Children with CP also generally occur pain and this affect to daily life activities, participation in rehabilitation, social life. Pain is also important for children to reduce motivation that induce human action. Distraction is one of the successful methods to reduce pain and behavioral distress for children suffered by pain. Pillay reported that interactive distraction that child attend activity the distraction task continuously require central attention resources much more effective than passive distraction activities that do not necessary management of central attentional functions such as watching cartoons. These interactive distraction activities consist of videogames, interactive musical storybooks, interactive toy robots and educational elec‐ tronic games that reduce acute pain in children [81]. Law et al aimed to investigate effect of passive and active distraction task. They assessed pain by cold pressure tolerance. Participants separated two groups according to their age (6-9 years and 10-15 years). Because children react distraction differently associated to the age. Researches explained that attentional control improve rapidly during early childhood and develop greatly between 7-9 years and is relatively mature by 12 years. They used Nintendo Wii game system. Law et al found that there was significant improvement in pain tolerance all the interactive and passive distraction. But interactive distraction by increasing attentional load resulted higher improvements in pain tolerance. Their results are supported to the other researches in literature. In addition their findings showed that there were developmental differences on response to interactive distraction. Both of children have benefits on passive and interactive distraction but especially interactive distraction is much better. Also, older children response pain interactive distraction better than younger [82]. Current literature is required to research relationship between pain and VR interventions in CP.

## **13. Conclusion**

fitness for children with CP [26]. Hurkmans et al investigated effects on energy expenditure (EE) among adults with CP when playing Wii sports. Several researches compared EE measured with indirect calorimetry or by an activity monitor during play of different motion interactive video games to EE during other activities of various physical exertions [75]. Generally activity levels compare with metabolic equivalent units (MET). MET is a physio‐ logical concept expressing the energy cost of physical activities and is determined as the ratio of metabolic rate during a specific physical activity to a reference rate of the metabolic rate at complete rest. Therefore 1 MET corresponds to the metabolic rate while at complete rest and 2 METs represent a doubling of the energy consumption. A common grading of physical activity according to METs is: *sedentary* (<3METs); *moderate* (3-6 METs); *vigorous* (6-9 METs); and *very vigorous* (>9 METs). Playing motion interactive games found to increase EE to light or moderate levels around 3 METs, same as brisk walking, skipping, jogging or stair climbing. Sustained vigorous activity above 6 METs is generally not obtained during play. Energy expenditure during play depends on engagement and type of game played. Games that playing on upper body movements compared to games with playing lower EE and higher values are achieved when all body movements are achieved [76]. As result studies demon‐ strated that active video games generates higher EE compared to rest and sedentary screen time activities but not as high EE values as performing the corresponding real activity in itself.

292 Cerebral Palsy - Challenges for the Future

**12. Studies focused on other conditions associated with cerebral palsy**

Most of children with CP suffer from several comorbidities in addition to motor handicap such as behavioral, cognitive, and learning disabilities, further impeding their overall functional capacity. Approximately 40 percent of them have learning disabilities and common behavioral symptoms in high-functioning children with cerebral palsy are attention deficits and impul‐ sivity, especially premature birth compatible with the diagnosis of attention-deficit hyperac‐ tivity disorder (ADHD). ADHD is one of the major causes of behavioral, friendship and school problems [77]. Pollak et al investigated effects of VR intervention on children with ADHD and produced virtual reality schoolroom environment to motivate children, to support active participation, to evaluate attention and motor behaviors in challenging. Their VR classroom designed according to Rizzo et al Digital Media Works and has head mounted display and gives visual-auditory stimuli with in the VE. In experimental group had 20 boys with ADHD, the control group consisted of 17 boys without ADHD. They assessed with Test of Variables of Attention (TOVA) and virtual reality continuous performance tasks (VR-CPT). According to VR-CPT findings, children with ADHD had slower reaction time, higher variability in RT is more errors of omission and commission than control group. They demonstrated VE provide test and training situations that are ecologically valid, motivating and dynamic. These findings consistent with literature that VR-CPT is a user-friendly method for children with ADHD, autism and intellectual disability [78]. Future researches may focus on VR applications on children with ADHD and CP. Akhutina et al administered VR therapy to the treatment group for 30-60 minutes, 6-8 times for 1 month in a semi-experimental study they conducted with 12 treatment and 9 control subjects. They showed that the visual-spatial abilities developed more

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## **Author details**

Mintaze Kerem Gunel, Ozgun Kaya Kara, Cemil Ozal\* and Duygu Turker

Hacettepe University, Faculty of Health Sciences, Department of Physiotherapy and Reha‐ bilitation, Ankara, Turkey

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## *Edited by Emira Švraka*

Writing a comprehensive scientific book about the cerebral palsy is a great challenge. Many different interventions are available for persons with CP. Increasingly, it is recognized that intervention needs to be evidence-based and family-centered. Related therapies can offer improvement in some cases but do not offer a cure. Lifelong re/ habilitation (habilitation and rehabilitation) in person with cerebral palsy is the first part of this book which has four chapters about management in children and adults with cerebral palsy through the life span, providing support and services. Three chapters of the second part are exploring the new therapy options which could improve the family quality of life. Third part has two chapters about complementary therapies with new possibilities for the future.

Photo by Josep Maria Barres / iStock

Cerebral Palsy - Challenges for the Future

Cerebral Palsy

Challenges for the Future

*Edited by Emira Švraka*


**Introduction**

Mrs. Vinitha Mohan. Her support, encouragement, quiet patience, and unwavering love un‐

grateful to the IntechOpen publishing team specially Mr. Markus Mattila, Publishing Proc‐

Professor, Department of Electronics and Communication Engineering

Dr. Mahalingam College of Engineering and Technology

S.V. Hemesh for bearing my preoccupation, understanding, and love he gave me.

