28], and Mexico [29] and those commercially available from Israel [20] and Japan [23].

Herein, we report a liquid chromatography and single quadrupole mass detection (LC/MS) based method using a C30 column and methanol and methyl *tert*-butyl ether to assay and quantitatively separate both fat-soluble vitamins (vitamin A acetate and palmitate, Vitamin D2 and D3, vitamin K1, α-, δ-, and γ-vitamin E isomers) and carotenoids (β-cryptoxanthin, zeaxanthin, lutein, β-carotene, and lycopene) simultaneously in avocado fruit.

#### **2. Results and Discussion**

#### *2.1. Stationary Phase Selection and Green Chemistry*

Where other alkyl modified stationary phases failed (Table 1), the C30 allowed an excellent separation of fat-soluble compounds even between structurally related molecules using a MeOH/*tert*-butyl methyl ether (MTBE)-based mobile phase (Table 2). The solvent selection not only ensured good compound solubility and chromatographic separation, but it also helped improve column life span as no water was involved and the column could be safely stored under 80% MeOH.

**Table 1.** Performance of other stationary phases and conditions tested to try to separate calciferol and tocopherol isomers.

**Table 2.** Optimized Mass Spectrometry (MS) parameters for the assayed compounds, in order of *m*/*z*.

Some methods have selected chlorinated solvents as an effective way to extract [28] or separate carotenoids [31]. However, we chose MTBE as a greener alternative to chlorinated solvents [32]. Additionally, our chromatographic separation was mostly based on MeOH. The high degree of shape recognition of the C30 was validated early [33] and was, once again, here, demonstrated. It is recommended for analysis of retinoid as well as carotenoid molecules [34]. However, herein, we exploited the versatility of the C30 column further. Furthermore, as avocado lacks the presence of

lycopene [20,28], this compound when introduced into the separation (especially in its deuterated form), can be used as an internal standard (IS). Though lycopene is considered a relative liable carotenoid, it has been used successfully as an IS [35]. Other more stable molecules have been used as well and could be considered (e.g., canthaxanthin [35], sudan I [36]; 80 -apo-80 -β-carotenal [37], echinenone [38]).

#### *2.2. Singular Ion Monitoring Parameter Selection*

As expected, using reverse phase chromatography, fat-soluble vitamins eluted during the first 8 min (except for retinyl palmitate, an esterified compound with an extra C15 alkyl chain) (Table 2). Both retinoids assessed were prone to retain monovalent cations such as K+ ([M + K]+). Retinyl acetate and retinyl palmitate share a similar fragmentation pattern, which includes ion 269 *m*/*z* as a base peak (Table 2). The retinoid alkyl chain did not seem to affect ionization voltage, indicating that the C20H29OH base was governing their behavior. Ion 296 *m*/*z* found for retinoids corresponded to the protonation and elimination of water and acetate during positive ion electrospray [34].

All tocopherol isomers, as well as zeaxanthin, β-cryptoxanthin, β-carotene, and lycopene (the heavier analogs), exhibited deprotonated species as molecular ions ([M+]). Electrospray ionization (ESI+) ions are usually preformed in solution by acid/base reactions (i.e., [M + nH]n+), some ions are probably formed by a field desorption mechanism at the surface. Hence, the production of abundant cations, with little fragmentation [34]. Meanwhile, phylloquinone, the acidic carotenoid astaxanthin [34], and lutein all ionized through protonated species ([M + H]+) (Table 2). Interestingly, the highly related compounds α-, γ-, and β-tocopherols exhibited very different ionization energies (i.e., 80, 140, and 220 V, respectively) (Table 2).

