**2. Current Treatment Options and Limitations**

The progressive erosion of articular cartilage is a prevalent symptom of OA [35].  Disruption of the articular cartilage prevents pain-free movement and affects the load-bearing abilities of the joint. Current treatments for OA can include intra-articular joint injections of steroids and arthroscopic lavage with debridement; however, these may have short-term benefits without long-term benefit to the cartilage [22,37,38]. Anti-inflammatory and analgesic drugs may help to address some of the symptoms of OA, but they do not tackle the fundamental pathologies involved in the inexorable degenerative process, in addition to having significant side effects associated with prolonged use [39–42]. Surgery and joint replacement, if possible in the early stages of OA, are expensive and may need to be performed multiple times during an individual's life [22,43]. Alternative modalities of treatment may well be helpful in the short term, but may not be a sustainable strategy for OA treatment and potential prevention [44,45].

The best way to combat the root cause of joint degeneration in OA may be through the exploration of the various possibilities that genome editing offers [46,47]. There is increasing evidence that genetic and epigenetic modifications play a substantive role in OA; however, it has been difficult to separate the individual effects from the combined effects of genetic and environmental factors acting together to cause progressive joint degeneration [48–51]. Characterizing and analyzing the genetic factors underpinning the pathology of OA may provide viable options for the diagnosis, prognosis, and development of novel treatment targets for future personalized biological therapies.

#### **3. CRISPR**/**Cas**

Several gene therapy systems such as viral, engineered scaffold, and other approaches hold promise [52]. However, while such systems hold promise, the advantages are offset by some potential disadvantages. Here we focus on the CRISPR/Cas9 system, a very powerful gene therapy tool.

CRISPR/Cas is a novel, versatile, and promising genome-editing technique that is opening up new avenues and possibilities in the effective treatment of OA [53] and other degenerative joint diseases [54,55]. CRISPR is an acronym for "clustered regularly interspaced short palindromic repeats", discovered through investigation of the prokaryotic adaptive immune system. It was identified as an effective system used by bacteria and archaea to remember infecting agents such as phage viruses and destroy them upon subsequent exposure, similarly to the memory cells in the human immune system. When paired with different proteins, specifically enzymes such as Cas, that are produced naturally by the prokaryotic cells, the CRISPR system can be used to make deletions, insertions, substitutions, or other changes at specific sites of the prokaryotic and eukaryotic genome [56,57]. From finding a cure for cancer, to treating sickle-cell disease, to growing drought- and pest-resistant crops, CRISPR has many exciting possibilities and potential in several fields [58].

The prokaryotic CRISPR/Cas system has three main components: a Cas nuclease, a crRNA (CRISPR RNA), and a tracrRNA (trans-activating crRNA). In bacterial cells, the CRISPR/Cas system works by recognizing the invading bacteriophage DNA, chopping it up into several pieces, and incorporating them into its DNA. These CRISPR pieces are then transcribed, generating a crRNA and a tracrRNA to create a double-stranded RNA structure that can recruit the Cas proteins. When the offending phage is encountered again, the CRISPR/Cas system is directed to a specific location on the foreign DNA because of a protospacer adjacent motif (PAM) short nucleotide base sequence which is upstream of the crRNA targeted sequence. The Cas protein is programmed to be the "molecular scissors" of the system which carries out the cutting, splicing, and any other editing that is desired [59–61]. The therapeutic application of CRISPR/Cas is illustrated in Figure 2.

**Figure 2.** CRISPR/Cas mechanism. Trans-activating RNA (orange) with CRISPR RNA (blue) the guide RNA. The guide RNA assembles with the Cas9 protein to form the CRISPR complex. Using the guide RNA for specificity, the CRISPR complex binds to the target DNA. Transgenic DNA can be inserted using homology arm inserts.

The most widely used of the six major types of CRISPR/Cas system, the Type II system, is derived from the *Streptococcus pyogenes* bacteria. It uses the Cas9 protein because of its wide working range and efficiency [62]. The CRISPR/Cas9 system that is used currently by researchers and scientists worldwide consists of a single guide RNA (sgRNA) with a binding end (analogous to tracrRNA) for the Cas9 nuclease to attach and a targeting end (similar to crRNA) with nucleotide base pairs that are complementary to the DNA sequence that is meant to be edited (Figure 2). Only the targeting end of the sgRNA needs to be synthesized for any specific targeting sequence, while the binding end does not need to be redesigned every time, thus reducing the time needed to get the tool ready for editing. Cas9 recruitment to the exact DNA target sequence is mediated by the sgRNA. Cas9-induced double-stranded breaks (DSBs) are repaired either by spontaneously nonhomologous end joining (NHEJ) or by homology-directed repair (HDR) using a synthetic donor DNA template [63]. CRISPR/Cas RNA-guided DNA endonuclease genome targeting is much easier to design and apply when compared to other available site-specific editing tools using engineered nucleases such as transcription activator-like effector nuclease (TALENS) and zinc finger nucleases (ZFNs), which are controlled by protein–DNA interactions. CRISPR/Cas is also much more cost- and time-effective because researchers only need to code for a small section of sgRNA [64].