I have no words to thank my son

I am

India

**Dr. R. Sudhakar**

deniably led me to the successful completion of the work.

VIII Preface

ess Manager, who constantly helped me in bringing out this book.

**Chapter 1**

**Provisional chapter**

**Introductory Chapter: Understanding Wavelets**

**Introductory Chapter: Understanding Wavelets**

DOI: 10.5772/intechopen.78388

In this section, let us discuss some fundamentals which are required to understand wavelets. Signals which are coming from a source are normally in time domain. Examples are sinusoidal signal, bio-medical signal, etc. Anytime domain signal can be processed or transformed into frequency domain (spectral domain) using mathematical transformations. Fourier transform is one of the popular or famous transform that will convert a time domain signal into

While plotting time domain signal, we use time in the x-axis and amplitude in the y-axis. The hidden information present in the signal cannot be revealed in the time domain hence a transform domain is required. The frequency content or spectrum of a signal is simply the frequency content (spectral components) of the signal. The frequency spectrum of a signal depicts what are all the frequencies exist in the signal. When plotting frequency domain, we

Normally for any signal, if the frequency content is not changing with respect to time is called as stationary signal. Example can be a sinusoidal signal where the frequency 'X' Hz is not changing irrespective of the cycle. Unfortunately, real time signals are nonstationary signal where the frequency content of the signal is keeping on changing. The best example is biological signals. Suppose when we are looking at an ECG (electrocardiograph) signal. The typical shape of a healthy ECG signal is well known to cardiologists. Any significant deviation from that shape is usually considered to be a symptom of a pathological condition. Doctors analyse these cases not only in time domain, they are using frequency domain also to confirm the

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

Sudhakar Radhakrishnan

**1. Introduction**

pathological condition.

Additional information is available at the end of the chapter

frequency domain signal without any loss of generality.

use frequency in the x-axis and amplitude in the y-axis.

Sudhakar RadhakrishnanAdditional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78388

#### **Introductory Chapter: Understanding Wavelets Introductory Chapter: Understanding Wavelets**

DOI: 10.5772/intechopen.78388


**4. Ionic liquids**

Ionic liquids (ILs), defined here as materials that are made up of cations and anions (salts) which melt at or below 100°C, evolved from the nineteenth century. This field started with a report by Paul Walden, in which he studied the physical properties of ethylammonium nitrate ([EtNH3][NO3]), a salt which melted at around 14°C [96]. Ionic liquids are commonly formed through the combination of an organic cation (usually heterocyclic), such as dialkylimidazolium, and either an inorganic or organic anion (such as halides or methanesulfonate) [97]. The advantage with ionic liquids is their low vapor pressure, meaning the risk of atmospheric contamination and related health issues are reduced by using these solvents. It is for this particular reason that they are viewed as green solvents [98]; however, low volatility alone is not the only property that makes ionic liquids green. For instance, toxic and non-biodegradable ionic liquids will not be referred to as a green solvent even though they have negligible volatility [97]. In this regard, ionic liquids composed of bio-derived components have the added advantage and are outstanding candidates as sustainable and green solvents.

### **4.1 Sugar-based ionic liquids**

Since the depolymerization of hard-to-dissolve carbohydrate polymers can be achieved using ILs, it would be beneficial to develop sugar-based ILs with the aim of employing these in a 'closed-loop' carbohydrate polymer depolymerization process [99]. Some sugar-based ionic liquids which have potential in this regard have already been synthesized, even though they have been used for various other processes. The glucose-linked 1,2,3-triazolium ionic liquids were synthesized by copper(I)-catalysed regioselective cycloaddition of a glucose azide to a glucose alkyne, followed by quaternization with methyl iodide (**Figure 6**) [100]. The ILs were used as reusable chiral solvents and ligands in copper(I)-catalysed amination of aryl halides with aqueous ammonia. The triazolium salt affords the compound in its liquid state at room temperature, and hence the compound can be used as a solvent, while the free hydroxyl groups of the glucose moiety aids in stabilizing the copper(I) species during the reaction.

Methyl-D-glucopyranoside has also been used to synthesize an ionic liquid with promising solvent potential [101]. The synthetic sequence involved uses thexyldimethylsilyl chloride (TDSCl) to protect the hydroxyl at the primary position. The other secondary hydroxyl groups were converted to methyl ethers followed by reduction of the anomeric position and further deprotection of the primary hydroxyl. After deprotection of the primary hydroxyl group, it was then converted to a triflate to form an intermediate. This triflate intermediate finally underwent a nucleophilic substitution reaction using diethyl sulphide to afford an ionic liquid, with a triflate anion and a sulfonium cation, which was a liquid at room temperature (**Figure 6**).

Handy et al. have used fructose to synthesize room temperature ionic liquids [102]. In their synthetic protocol, copper carbonate, ammonia and formaldehyde were used to ring-close fructose and form hydroxymethylene imidazole. This imidazole was then taken through a series of alkylation steps (with 1-bromobutane followed by iodomethane) to form an imidazolium cation. Anion metathesis was performed to give a series of room temperature ionic liquids (**Figure 7**), which were used as recyclable solvents for Mizoroki-Heck cross-coupling of aryl iodides with alkenes.