#### *2.3. Method Performance Data*

For the vitamin group, the higher sensitivity was exhibited by α-, γ-, and retinyl palmitate (Table 2). On the other hand, carotenoids with a lower limit of detection were astaxanthin, lutein, and zeaxanthin (Table 3). Electrospray analysis of carotenoids, since some years ago, has demonstrated high sensitivity (i.e., in the pmol range) [39]. These compounds, as expressed in the matrix of interest, could be detected as low as 1 µg/100 g dry matter (Table 3). The resolution obtained between the compounds analyzed ranged from 2.18–71.90; the lowest value recommended is 2 (Table 2, Figure 1A) [40]. Several compounds were very close to the theoretical value of 1 (i.e., a perfect peak with a Gaussian distribution and completely symmetrical) though ergocalciferol (1.707), and lutein (1.348) exhibited some tailing. Fronting (leading peak) can also be observed for retinyl acetate (0.709) (Table 3). Column efficiency was very high for compounds eluted above 8 min, such as phylloquinone, zeaxanthin, retinyl palmitate, β-cryptoxanthin, and β-carotene (Table 3). A good baseline definition was observed for all compounds analyzed (i.e., αs ranging from 1.07 to 1.76) (Table 3).

**Table 3.** Method performance parameters obtained during validation.

(red line).

**Table 3.** *Cont.*

Lycopene 37.39 1.00 0.28 0.34 0.14 1.04 - - - 118.31

**Figure 1.** Selected ion monitoring (SIM) chromatogram for (**A**). (**A**) A standard mixture of 14 analytes at 1 μg mL−1 for liposoluble vitamins and 0.05 μg mL−1 for carotenoids. 1. Retinyl acetate. 2. Ergocalciferol. 3. Cholecalciferol. 4. δ-Tocopherol. 5. γ-Tocopherol. 6. α-Tocopherol. 7. Phylloquinone. 8. Astaxanthin. 9. Lutein. 10. Zeaxanthin. 11. Retinyl palmitate. 12. β-Cryptoxanthin. 13. β-Carotene. 14. Lycopene. (**B**) The saponified avocado sample analyzed using the proposed chromatographic method (blue line), and a sample spiked with 5 μmol for each vitamin and 1 μmol for each carotenoid **Figure 1.** Selected ion monitoring (SIM) chromatogram for (**A**). (**A**) A standard mixture of 14 analytes at 1 µg mL−1 for liposoluble vitamins and 0.05 µg mL−1 for carotenoids. 1. Retinyl acetate. 2. Ergocalciferol. 3. Cholecalciferol. 4. δ-Tocopherol. 5. γ-Tocopherol. 6. α-Tocopherol. 7. Phylloquinone. 8. Astaxanthin. 9. Lutein. 10. Zeaxanthin. 11. Retinyl palmitate. 12. β-Cryptoxanthin. 13. β-Carotene. 14. Lycopene. (**B**) The saponified avocado sample analyzed using the proposed chromatographic method (blue line), and a sample spiked with 5 µmol for each vitamin and 1 µmol for each carotenoid (red line).

The method was successfully applied to avocado fruits (Figure 2B). The lack of available certified reference materials for matrices such as fruits obliges the use of spike solutions to demonstrate both The method was successfully applied to avocado fruits (Figure 2B). The lack of available certified reference materials for matrices such as fruits obliges the use of spike solutions to demonstrate both matrix effects (if any) and extraction efficiency of vitamins and carotenoids in avocado specifically.

matrix effects (if any) and extraction efficiency of vitamins and carotenoids in avocado specifically.

(red line).

 Selected ion monitoring (SIM) chromatogram for (**A**). (**A**) A standard mixture of 14 analytes at 1 μg mL−1 for liposoluble vitamins and 0.05 μg mL−1 for carotenoids. 1. Retinyl acetate. 2. Ergocalciferol. 3. Cholecalciferol. 4. δ-Tocopherol. 5. γ-Tocopherol. 6. α-Tocopherol. 7. Phylloquinone. 8. Astaxanthin. 9. Lutein. 10. Zeaxanthin. 11. Retinyl palmitate. 12. β-Cryptoxanthin. 13. β-Carotene. 14. Lycopene. (**B**) The saponified avocado sample analyzed using the proposed chromatographic method (blue line), and a sample spiked with 5 μmol for each vitamin and 1 μmol for each carotenoid

The method was successfully applied to avocado fruits (Figure 2B). The lack of available certified

matrix effects (if any) and extraction efficiency of vitamins and carotenoids in avocado specifically.