#### **4. Mesenchymal Stem Cells and Tissue Regeneration**

Tissue regeneration and self-renewal of articular cartilage, in general, is a very limited process [65]. The avascularity of articular cartilage may hinder progenitor cells access to the site of injured cartilage [66]). It may also limit molecular factors that are vital to extracellular matrix repair and homeostasis [67–70].

Chondrocytes originate from mesenchymal stem cells [71,72]. Bone-marrow-derived MSCs (BM-MSCs) have much promise in aiding articular cartilage repair due to their proximity to the joint, high differentiation capability, and ability to secrete different growth, anti-inflammatory, and immunomodulatory factors [73–77]. They could affect a clinically relevant improvement in joint pain and function. Additional studies are needed, however, to demonstrate the efficacy of cultured

versus noncultured BM-MSCs and the best ways to deliver them into the joint. MSCs derived from fetal cells also have therapeutic properties, but ethical concerns have been raised about using them for treatment and therapeutic applications [78,79]. Additional challenges arise due to the potential of fetal MSCs to differentiate into several different types of cells, which might be more difficult to control and direct [76,80,81]. The capabilities of MSCs are usually age-dependent. MSCs have a short lifespan but can secrete paracrine factors that may be beneficial in tissue regeneration [81,82]. In addition to BM-MSCs, MSCs derived from other sites such as adipose tissue can be isolated, expanded, characterized, and used to regenerate cartilage [83,84]. However, MSCs tend to form mechanically inferior fibrocartilage instead of the glassy, hyaline cartilage that covers the ends of bones at articulating joints [85].


**1. Introduction**

One of the most common models used in pre-clinical studies is nude mice implanted with brain tumors. In fact, owing to a deficiency in their immune systems, nude mice allow many tumor models to be studied and a wide range of therapeutic treatments to be investigated.

The best way to evaluate the efficiency of a treatment is to compare the kinetics of the tumor volume between a control group and a treatment group [1-3]. Since brain tumors generally evolve very quickly (7 to 15 days) in mice, the tumor must be detected early and characterized daily.

The advantages of non-invasive imaging methods are evident compared with conventional methods such as histochemistry, where animal sacrifice, end-point analysis only, and 2D tumor-diameter measurement are mandatory.

However, obtaining images of high spatial resolution and high contrast for the same animal in a longitudinal study is not trivial.

As in clinical MR imaging, the tumor can be detected in two possible ways. The first consists of using a gadolinium-based contrast agent injected intravenously to visualize the breakdown of the blood–brain barrier. Using a T1-weighted 3D gradient-echo sequence, high-resolution images can be obtained in a reasonable acquisition time. Nevertheless, because of the injuries caused by repeated injection of contrast agent into the tail vein, experiments cannot be performed frequently [1]. The other way consists of using T2 weighted sequences. RARE imaging, with or without magnetization transfer preparation [3– 5], allows small tumors to be detected noninvasively. The sequence is usually acquired in multi-slice 2D imaging in order to limit the total acquisition time. However, high-resolution,

3D TrueFISP MRI Provides Accurate Longitudinal Measurements of Glioma Volumes in Mice 127

 (1) The actual resolution is inversely proportional to the relaxation time, T2\*, and to the

 (2) The advantages of using intense magnetic field gradients are thus obvious, particularly at

Commercial gradient systems have been developed with intensities of greater than 400 mT/m over 10 cm, up to 1 T/m over 3 cm. Because the target diameter of these gradient systems is spatially limited, they can only be used to study animals such as rats or mice.

Fig. 1. Photograph of a 1-T/m gradient system. The system can be inserted into a magnet equipped with a 12-cm-diameter tunnel and can contain an antenna up to 6 cm in diameter.

Image quality is also significantly affected by the choice of antenna. The S/N depends entirely on this component as it is proportional to the square root of the antenna's quality factor, Q. Thus, a well-designed antenna is recommended. In addition, the S/N is directly

 (3) Optimal image quality will therefore be obtained using an antenna with a size and shape perfectly adapted to the zone to be imaged. Several types of antennae have been developed and can be used to meet these criteria. Volumetric emission/reception antennae are the most common. They provide a very homogeneous radio-frequency field, often required when

proportional to the filling factor for the antenna, represented by η in Eq. [3].

The gradient is linear over a distance of approximately 3 cm.