An arabinose-based imidazolium IL was synthesized in 2018 starting with 2,3,5-tri-*O*-benzyl-D-arabinofuranose [103]. The pentofuranoside starting material was prepared by benzylating all the hydroxyl groups of D-arabinose, except the hydroxyl group on the carbon adjacent the ring oxygen atom. The free hydroxyl group was then reacted with propane-1,3-diyldioxyphosphoryl chloride in the presence of 1-methylimidazole to form a mixture of anomeric phosphates. This was then reacted with 1-methylimidazolium chloride and trimethylsilyl triflate, in catalytic amounts, to give a pure anomeric ionic liquid with a chloride anion. Anion metathesis reactions gave two additional ionic liquids (**Figure 7**), which were used as co-solvents in the synthesis of alcohols from aromatic aldehydes.

**13**

*Bio-Solvents: Synthesis, Industrial Production and Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.86502*

**4.2 Alkaloid-based ionic liquids**

*ILs based on pentoses [(A) fructose-based ILs; (B) arabinose-based ILs].*

**Figure 6.**

**Figure 7.**

solvating agents (**Figure 8**) [106].

**4.3 Lipid-based ionic liquids**

Ionic liquids which contain ampicillin as active pharmaceutical ingredients

were developed by Ferraz et al., by neutralizing basic ammonia solutions of ampicillin with different organic cation hydroxides. These ampicillinbased ILs may be useful in the development of bioactive materials [104]. A chiral IL derived from ephedrine was synthesized by Wasserscheid et al. N-methylephedrine was synthesized from ephedrine and alkylated with dimethyl sulphate followed by ion exchange to form the IL, with a melting point of 54°C [105]. Heckel et al. reported the synthesis of ionic liquids derived from nicotine by the quaternization of the pyridine ring of nicotine with methyl iodide and ethyl bromide. The resulting chiral nicotine-based ILs were examined as chiral

*Glucose-based ionic liquids [(A and B) glucose-tagged triazolium ILs; (C) glucopyranoside-based IL].*

Linoleate and oleate were used in the syntheses of four ILs with melting points below −21°C (**Figure 9**). Unsaturated fatty acids were initially taken through neutralization reactions with NaOH followed by ion exchange with either *Bio-Solvents: Synthesis, Industrial Production and Applications DOI: http://dx.doi.org/10.5772/intechopen.86502*

**Figure 6.** *Glucose-based ionic liquids [(A and B) glucose-tagged triazolium ILs; (C) glucopyranoside-based IL].*

**Figure 7.**

*Solvents, Ionic Liquids and Solvent Effects*

candidates as sustainable and green solvents.

**4.1 Sugar-based ionic liquids**

copper(I) species during the reaction.

ture (**Figure 6**).

alkenes.

inorganic or organic anion (such as halides or methanesulfonate) [97]. The advantage with ionic liquids is their low vapor pressure, meaning the risk of atmospheric contamination and related health issues are reduced by using these solvents. It is for this particular reason that they are viewed as green solvents [98]; however, low volatility alone is not the only property that makes ionic liquids green. For instance, toxic and non-biodegradable ionic liquids will not be referred to as a green solvent even though they have negligible volatility [97]. In this regard, ionic liquids composed of bio-derived components have the added advantage and are outstanding

Since the depolymerization of hard-to-dissolve carbohydrate polymers can be achieved using ILs, it would be beneficial to develop sugar-based ILs with the aim of employing these in a 'closed-loop' carbohydrate polymer depolymerization process [99]. Some sugar-based ionic liquids which have potential in this regard have already been synthesized, even though they have been used for various other processes. The glucose-linked 1,2,3-triazolium ionic liquids were synthesized by copper(I)-catalysed regioselective cycloaddition of a glucose azide to a glucose alkyne, followed by quaternization with methyl iodide (**Figure 6**) [100]. The ILs were used as reusable chiral solvents and ligands in copper(I)-catalysed amination of aryl halides with aqueous ammonia. The triazolium salt affords the compound in its liquid state at room temperature, and hence the compound can be used as a solvent, while the free hydroxyl groups of the glucose moiety aids in stabilizing the

Methyl-D-glucopyranoside has also been used to synthesize an ionic liquid with

Handy et al. have used fructose to synthesize room temperature ionic liquids [102]. In their synthetic protocol, copper carbonate, ammonia and formaldehyde were used to ring-close fructose and form hydroxymethylene imidazole. This imidazole was then taken through a series of alkylation steps (with 1-bromobutane followed by iodomethane) to form an imidazolium cation. Anion metathesis was performed to give a series of room temperature ionic liquids (**Figure 7**), which were used as recyclable solvents for Mizoroki-Heck cross-coupling of aryl iodides with

An arabinose-based imidazolium IL was synthesized in 2018 starting with 2,3,5-tri-*O*-benzyl-D-arabinofuranose [103]. The pentofuranoside starting material was prepared by benzylating all the hydroxyl groups of D-arabinose, except the hydroxyl group on the carbon adjacent the ring oxygen atom. The free hydroxyl group was then reacted with propane-1,3-diyldioxyphosphoryl chloride in the presence of 1-methylimidazole to form a mixture of anomeric phosphates. This was then reacted with 1-methylimidazolium chloride and trimethylsilyl triflate, in catalytic amounts, to give a pure anomeric ionic liquid with a chloride anion. Anion metathesis reactions gave two additional ionic liquids (**Figure 7**), which were used

as co-solvents in the synthesis of alcohols from aromatic aldehydes.

promising solvent potential [101]. The synthetic sequence involved uses thexyldimethylsilyl chloride (TDSCl) to protect the hydroxyl at the primary position. The other secondary hydroxyl groups were converted to methyl ethers followed by reduction of the anomeric position and further deprotection of the primary hydroxyl. After deprotection of the primary hydroxyl group, it was then converted to a triflate to form an intermediate. This triflate intermediate finally underwent a nucleophilic substitution reaction using diethyl sulphide to afford an ionic liquid, with a triflate anion and a sulfonium cation, which was a liquid at room tempera-