Peak Widt h

Symmetr y

Rs *k* α *N*, ×104

Height , ×104

**Figure 2.** Average calibration curves and error bars depicting variability obtained for two of the target analytes (**A**) δ-tocopherol and (**B**) zeaxanthin. Mean and standard deviations (used as error) calculated from *n* = 3 independently constructed calibration curves injected on different days.

#### *2.4. Performance during Saponification*

Saponification-wise, using the same starting mass and sample, we proceeded to optimize the conditions needed (i.e., base concentration and time) to improve analyte recovery. The differential analysis showed that, overall, samples treated at 80 ◦C for one hour and using 1 mol KOH L−1 exhibited the best results in the case of the analytes of interest, for avocado (Table 4). Variables tested showed a profound and significant effect over analyte recovery (*p* < 0.05 for all cases) (Table 4). Reaction parameters must be optimized to ensure proper hydrolysis within the complex, considerably oily (ranging from 35.3 to 39.1 g fat/100 g dry weight basis), food matrix that is found in the ripe avocado fruit [41]. Carotenoids are increasingly sensitive to heat. Hence, hot saponification was carried out using an organic solvent with a relatively low boiling point [6] (i.e., 78.37 ◦C at Standard Pressure and Temperature [STP] for ethanol) and pyrogallol was used as a radical sink to protect the compounds of interest. However, the improvement in recovery was achieved by increasing the temperature to 80 ◦C. A procedure that might be justified as (i) the thermal effect must be sufficient to break the cell walls from the avocado fruit and provide a rapid molecular diffusion to promote reaction; (ii) higher temperatures increase solubility of lipophilic compounds and enhance kinetics of saponification (i.e., favors localized "hot spots" which deliver sufficient energy for the molecules to react) [42]. We chose hot saponification to diminish reaction time; a similar approach has been reported elsewhere [43].

**Table 4.** Optimization of saponification conditions.

a Brackets indicate bias, expressed as a fraction, with respect to the saponification treatment of 1 h at 80 ◦C using a 1 mol L−1 base concentration. ND: not detected.

#### *2.5. Quantification, Linearity, and Calibration Curve Construction*

Five-point calibration curves were constructed to quantitate the analytes. Slopes (*mx*) ranging from 4.05 × 103 (cholecalciferol) to 5.51 × 104 (ergocalciferol) and 5.45 × 104 (β-cryptoxanthin) to 6.49 × 106 (zeaxanthin) for vitamins and carotenoids, respectively, were obtained. Determination coefficients spoke toward excellent linearity ranging from 0.9906 to 0.9964 (Figure 2A,B). For vitamins, standard calibration curves were constructed as follows: from 1.00 to 10.00 mg L−1 for retinyl acetate, ergocalciferol, γ-, and α-tocopherol and retinyl palmitate; from 2.50 to 30.00 mg L−1 for cholecalciferol, δ-tocopherol, and phylloquinone. Finally, considering lower concentrations found in the target matrix and carotenoid sensitivity, standard calibration curves were constructed as follows: 0.05 to 0.80 mg L −1 for astaxanthin, β-cryptoxanthin, and β-carotene and from 0.1 to 2 mg L−1 for zeaxanthin and lutein (Figure 2A,B). Concentrated stock solutions were prepared by dissolving the solid standard in 2-propanol for vitamins and chloroform for carotenoids; dilutions performed after that were matched with the mobile phase (i.e., the gradient at the start of the chromatographic run).

#### *2.6. Analyte Recovery and Method Accuracy*

Overall, vitamin recovery, in spiked avocadoes, exhibited better performance than for carotenoids (except for β-carotene with a recovery of 108.63%). Structurally, the lower recoveries (ranging from 43.80% to 63.68%) were found for those carotenoids that were oxygenated (Table 5). Noteworthy, when zeaxanthin and β-cryptoxanthin were extracted using a mixture of ethyl ether, and hexane (50:50) obtained/experimental mass increased between 12.35% and 15.56%. Furthermore, when nitrogen flushing was performed, in conjunction, an additional increment between 13.35% to 19.66%, was observed (data not shown). Carotenoids, among several mechanisms of transformation [44,45], are susceptible to thermal degradation [46,47], β-carotene may suffer from symmetrical oxidative cleavage (which generates, the apocarotenoid, retinol) [48], and β-cryptoxanthin can undergo light-induced oxidation and isomerization [49].