**2.3 Coil**

gradient intensity and application time (Eq. [2]).

strong magnetic fields, with very short T2\*.

accurate 3D information is very important in longitudinal studies such as, for instance, the evaluation of a therapeutic treatment.

An alternative to RARE T2 [6] or 3D contrast-enhanced T1 imaging is fully balanced SSFP imaging (also called bSSFP, TrueFISP or FIESTA) [7]. In fact, it has recently been shown that this sequence can be used at high field, in 3D, to detect tumors of very small size [8]. The advantage of this sequence is the ability to combine the speed of 3D gradient echo and T1/T2 contrast.

The purpose of this study is to demonstrate that a 3D TrueFISP MRI sequence is applicable, at high magnetic field, to glioma-bearing mouse models in longitudinal studies. Theoretical considerations of tumor contrast and signal-to-noise ratio as a function of sequence parameters (TE/TR/flip angle) were carried out and compared with experimental data.

The 3D TrueFISP MRI sequence was also compared with the sequence most widely used in clinical applications: 2D RARE. Finally, the sequence was used to perform accurate longitudinal measurements of glioma volumes in mice.


**About the Editors**

#### **Yuya Kumagai**

Dr. Yuya Kumagai received B.S., M.S., and Ph.D. degrees in Fisheries Science from the Hokkaido University, Hakodate, Japan in 2005, 2008, and 2010, respectively. He is currently an Associate Professor of Faculty of Fisheries Science with Hokkaido University, Hakodate, Japan. His research interests include Marine Biology and Biochemistry, the characterization of functional materials from seaweed, enzymes, and the modification of them.

#### **Hideki Kishimura**

Dr. Hideki Kishimura is a Professor of Fisheries Sciences, Hokkaido University in Hokkaido, Japan. His research fields are the "purification of biochemical compounds from fisheries by-products and underused marine organisms" and the "determination of their structures and investigation of their health benefits". He is a society board member of the Japanese Society for Marine Biotechnology and a secretary board member of the Hokkaido Branch of the Japanese Society of Fisheries Science and serves on the Editorial Board of Marine Drugs.

#### **Benwei Zhu**

Dr. Benwei Zhu is a Professor at College of Food Science and Light Industry, Nanjing Tech University in Nanjing, China. He was also a Visiting Researcher in Prof. Kishimura's laboratory in 2020-2021. His research interests include the discovery and enzymatic and structural characterization of new marine polysaccharide-degrading enzymes.


**4.1 Mineral identification for the solid phase**

For mineral identification when enough new solid phase appeared either in the stable equilibrium system or in the metastable equilibrium system, the wet residue mixtures were taken from the solution according to the experimental method. Firstly, as to the minerals of Na2B4O7·10H2O and K2B4O7·4H2O, the former belongs to monoclinic system, and the dual optical negative crystal i.e. 2ν(-) whereas the later belongs to trimetric system, and the dual optical positive crystal i.e. 2ν(+). Secondly, to the minerals NaCl and KCl, they can be identified through the property of refractive index. The refractive index of NaCl is higher than that of KCl. Observed with a XP-300D Digital Polarizing Microscopy using an oil immersion method, the crystal photos of the single and orthogonal polarized light on representative solid phases in the invariant points (NaCl + KCl + Na2B4O7·10H2O) and (Na2B4O7·10H2O + K2B4O7·4H2O + KCl) are presented in Figure 3.

single polarized light (10×10) orthogonal polarized light (10×10) (a) Invariant point (NaCl + KCl + Borax)

metastable evaporation, the solutions were not stirred, and the crystal behavior of solid phase was observed periodically. When enough new solid phase appeared, the wet residue mixtures were taken from the solution. The solids were then approximately evaluated by the combined chemical analysis, of XP-300D Digital Polarizing Microscopy (Shanghai Caikon Optical Instrument Co,. Ltd., China) using an oil immersion, and further identification with X-ray diffraction (X'pert PRO, Spectris. Pte. Ltd., The Netherlands). Meanwhile, a 5.0 cm3 sample of the clarified solution was taken from the liquid phase of each polyethylene container through a filter pipette, and then diluted to a 250.0 cm3 final volume in a volumetric flask filled with DDW for the quantitative analysis of the compositions of the liquid phase. Some other filtrates were used to measure the relative physicochemical properties individually according to the analytical method. The remainder of the solution continued to be evaporated and reached a new metastable

For mineral identification when enough new solid phase appeared either in the stable equilibrium system or in the metastable equilibrium system, the wet residue mixtures were taken from the solution according to the experimental method. Firstly, as to the minerals of Na2B4O7·10H2O and K2B4O7·4H2O, the former belongs to monoclinic system, and the dual optical negative crystal i.e. 2ν(-) whereas the later belongs to trimetric system, and the dual optical positive crystal i.e. 2ν(+). Secondly, to the minerals NaCl and KCl, they can be identified through the property of refractive index. The refractive index of NaCl is higher than that of KCl. Observed with a XP-300D Digital Polarizing Microscopy using an oil immersion method, the crystal photos of the single and orthogonal polarized light on representative solid phases in the invariant points (NaCl + KCl + Na2B4O7·10H2O) and

> single polarized light (10×10) orthogonal polarized light (10×10) (a) Invariant point (NaCl + KCl + Borax)

Borax

equilibrium.