**12**

*ILs based on pentoses [(A) fructose-based ILs; (B) arabinose-based ILs].*

### **4.2 Alkaloid-based ionic liquids**

Ionic liquids which contain ampicillin as active pharmaceutical ingredients were developed by Ferraz et al., by neutralizing basic ammonia solutions of ampicillin with different organic cation hydroxides. These ampicillinbased ILs may be useful in the development of bioactive materials [104]. A chiral IL derived from ephedrine was synthesized by Wasserscheid et al. N-methylephedrine was synthesized from ephedrine and alkylated with dimethyl sulphate followed by ion exchange to form the IL, with a melting point of 54°C [105]. Heckel et al. reported the synthesis of ionic liquids derived from nicotine by the quaternization of the pyridine ring of nicotine with methyl iodide and ethyl bromide. The resulting chiral nicotine-based ILs were examined as chiral solvating agents (**Figure 8**) [106].

## **4.3 Lipid-based ionic liquids**

Linoleate and oleate were used in the syntheses of four ILs with melting points below −21°C (**Figure 9**). Unsaturated fatty acids were initially taken through neutralization reactions with NaOH followed by ion exchange with either

**Figure 8.** *Alkaloid-based ILs [(A) ampicillin-based ILs; (B) ephedrine-based IL; (C) nicotine-based ILs].*

**Figure 9.**

*Anions and cations used in the syntheses of lipid-based ILs.*

**Figure 10.** *Lipid-based imidazolyl ILs.*

tetraoctylammonium or methyltrioctylammonium chloride. The ILs were then successfully used as solvents in the extraction of metal ions from aqueous solutions [107].

Kwan et al. also synthesized ILs using lipids through alkylating a tertiary amine (**Figure 10**). The lipids used in this instance were methyl oleate and methyl stearate. In a third instance, cyclopropanated oleic acid methyl ester synthesized the reaction of the double bond of the oleate with diiodomethane, and diethylzinc was used to alkylate the tertiary amine. After reacting the obtained alkyl iodide with the imidazoles, anion exchange of the iodide with bistriflimide gave imidazolium bistriflimide ILs [108].


**6. Conclusion and future work**

In this study, a fast and effective method is proposed for hair-occluded removal in dermoscopic images. The implementation of the hair removal process is divided into two main stages: hair detection and inpainting. In hair detection, a morphological bottom-hat operation is implemented on Y-channel image of the YIQ color space followed by a binarization operation. In inpainting, the repaired Y-channel is partitioned into 256 non-overlapped blocks and for each block, white pixels are

*An Efficient Block-Based Algorithm for Hair Removal in Dermoscopic Images DOI: http://dx.doi.org/10.5772/intechopen.80024*

replaced by locating the highest peak of using a histogram function and a morphological close operation.

Our achieved results indicate high accuracy, and the proposed method can be dedicated to Dermatologists as a pre-processing stage before the lesion segmentation and classification. However, our proposed algorithm reports a true positive rate (sensitivity) of 97.36%, a false positive rate (fall-out) of 4.25%, and a true negative rate (specificity) of 95.75%. The diagnostic accuracy achieved is recorded at a high level of 95.78%.

The following opportunities are suggested for future work:


*Article* **Density and Refractive Index of Binary Ionic Liquid Mixtures with Common Cations/Anions, along with ANFIS Modelling**

**G. Reza Vakili-Nezhaad 1,\*, Morteza Mohammadzaheri 2, Farzaneh Mohammadi 3,\* and Mohammed Humaid 1**

	- 3 School of Health, Isfahan University of Medical Sciences (MUI), Isfahan 81746-73461, Iran

**\*** Correspondence<EMAIL_ADDRESS>(G.R.V.-N<EMAIL_ADDRESS>(F.M.)

**Abstract:** Ionic liquids have many interesting properties as they share the properties of molten salts as well as organic liquids, such as low volatility, thermal stability, electrical conductivity, nonflammability, and much more. Ionic liquids are known to be good solvents for many polar and nonpolar solutes. Combined with their special properties, ionic liquids are good replacements for the conventional toxic and volatile organic solvents. Each ionic liquid has different properties than others. In order to alter, tune, and enhance the properties of ionic liquids, sometimes, it is necessary to mix different ionic liquids to achieve the desired properties. However, using mixtures of ionic liquids in chemical processes requires reliable estimations of the mixtures' physical properties such as refractive index and density. The ionic liquids used in this work are 1-butyl-3-methylimidazolium thiocyanate ([BMIM][SCN]), 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), 1-hexyl-3-methylimidazolium tetrafluoroborate ([HMIM][BF4]), and 1-hexyl-3-methylimidazolium hexafluorophosphate ([HMIM][PF6]). These ionic liquids were supplied by Io-li-tec and used as received. However, new measurements for the density and refractive index were taken for the pure ionic liquids to be used as reference. In the present work, the densities and refractive indices of four different binary mixtures of ionic liquids with common cations and/or anions have been measured at various compositions and room conditions. The accuracy of different empirical mixing rules for calculation of the mixtures refractive indices was also studied. It was found that the overall absolute average percentage deviation from the ideal solution in the calculation of the molar volume of the examined binary mixtures was 0.78%. Furthermore, all of the examined mixing rules for the calculation of the refractive indices of the mixtures were found to be accurate. However, the most accurate empirical formula was found to be Heller's relation, with an average percentage error of 0.24%. Furthermore, an artificial intelligence model, an adaptive neuro-fuzzy inference system (ANFIS), was developed to predict the density and refractive index of the different mixtures studied in this work as well as the published literature data. The predictions of the developed model were analyzed by various methods including both statistical and graphical approaches. The obtained results show that the developed model accurately predicts the density and refractive index with overall *R*2, RMSE, and AARD% values of 0.968, 7.274, 0.368% and 0.948, 7.32 × 10−3 and 0.319%, respectively, for the external validation dataset. Finally, a variance-based global sensitivity analysis was formed using extended the Fourier amplitude sensitivity test (EFAST). Our modelling showed that the ANFIS model outperforms the best available empirical models in the literature for predicting the refractive index of the different mixtures of ionic liquids.