**Table 5.** Spiked avocado samples and recovery for representatives for fat-soluble vitamins and carotenoids.

a Brackets represent recovery values recommended by AOAC [50].

#### *2.7. Mass Spectra Analysis*

Retinyl acetate and β-cryptoxanthin showed, under our conditions, a higher degree of fragmentation compared to tocopherol and an oxygenated carotenoid. Additional to the signals analyzed above for retinoids, ion 369.3 represented the retinyl acetate molecular ion plus a potassium ion, [M + K]+ (Figure 3A). On another hand, tocopherols usually are characterized to present few fragmentation processes [51] (Figure 3B). Major ions are formed by cleavage through the non-aromatic portion of the chromanol ring, both with and without hydrogen transfer and by a loss of the isoprenoid side chain [51]. In contrast, we found none of the usual fragments reported elsewhere for the fragmentation of γ-tocopherol (e.g., C9H11O2 + *m*/*z* 151 amu; [51]) probably because the total

ion chromatogram was obtained using lower energy than required. Also, there may have been some instrument limitations as a single quadrupole was used throughout the experiments, and the fragmentation ions were the result of molecule degradation in the ion source not in the collision chamber used during tandem mass spectrometry. Hence, the lack of tandem mass detection justified the absence, in some cases, of multiple fragmentation patterns [52]. However, the molecular ion [M+] for γ-tocopherol was unmistakable and could be used to differentiate nuances among tocopherols (e.g., the difference between γ-tocopherol and α-tocopherol is a methyl group in the aromatic ring (∆15 amu)). As an example of calciferol identification, cholecalciferol total ion chromatogram (TIC)-mass spectra showed relevant fragments at 365.1 (loss of H2O), 337.1 (subsequent loss of both –CH3 from the isopropyl moiety), 301.2, and 227.0 (loss of –CH3 and =CH2 or C17H23 3• ) *m*/*z* (data not shown). *Molecules* **2019**, *24*, x FOR PEER REVIEW 8 of 16

**Figure 3.** Experimental mass spectra obtained for (**A**) retinyl acetate, (**B**) γ-tocopherol, (**C**) Lutein, (**D**) β-cryptoxanthin. Total ion chromatograms at 100 mg L−1 each. **Figure 3.** Experimental mass spectra obtained for (**A**) retinyl acetate, (**B**) γ-tocopherol, (**C**) Lutein, (**D**) β-cryptoxanthin. Total ion chromatograms at 100 mg L−1 each.