**Keywords:** refractive index; density; ionic liquids; mixtures; ANFIS

#### **1. Introduction**

Ionic liquids are salts in the liquid state. Due to the strong ionic bond between the cation and the anion, most ionic compounds exist in the form of crystal lattice (solid state) at room temperature. However, many asymmetric organic based ionic liquids appear in liquid

**Citation:** Vakili-Nezhaad, G.R.; Mohammadzaheri, M.; Mohammadi, F.; Humaid, M. Density and Refractive Index of Binary Ionic Liquid Mixtures with Common Cations/Anions, along with ANFIS Modelling. *Liquids* **2022**, *2*, 432–444. https://doi.org/10.3390/ liquids2040025

Academic Editors: William E. Acree, Jr. and Juan Ortega Saavedra

Received: 12 October 2022 Accepted: 26 November 2022 Published: 5 December 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 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 (https:// creativecommons.org/licenses/by/ 4.0/).

form at room temperature due to the weaker ionic bonding between the cation and anion. Ionic liquids have many interesting properties, as they share the properties of molten salts as well as organic liquids, such as low volatility, thermal stability, electrical conductivity, non-flammability, and much more. Ionic liquids are known to be good solvents for many polar and nonpolar solutes. Combined with their special properties, ionic liquids are good replacements for the conventional toxic and volatile organic solvents. Each ionic liquid has different properties to others. In order to alter, tune, and enhance the properties of ionic liquids, sometimes, it is necessary to mix different ionic liquids to achieve the desired properties.

However, using mixtures of ionic liquids in chemical processes requires the reliable estimations of the mixtures' physical properties, such as refractive index and density. Many general mixing rules for liquids have been proposed so far, which describe specific types of systems. This emphasizes the need to examine these mixing rules with respect to ionic liquid mixtures and to determine the best mixing rule for each physical property. Furthermore, assuming ideal behavior for the mixtures simplifies their complexity. Hence, the validity and accuracy of an ideal mixture assumption are uncertain and need to be examined. This will give a clearer picture in the design stage about the uncertainty of the calculations and in estimating the safety factor required for the design.

In addition to the existing empirical rules for the estimation of the different properties of the ionic liquid mixtures, such as refractive index, artificial intelligence (AI) models such as artificial neural networks (ANNs), regression models, fuzzy logic, support vector machine (SVM), and neural-based fuzzy interference system (ANFIS), can be used to predict the behavior of such complex systems. Different techniques have already been applied for the calculation of the various thermophysical properties of ionic liquid mixtures. Among various AI techniques, ANN alone or along with evolutionary algorithms such as genetic algorithms (GAs) and particle swarm optimization (PSO) has been used effectively to predict the properties of ionic liquid binary mixtures [1–4]. These techniques can predict responses with high accuracy, regardless of variation in input parameters. Very few studies have assessed the ability of the ANFIS model for this purpose [5]. ANFIS, however, is a potential soft computational modelling technique that combines the power of ANN with fuzzy logic [6–8]. ANFIS, as with the ANN, learns from training data with any complex relationships, then implements the solutions on a fuzzy inference system (FIS). ANFIS can use FIS to define hidden layers and to improve its predictive ability; thus, it eliminates the difficulty of defining the hidden layers that often exist in ANN; however, the number of membership functions (MFs) should be defined per input. The number of MFs depends on the number of the existing dataset. Their ability to overcome problems with experimental and deterministic models makes them ideal for complex chemical processes. However, determining the structure of ANN has become a major challenge in developing a highly accurate model [9]. Consequently, Hosoz et al. [10] pointed out that ANFIS, according to other studies, can predict more accurately than ANN. However, in other studies, it has been stated that the accuracy of these techniques depends on how they are implemented and their applications [11]. Considering all the aforementioned facts, in the present study, we have made an attempt to develop and examine an ANFIS model to predict the properties of ionic liquid binary mixtures. Our measured density and refractive index of binary ionic liquid mixtures as well as the available published data on these properties have been used in this work.

#### **2. Properties of Binary Liquid Mixtures**

#### *2.1. Molar Volume*

For ideal liquid mixtures, the molar volume is defined as:

$$
v\_{\text{ideal\\_mix}} = \sum \mathbf{x}\_i \mathbf{v}\_i \tag{1}$$

where *vmix* is the molar volume of the mixture, *vi* is the individual molar volume of component *i*, and *xi* is mole fraction of component *i*. Many liquids do not form ideal mixtures and hence do not show volume additivity. The deviation from ideality can be calculated by introducing excess molar volume term to the previous equation. Hence, the equation is written as:

$$
\upsilon\_{\text{real\\_mix}} = \upsilon\_{\text{ideal\\_mix}} + \upsilon^{\text{excess}} \tag{2}
$$