On another hand, Atmospheric-pressure chemical ionization (APCI), Fast atom bombardment (FAB), electron ionization (EI), and ESI all have mass-based techniques used to assess carotenoids [53]. While APCI is a popular approach for the ionization of lipophilic compounds, we selected ESI+. In this scenario, some modifications were introduced into the mobile phase to enhance ionization. In this specific case, formic acid was selected as it has been described to decrease signal suppression [54]. For the case of lutein the signal 551 *m*/*z* (i.e., [M + H − 18] which corresponds to the loss of H2O) and 463 *m*/*z* ([M + H − 106], loss of two water molecules and xylene from the polyene chain) were observable ([53,55]; Figure 3C). Additionally, as zeaxanthin and lutein differed from each other by a position of a double bond, in a ε-ring, they rendered similar spectra [53]. Further fragmentation for both compounds responded to the loss of said rings. Finally, for β-cryptoxanthin, signal 552.5 ([M+]) and 553.2 *m*/*z* ([M + H]+) were evident, fragments 425.1 [C32H40]+ and 399 [M + H − 153]+ *m*/*z* responded to the partial breakup of both β-rings and the complete loss of the oxygenated β-ring plus a methyl group (Figure 3D). On another hand, Atmospheric-pressure chemical ionization (APCI), Fast atom bombardment (FAB), electron ionization (EI), and ESI all have mass-based techniques used to assess carotenoids [53]. While APCI is a popular approach for the ionization of lipophilic compounds, we selected ESI+. In this scenario, some modifications were introduced into the mobile phase to enhance ionization. In this specific case, formic acid was selected as it has been described to decrease signal suppression [54]. For the case of lutein the signal 551 *m*/*z* (i.e., [M + H − 18] which corresponds to the loss of H2O) and 463 *m*/*z* ([M + H − 106], loss of two water molecules and xylene from the polyene chain) were observable ([53,55]; Figure 3C). Additionally, as zeaxanthin and lutein differed from each other by a position of a double bond, in a ε-ring, they rendered similar spectra [53]. Further fragmentation for both compounds responded to the loss of said rings. Finally, for β-cryptoxanthin, signal 552.5 ([M+]) and 553.2 *m*/*z* ([M + H]+) were evident, fragments 425.1 [C32H40] + and 399 [M + H − 153]+ *m*/*z* responded to the partial breakup of both β-rings and the complete loss of the oxygenated β-ring plus a methyl group (Figure 3D).

#### *2.8. Chromatographic Separation of Tocopherol Isomers 2.8. Chromatographic Separation of Tocopherol Isomers*

tocopherol (Table 1, Figure 4A).

Under our chromatographic conditions, tocopherol isomers were easily segregated (Figure 4A). Using the tocopherol mixture containing α-, β-, δ-, and γ-tocopherols, we were able to assess further that no additional [M+] signal was necessary for the detection of β-tocopherol, as β- and γ-tocopherol Under our chromatographic conditions, tocopherol isomers were easily segregated (Figure 4A). Using the tocopherol mixture containing α-, β-, δ-, and γ-tocopherols, we were able to assess further that no additional [M+] signal was necessary for the detection of β-tocopherol, as β- and γ-tocopherol

share the same molecular mass (Figure 4B,C). The signal for β-tocopherol was observed at a *tR* of 5.387 min (Figure 4A). Hence, the four tocopherol isomers eluted as follows: δ-, β-, γ-, and α-

share the same molecular mass (Figure 4B,C). The signal for β-tocopherol was observed at a *tR* of 5.387 min (Figure 4A). Hence, the four tocopherol isomers eluted as follows: δ-, β-, γ-, and α-tocopherol *Molecules*  (Table 1, Figure 4A). **2019**, *24*, x FOR PEER REVIEW 9 of 16

**Figure 4.** (**A**) Chromatogram of a mixture of tocopherols (W530066 70, 13, 523, 105 mg g−1 for α- (peak 4), β- (peak 2), γ- (peak 3), and δ-tocopherol (peak 1), respectively). Selected [M + H]+ ion for (**B**) δtocopherol (402.1 *m*/z), (**C**) β/γ-tocopherol (416.4 *m*/z), and (**D**) α-tocopherol (430.4 *m*/z). Selected ion monitoring (SIM) at 700, 130, 5230, 1050 μg mL−1. **Figure 4.** (**A**) Chromatogram of a mixture of tocopherols (W530066 70, 13, 523, 105 mg g−1 for α- (peak 4), β- (peak 2), γ- (peak 3), and δ-tocopherol (peak 1), respectively). Selected [M + H]+ ion for (**B**) δ-tocopherol (402.1 *m*/*z*), (**C**) β/γ-tocopherol (416.4 *m*/*z*), and (**D**) α-tocopherol (430.4 *m*/*z*). Selected ion monitoring (SIM) at 700, 130, 5230, 1050 µg mL−1 .