#### *2.2. Mixture Density*

The density of a mixture can be defined as the overall mass of mixture occupying one unit volume. It can be calculated by:

$$
\rho\_{\text{mix}} = \frac{m\_{total}}{V\_{total}} \tag{3}
$$

where *ρmix* is the mixture density, *mtotal* is the total mass of mixture, and *Vtotal* is the total volume of mixture. For ideal liquid mixtures, using volume additivity, this equation can be written in terms of an individual component's densities as follows:

$$\frac{1}{\rho\_{\text{ideal\\_mix}}} = \sum \frac{x\_i}{\rho\_i} \tag{4}$$

where *ρi* is the density of component *i* and *xi* is the mass fraction of component *i*. The average absolute relative difference percent (AARD%) is a good statistical parameter for analyzing the success of the proposed correlations for different properties such as density, which is defined as:

$$AARD\% = \frac{100\sum \left| \frac{\rho\_{ideal\ mix} - \rho\_{\min,\ exp}}{\rho\_{\min,\ exp}} \right|}{n} \tag{5}$$

#### *2.3. Refractive Index*

There are several mixing rules for the refractive index of mixtures in the literature. The most well-known correlations which have been used in this work are the following:

$$\frac{n\_{\rm mix}{}^2 - 1}{n\_{\rm mix}{}^2 + 2} = \sum \frac{n\_i{}^2 - 1}{n\_i{}^2 + 2} \,\phi\_i \tag{6}$$

where *nmix* is the refractive index of the mixture, *ni* is the refractive index of pure component *i*, and *φi* is the volume fraction of component *i* in the mixture.

$$n\_{\rm mix} - 1 = \phi\_1(n\_1 - 1) + \phi\_2(n\_2 - 1) + \dots + \phi\_n(n\_n - 1) \tag{7}$$

$$n\_{\rm mix} = \phi\_1 n\_1 + \phi\_2 n\_2 + \dots + \phi\_n n\_n \tag{8}$$

$$\frac{n\_{\rm mix}{}^2 - n\_1{}^2}{n\_{\rm mix}{}^2 + 2n\_1{}^2} = \sum\_{j \neq 1} \frac{n\_i{}^2 - n\_1{}^2}{n\_1{}^2 + 2n\_1{}^2} \phi\_{\bar{i}} \tag{9}$$

.

$$\frac{m\_{\rm mix} - n\_1}{n\_1} = \frac{3}{2} \sum\_{i \neq 1} \frac{m\_i^2 - 1}{m\_i^2 + 2} \phi\_i \tag{10}$$

where *mi* = *ni n*1

#### **3. Materials and Experiments**

The ionic liquids used in this work are 1-butyl-3-methylimidazolium thiocyanate ([BMIM][SCN]), 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), 1-hexyl-3 methylimidazolium tetrafluoroborate ([HMIM][BF4]), and 1-hexyl-3-methylimidazolium hexafluorophosphate ([HMIM][PF6]). These ionic liquids were supplied by Io-li-tec and used as received. However, new measurements for the density and refractive index were taken for the pure ionic liquids to be used as reference. Table 1 shows the purity of each ionic liquid reported by Io-li-tec and their molecular weights.

**Table 1.** Purity of the ionic liquids used in this work.

A pipette was used to transfer exact amounts of ionic liquids in a graduated cylinder to measure the total volume, each with uncertainty of 0.05 and 0.1 cm3, respectively. A mass balance of an uncertainty of 1 × 10−4 g was used to measure the mass of the samples. The refractive index was measured using a programmable digital KEM Refractometer (Kyoto Electronics Manufacturing Co., LTD., Model RA 620, Kyoto, Japan) connected to a water bath to maintain constant temperature. The uncertainty in the refractive index measurement is 1 × 10−5, and the uncertainty in the temperature measurement is 0.1 K. The density was measured using an Anton Paar U-tube Densitometer (Model DMA 4500 M, Anton Paar GmbH, Graz, Austria) connected to a water bath. The uncertainty in the density measurement is 5 × 10−5 g cm−3, while the uncertainty in the temperature measurement was 0.1 K.

The density and refractive index of all samples were measured at 20 ◦C for the pure ionic liquids using an Anton Paar U-tube Densitometer and a Programmable Digital KEM Refractometer, respectively. The temperature was constantly maintained at 20 ◦C by connecting both the densitometer and the refractometer to a water bath set to a temperature of 20 ◦C. Binary mixtures of different ionic liquids were prepared from different volume compositions. The mass of each ionic liquid as well as the total mass of the mixture were measured before transfer to the graduated cylinder. A droplet was taken to be used in the refractometer to measure the refractive index. The remainder of the mixture was used to measure the mixture density using the density meter.

#### **4. The Developed ANFIS Model and EFAST Sensitivity Analysis**

Fuzzy logic is an appropriate technique for solving complex and nonlinear problems. ANNs have a strong ability to learn from existing data. Fuzzy logic theory is a powerful tool to deal with uncertainty. In general, fuzzy logic is an approach to calculate the degree of accuracy instead of using two-state true or false logic. Therefore, combining fuzzy logic theory with ANNs could provide great results for describing complex patterns, which is called ANFIS modelling. FIS assigns fuzzy rules and a membership function (MF) which ANN can optimize. Takagi–Sugeno and Mamdani are two well-known structures of FISs. Each FIS consists of a number of fuzzy rules, and each fuzzy rule has an antecedent and a consequent. In Mamdani-type FISs, both antecedents and consequents include fuzzy values; however, in Takagi–Sugeno-type FISs, the consequent of fuzzy rules are in the form of a fixed number (for zero type Takagi–Sugeno FISs) or a linear combination of inputs; this type of FISs are often used in ANFIS modelling. In this study, an ANFIS model was developed using the Takagi–Sugeno structure with the Neuro-Fuzzy Designer app in MATLAB 2017a software [9]. The ANFIS structure comprises four layers, which are fuzzy, product, consequent calculation, and output layer. The first layer includes antecedent

fuzzy values (also known as membership functions), the inputs enter these fuzzy values, and a membership grade is produced for each fuzzy value in each rule. In layer 2, the product of membership grades in a fuzzy rule is used as the firing strength of the rule in this this research. Then, in layer 4 (in parallel with layers 1 and 2), the output of each rule is calculated using the input values. In the last layer, the output of the FIS is calculated by the output values and firing strengths of all rules. In this research, the weighted sum of outputs was used, where the weight of each rule output is the firing strength of the same rule. The unknowns of this modelling problem were the number of rules and fuzzy values (membership functions) of rules and consequent parameters. These were identified by using the experimental data.