#### *2.9. Method Application in Real Samples*

*2.9. Method Application in Real Samples*  Simmonds variety characterizes itself for having an oblong oval to pear-shape large-sized fruit of light green-colored smooth skin, and a seed of medium size, usually tight. Meanwhile, Guatemala has a medium to large size and nearly round shape, smooth, thick, granular, and green skin with a small seed. Finally, Hass fruit possesses an ovoid to pear shape, is of medium size, with tough, Simmonds variety characterizes itself for having an oblong oval to pear-shape large-sized fruit of light green-colored smooth skin, and a seed of medium size, usually tight. Meanwhile, Guatemala has a medium to large size and nearly round shape, smooth, thick, granular, and green skin with a small seed.  We found in avocado both non-provitamin A (lutein and zeaxanthin) and provitamin A (βcarotene and β-cryptoxanthin) carotenoids [57] (Table 6). All carotenoids encountered have been previously identified for the fruit (see, for example, [11,20,21,23,28,29]). Our data indicated that, overall, all three varieties of avocado exhibited concentrations, of carotenoids and vitamins, in line (except for provitamin A carotenoids which levels were considerably higher for Costa Rican avocadoes) with those reported elsewhere [28]. Considering the above, Costa Rican avocado would supply to diet retinol equivalents [58] ranging from 1085.21 to 425.01 μg on a dry weight basis. Though three different varieties of avocado have been examined, it should be clear that any number of factors can affect the concentrations of such molecules, including edaphoclimatic conditions, genotypic differences, and nutritional status of the plants [59]. Hass and Guatemala varietals showed a somewhat similar profile for both fat-soluble vitamins as carotenoids. Meanwhile, the Simmonds We found in avocado both non-provitamin A (lutein and zeaxanthin) and provitamin A (β-carotene and β-cryptoxanthin) carotenoids [57] (Table 6). All carotenoids encountered have been previously identified for the fruit (see, for example, [11,20,21,23,28,29]). Our data indicated that, overall, all three varieties of avocado exhibited concentrations, of carotenoids and vitamins, in line (except for provitamin A carotenoids which levels were considerably higher for Costa Rican avocadoes) with those reported elsewhere [28]. Considering the above, Costa Rican avocado would supply to diet retinol equivalents [58] ranging from 1085.21 to 425.01 µg on a dry weight basis. Though three different varieties of avocado have been examined, it should be clear that any number of factors can affect the concentrations of such molecules, including edaphoclimatic conditions, genotypic differences, and nutritional status of the plants [59]. Hass and Guatemala varietals showed a somewhat similar profile for both fat-soluble vitamins as carotenoids. Meanwhile, the Simmonds variety showed higher levels for almost all analytes tested (except for lutein) (Table 6). Interestingly, the δ/α ratio of isomers is close to 1 for all varieties (i.e., 0.75–1.22).

variety showed higher levels for almost all analytes tested (except for lutein) (Table 6). Interestingly,

**Table 6***.* Fat-soluble vitamins and carotenoids obtained from Costa Rican avocadoes.

**Compound Simmonds Hass Guatemala**

**Concentration, mg/100 g dry Weight Basis**

the δ/α ratio of isomers is close to 1 for all varieties (i.e., 0.75–1.22).

γ-tocopherol 4.81 ± 0.48 2.42 ± 0.37 0.92 ± 0.16 α-tocopherol 34.80 ± 14.50 8.16 ± 0.97 8.20 ± 3.67 Astaxanthin 2.23 ± 0.14 0.64 ± 0.23 0.98 ± 0.55 Lutein 6.41 ± 2.03 15.13 ± 8.66 10.79 ± 2.77 Zeaxanthin 0.03 ± 0.01 0.02 ± 0.01 0.02 ± 0.01 β-cryptoxanthin 6.10 ± 1.39 3.37 ± 0.20 1.66 ± 0.85 β-carotene 3.43 ± 2.09 2.28 ± 1.56 1.71 ± 0.21