In this study, various membership functions were investigated for their use in the rules' antecedents, such as the triangular-shaped membership function (trimf) and others, for which the details can be found elsewhere [12]. The result of this comparison is given in Section 6.

To estimate the density parameter using ANFIS, 1670 datasets were collected from the literature, which were applied for model training and cross validation. Cross validation partition defines a random partition on a dataset. This partition is used to define training and validation sets for validating a model. In this study, the early stopping method was used for preventing overfitting and the total dataset partitioned into training (85%) and holdout cross validation (15%) partitions. The holdout cross validation method creates a random nonstratified partition for holdout validation on n observations. Then, to determine the predictive power of the model, the measured data from this study (16 samples) were introduced to the model as external validation or a test dataset. The same procedure was followed for modelling the refractive index parameter, in which 149 data were collected and utilized from the published data for training and validation. Finally, 16 new measured data from this study were entered into the model for external validation. The hybrid-learning algorithm (as detailed in [13]) was used for parameter estimation, and the validity of the optimized ANFIS model was evaluated using experimental test data. The coefficient of determination (*R*2), the root-mean-squared error (RMSE), and average absolute relative deviation (AARD%) were calculated to evaluate the model's performance [14,15].

$$R^2 = \frac{1 - \sum\_{i=1}^{n} \left(\boldsymbol{\chi}\_p - \boldsymbol{\chi}\_c\right)^2}{\sum\_{i=1}^{n} \left(\boldsymbol{\chi}\_p - \boldsymbol{\underline{\chi}\_c}\right)^2} \tag{11}$$

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left(\chi\_{\varepsilon} - \chi\_{p}\right)^{2}} \tag{12}$$

$$AARD\% = \frac{100}{n} \sum\_{i=1}^{n} \frac{\left| \Upsilon\_{\varepsilon} - \Upsilon\_{p} \right|}{\Upsilon\_{\varepsilon}} \tag{13}$$

where *Ye*, *Yp*, and *Ye* show the actual response, predicted response, and the average of the actual response, respectively, and *n* is the number of datasets.

For complex nonlinear models, such as the artificial intelligence models, global sensitivity analysis (GSA) techniques are able to provide appropriate information about parameter sensitivity. In the present study, the extended Fourier amplitude sensitivity test (EFAST), which is one of the efficient and well-known GSA methods, was applied for sensitivity analysis in MATLAB 2017 software. FAST is a variance-based global sensitivity analysis technique, which is based on conditional variances, indicating the individual or interaction effects of the uncertain inputs on the response parameter [16].

#### **5. Experiments**

#### *5.1. Pure Ionic Liquids*

Density and refractive index of the pure ionic liquids measured at 20 ◦C are shown in Table 2.

**Table 2.** Density and refractive index of the pure ionic liquids at 20 ◦C.

a Literature data at 298.15 K [17].

These values are used as references for the pure components in the analysis. Ionic liquid mixtures prepared for the experiments were labeled, and their measured masses and volumes at 20 ◦C are shown in Table 3.

Table 3 shows the volume and mass of each component in the mixture. The mass of each component was used to calculate the mass fraction and mole fraction needed for the rest of calculations.

#### *5.2. Mixtures of Ionic Liquids*

5.2.1. Molar Volume and Density of Ionic Liquid Mixtures

Table 4 shows the measured mixture density, ideal mixture density, AARD%, measured mixture molar volume, ideal mixture molar volume, excess molar volume, and AARD% of the prepared ionic liquids.

**Table 4.** Measured and calculated volumetric data for the ionic liquid mixtures studied in this work.

#### 5.2.2. Refractive Index of Ionic Liquid Mixtures

Table 5 shows the experimental refractive indices of the ionic liquid mixtures and the calculated values using different empirical mixing rules.

**Table 5.** Experimental refractive indices of the ionic liquid mixtures and the calculated values using different empirical mixing rules.

As we can see from Table 5, the refractive index of the ionic liquid mixtures can be confidently estimated using any of the discussed empirical formulae since the average relative error is around 0.25% for each correlation. However, Heller's relation (H) best estimates the refractive index of these ionic liquid mixtures with an average relative error of 0.242%.

#### **6. ANFIS Modelling**

The ANFIS models, developed to predict the density and refractive index of ionic liquid mixtures, are shown in Figures 1A and 2A. In this structure, we have employed the Takagi–Sugeno-type FIS with Gaussian curve membership functions. The ANFIS model has seven inputs of temperature (T), pressure (P), BMIM (mole fraction of BMIM ion), HMIM (mole fraction of HMIM ion, BF4 (mole fraction of BF4 ion), PF6 (mole fraction of PF6 ion), and SCN (mole fraction of SCN ion) for density and refractive index prediction. The grid partition technique is used to generate the rules for the model. The obtained results showed that the Gaussian membership function (gaussmf), compared to other membership functions, has less prediction errors in both models. Figures 1B and 2B illustrate the RMSE of the models' training and validation stages. During the training and validation process of the ANFIS model, the RMSEs were plotted versus the number of epochs. The RMSE reduces and then remains constant after some epochs. The RMSE values of the validation step for the density and refractive index models were equal to 8.730 and 7.45 × 10−3, respectively. The regression curves plotted in Figures 1C and 2C display the model outputs, which show a very satisfactory performance. This comparison showed a good consistency between the predicted and actual responses of the ANFIS models.