**Table 6.** Fat-soluble vitamins and carotenoids obtained from Costa Rican avocadoes.

#### *2.10. Method Application in Other Samples 2.10. Method Application in Other Samples*

As stated before, no standard reference material is available for avocado. However, as a quality control material, we subjected our method to infant formula to further assess method accuracy. We obtained values according to the provider, and no appreciable matrix effects were observed for this food either (Figure 5A). Also, our method showed promise to extrapolate to other matrices, especially fruits. Unambiguous signals of several vitamins of interest can be seen when a chloroform extract obtained from green tomatoes was injected (Figure 5B). As stated before, no standard reference material is available for avocado. However, as a quality control material, we subjected our method to infant formula to further assess method accuracy. We obtained values according to the provider, and no appreciable matrix effects were observed for this food either (Figure 5A). Also, our method showed promise to extrapolate to other matrices, especially fruits. Unambiguous signals of several vitamins of interest can be seen when a chloroform extract obtained from green tomatoes was injected (Figure 5B).

**Figure 5.** (**A**) Infant formula with certified values for fat-soluble vitamins. The box shows the amplification of the region from 1 to 10 min of the said chromatogram. FAPAS®® reference material TYG009RM. Vitamin A, vitamin D3, and vitamin E at 508 ± 12, 7.16 ± 0.33, and 10,900 ± 400 μg/100 g. (**B**) Non-saponified sample of green tomatoes extracted after mechanical shearing and chloroform extraction and analyzed using the proposed method. **Figure 5.** (**A**) Infant formula with certified values for fat-soluble vitamins. The box shows the amplification of the region from 1 to 10 min of the said chromatogram. FAPAS®® reference material TYG009RM. Vitamin A, vitamin D3 , and vitamin E at 508 ± 12, 7.16 ± 0.33, and 10,900 ± 400 µg/100 g. (**B**) Non-saponified sample of green tomatoes extracted after mechanical shearing and chloroform extraction and analyzed using the proposed method.

#### **3. Materials and Methods 3. Materials and Methods**

*3.2. Sample Treatment and Preparation*

was then processed immediately for saponification.

#### *3.1. Reagents 3.1. Reagents*

*tert*-Butyl methyl ether (99%, catalog 34875, MTBE, chromatographic grade), methanol (≥99.9%, catalog 646377, MeOH, chromatographic grade) and potassium hydroxide (ACS reagent, catalog<PHONE_NUMBER>) were acquired from Merck Millipore (Burlington, MA, USA). Retinyl acetate (catalog 46958), retinyl palmitate (catalog 46959-U), cholecalciferol (catalog C9774), ergocalciferol (catalog 47768), 3-phytylmenadione catalog (95271), α-tocopherol (catalog 47783), δ-tocopherol (catalog 47784), γ-tocopherol (catalog T1782), tocopherols (mixed, W530066), lutein (catalog 071068), βcarotene (catalog C4582), β-cryptoxanthin (≥97%, catalog C6368), zeaxanthin (catalog 14681), all*trans*-astaxanthin (catalog 41659), and lycopene (catalog 75051) from Sigma-Aldrich (unless stated otherwise, all standards were of analytical grade, St. Louis, MO, USA). Chloroform (ACS reagent, catalog 366919), ethanol (200 proof, ACS reagent, ≥99.5%, 459844), 2-propanol (HPLC Plus, 650447), *tert*-Butyl methyl ether (99%, catalog 34875, MTBE, chromatographic grade), methanol (≥99.9%, catalog 646377, MeOH, chromatographic grade) and potassium hydroxide (ACS reagent, catalog<PHONE_NUMBER>) were acquired from Merck Millipore (Burlington, MA, USA). Retinyl acetate (catalog 46958), retinyl palmitate (catalog 46959-U), cholecalciferol (catalog C9774), ergocalciferol (catalog 47768), 3-phytylmenadione catalog (95271), α-tocopherol (catalog 47783), δ-tocopherol (catalog 47784), γ-tocopherol (catalog T1782), tocopherols (mixed, W530066), lutein (catalog 071068), β-carotene (catalog C4582), β-cryptoxanthin (≥97%, catalog C6368), zeaxanthin (catalog 14681), all-*trans*-astaxanthin (catalog 41659), and lycopene (catalog 75051) from Sigma-Aldrich (unless stated otherwise, all standards were of analytical grade, St. Louis, MO, USA). Chloroform (ACS reagent, catalog 366919), ethanol (200 proof, ACS reagent, ≥99.5%, 459844), 2-propanol (HPLC Plus, 650447), pyrogallol (ACS

Three different varieties of avocado collected from Costa Rica farms, two varietals from low and one highland, i.e., Simmonds (from 0 to 1000 m amsl), Guatemala (from 600 to 1500 m amsl), and Hass (from 1000 to 2000 m amsl), respectively [30,56]. Three batches of each variety were analyzed, each with eight days of maturation. A previously homogenized subsample (2 g) of freeze-dried material was weighed, and chloroform (20 mL, ACS reagent, Sigma-Aldrich 366919) was added. After that, the mixture was stirred continuously (30 min) using an Ultraturrax® (T25, at 7500 rpm, IKA Works Staufen, Germany). The remnant suspension was centrifuged, and the supernatant liquid recollected. The extraction procedure was repeated twice. The solvent was evaporated using a rotary evaporator (Multivapor™ P-6, Büchi, Flawil, Switzerland) until the lipid fraction was attained, which

pyrogallol (ACS reagent, ≥99%, catalog 16040), and sodium sulfate (anhydrous, granular, freeflowing, Redi-Dri™, ACS reagent, ≥99%, catalog 798592) were also acquired from Sigma-Aldrich.

reagent, ≥99%, catalog 16040), and sodium sulfate (anhydrous, granular, free-flowing, Redi-Dri™, ACS reagent, ≥99%, catalog 798592) were also acquired from Sigma-Aldrich.

### *3.2. Sample Treatment and Preparation*

Three different varieties of avocado collected from Costa Rica farms, two varietals from low and one highland, i.e., Simmonds (from 0 to 1000 m amsl), Guatemala (from 600 to 1500 m amsl), and Hass (from 1000 to 2000 m amsl), respectively [30,56]. Three batches of each variety were analyzed, each with eight days of maturation. A previously homogenized subsample (2 g) of freeze-dried material was weighed, and chloroform (20 mL, ACS reagent, Sigma-Aldrich 366919) was added. After that, the mixture was stirred continuously (30 min) using an Ultraturrax® (T25, at 7500 rpm, IKA Works Staufen, Germany). The remnant suspension was centrifuged, and the supernatant liquid recollected. The extraction procedure was repeated twice. The solvent was evaporated using a rotary evaporator (Multivapor™ P-6, Büchi, Flawil, Switzerland) until the lipid fraction was attained, which was then processed immediately for saponification.

#### *3.3. Optimization of Saponification Conditions*

An additional experiment was performed to enhance the recovery of the analytes of interest during the saponification reaction. The experimental design consisted of maintaining constant reaction time (1 h), the concentration of radical protection agent (0.1 g/100 mL), and the extraction solvent (hexane). Base concentration was contrasted (1 vs. 2 mol KOH L ethanol−1 [43] for each temperature), and the temperature was progressively increased (60, 80, and 95 ◦C). The conditions that rendered the most recoveries were selected to process the samples.

### *3.4.  Afterward, KOH in ethanol (1 mmol mL−1 ) and containing pyrogallol (0.1 g/100 g) was added (10 mL). The mixture was let to saponify (during 1 h at 80 ◦C) in a heat bath (1229U55, Boekel Scientific, Feasterville, PA, USA). The resulting mixture was let to cool to room temperature and transferred to a Squibb separatory funnel (PYREX®, 250 mL, Corning® 6402). The above ethanol/aqueous layer was subjected to a liquid-liquid extraction using hexane. The extraction procedure was repeated twice. The totality of the organic solvent layer was then collected and filtered through sodium sulfate (used as a desiccant). The resulting solution was evaporated to dryness under a nitrogen flow (Ultra-High Pure Nitrogen was purchased from Praxair Technology Inc., Danbury, Connecticut, USA) and then reconstituted with MTBE (1 mL) and 2-propanol (1 mL) used at the start of the chromatographic separation and transferred to an HPLC vial (Agilent technologies, Santa Clara, CA, USA).