We have used some statistical parameters as shown in Table 6 to examine the performance of the developed models.

**Table 6.** The performance of the statistical parameters for the proposed models.

It is noteworthy that the ranges of error parameters for two responses (density and refractive index) are suitable at the training, validation, and test stages. The use of more data in the training and validation stages for density resulted in high predictive power, therefore the test data that were externally validated (not used in the training stage) resulted in predictions with higher accuracy. Moreover, a variance-based global analysis was performed using an extended EFAST method to determine which parameter had the greatest effect on the density and refractive index [18]. According to Figure 3A, the first three main factors affecting density are PF6, SCN, and pressure. In addition, according to Figure 3B, the most effective input parameters for the refractive index were SCN, pressure, and PF6. The coefficient values of different parameters are given in Figure 3.

Figures 4 and 5 show the three-dimensional plots of the developed models for the density and refractive index (n). As shown in Figure 4A,B, the density parameter often decreases with increasing temperature and increases with increasing pressure. In addition, an increase in parameters BMIM and SCN lead to a decrease in density (Figure 4B,E). BF4 has very little effect on density (Figure 4D). HMIM and PF6 have a positive correlation with density, as shown in Figure 4C,E. It is evident from Figure 5A that temperature has a negative effect on refractive index, and pressure has shown a non-uniform effect on it. However, the effect of the temperature on the refractive index is very small compared to the effect of pressure. In addition, an increase in parameters BMIM, BF4, and SCN leads to a decrease in the refractive index (Figure 5B–D). HMIM has very little effect on

the refractive index (Figure 5C). PF6 has a positive correlation with the refractive index, which is shown in Figure 5D. The model dataset contains 1670 density values over a temperature range of 220–472 K and a pressure range of 100–300,000 kPa collected from the NIST ILThermo database [19]. The model dataset contains 1670 density values over a temperature range of 220–472 K and a pressure range of 100–300,000 kPa collected from the NIST ILThermo database [19]. Our dataset for the refractive index which contains 149 values also has been collected from the NIST ILThermo database [19] in the range of 280–353 K for temperature, and the range of 81–116 kPa for pressure. This collected database is available in the Supplementary file in excel.

**Figure 1.** (**A**) Developed ANFIS structure, (**B**) training error curve, (**C**) regression between ANFIS predictions, and experimental results for density.

**Figure 2.** (**A**) Developed ANFIS structure, (**B**) training error curve, (**C**) regression between ANFIS predictions, and experimental results for refractive index.

**Figure 3.** Relative importance of the input parameters on (**A**): density and (**B**): refractive index (n).

**Figure 4.** Three-dimensional mesh plot of the density variation using ANFIS model versus (**A**)–Temperature and Pressure, (**B**)–BMIM and Temperature, (**C**)–HMIM and Temperature, (**D**)–Pressure and BF4 and (**E**)–PF6 and SCN.

**Figure 5.** Three-dimensional mesh plot of the refractive index (n) variation using ANFIS model Versus, (**A**)–Pressure and Temperature, (**B**)–Pressure and BMIM, (**C**)–HMIM and BF4 and (**D**)–SCN and PF6.

#### **7. Conclusions**

Density and refractive index of different binary mixtures of ionic liquids were studied in this work. Some data were generated experimentally in this work and the rest of required data were collected from the literature. The effects of different variables such as temperature, pressure, and the molar concentrations of different functional groups in the ionic liquids were investigated. For analyzing the data, we first examined different models including empirical models for these properties. The deviation from the ideal mixture volume was calculated and found to be 0.78%. Therefore, it is a very accurate assumption to assume an ideal mixture and apply a volume additivity rule. Furthermore, the refractive indices of the binary ionic liquid mixtures were measured and compared with the estimated values using different empirical mixing rules. All of the empirical rules showed good performance for estimation of the refractive index of the binary ionic liquid mixtures, with an average percentage error around 0.25%. However, Heller's relation was found to be the best model to estimate these mixtures' refractive index with an average relative error of only 0.242%. For gaining a deep understanding of the effects of the different parameters on the density and refractive index of the studied mixtures, we have also developed artificial intelligence models. An ANFIS model was developed to predict a density and refractive index, and the grid partition technique was implemented. Our results showed that the Gaussian membership function, compared to other membership functions, has a low prediction error. Based on obtained results, the developed model showed excellent performance for predicting the density and refractive index of various mixtures, with overall R2, RMSE, and AARD% values of 0.985, 8.730, 0.649%, and 0.972, 7.45 × 10−3, and 0.444%, in cross validation, and 0.968, 7.274, 0.368%, and 0.948, 7.32 × 10−3, and 0.319% in the external validation stages, respectively. According to the sensitivity analysis using the EFAST method, the most effective input parameters for both properties were found to be SCN, pressure, and PF6.

**Supplementary Materials:** Supplementary data associated with this article can be found at: https: //www.mdpi.com/article/10.3390/liquids2040025/s1.

**Author Contributions:** Conceptualization, G.R.V.-N.; methodology, G.R.V.-N.; software, F.M.; formal analysis, G.R.V.-N. and F.M.; resources, G.R.V.-N.; data curation, M.H.; writing—original draft preparation, G.R.V.-N., F.M. and M.H.; writing—review and editing, F.M., M.M. and G.R.V.-N.; project administration, G.R.V.-N.; funding acquisition, G.R.V.-N. and M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors are thankful to Sultan Qaboos University for the financial support through the internal grant project number IG/ENG/PCED/22/02.

**Data Availability Statement:** Not applicable.

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

#### **References**