**4. Experimental results**

**4.1 Mineral identification for the solid phase**

(Na2B4O7·10H2O + K2B4O7·4H2O + KCl) are presented in Figure 3.

Borax

KCl NaCl

single polarized light (10×10) orthogonal polarized light (10×10)

(b) Invariant point (KCl + Borax + K2B4O7·4H2O)

Fig. 3. Identification of the invariant points for the solid phase in the reciprocal system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) with a polarized microscopy using an oil-immersion method. (a), the invariant point (NaCl + KCl + Na2B4O7·10H2O); (b), the invariant point (KCl + Na2B4O7·10H2O + K2B4O7·4H2O).

The metastable equilibria solid phases in the two invariant points are further confirmed with X-ray diffraction analysis, and listed in Figure 4, except in the invariant points (NaCl + KCl + Borax) in Figure 4a which shows that the minerals KCl, NaCl, Na2B4O7·10H2O and a minor Na2B4O7·5H2O are existed. The minor of Na2B4O7·5H2O maybe is formed due to the dehydration of Na2B4O7·10H2O in the processes of transfer operation and/or grinding.

(a), the X-ray diffraction photograph and the analytical data for the invariant point (NaCl + KCl + Borax)

Stable and Metastable Phase Equilibria in the Salt-Water Systems 409

100.00 100.00 0.00 0.00 100.00 96.79 85.85 0.00 11.98 24.64 41.25 96.67 90.05 90.59 94.45 93.36 92.13 93.83 95.55 96.67 98.30 96.19 96.05

Jänecke index

0.00 100.00 0.00 100.00 30.03 0.00 100.00 69.24 72.33 72.41 73.74 45.60 54.55 88.46 81.45 59.79 57.77 51.84 48.48 45.60 35.89 47.94 6.12

2- *J*(2Cl-) *J*(2K+) *J*(H2O)

*J*B, /[mol/100mol(2Na++2K+)] Equilirium

1807.5 2310.8 34623.3 7864.1 1526.2 1997.5 1807.8 5649.7 3947.5 3496.9 3181.6 1427.4 1672.8 2123.7 2191.0 1670.9 181.0 1602.8 1386.6 1427.4 1462.7 1406.5 1830.4

0 20 40 60 80 100

*J*(**2K+** )

**E**

**E F 1**

**E4**

0

2000

**E 3**

4000

6000

solid phase\*\*

NaCl KCl N10 K4 NaCl+KCl NaCl+N10 KCl +K4 N10 + K4 N10 + K4 N10 + K4 N10 + K4 N10 + K4 KCl + N10 + K4 KCl+K4 KCl+K4 KCl+K4 KCl+K4 KCl + N10 KCl + N10 NaCl + KCl NaCl + KCl NaCl+KCl+N10 NaCl+N10

No.

1 2 3 4 5, E1 6, E2 7, E3 8, E4 9 10 11 12 13, E 14 15 16 17 18 19 20 21 22, F 23

10.25 0.00 0.72 0.00 8.02 9.60 0.00 1.15 1.38 1.57 1.59 3.50 4.72 1.13 1.57 4.18 4.15 5.27 6.11 6.40 7.50 6.16 9.73

Composition of the solution 100 *w*B\*

Na+ K+ Cl- B4O7

15.80 12.58 0.00 0.00 17.68 14.33 12.35 0.00 0.92 12.35 3.83 12.24 14.55 12.65 12.35 14.96 13.96 15.50 17.52 17.52 17.73 17.55 15.35

\* *w*B is in mass fraction; \*\* K4, K2B4O7·4H2O; N10, Na2B4O7·10H2O.

0 20 40 60 80 100

*J*( **2Cl- Na2B4O7** ) **2NaCl**

**Na2B4O7**·**10H2O**

**K2B4O7 2KCl**

**K2B4O7**·**4H2O**

0

20

40

*J*( **2K+** )

60

**E4**

80

100

Table 3. Stable solubilities of the system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K

**E F**

**KCl**

**E3**

**E1**

**NaCl**

 (a) dry-salt phase diagram (b) water-phase diagram Fig. 5. Stable phase diagram of the quaternary system (NaCl- KCl – Na2B4O7 - K2B4O7 - H2O)

0

2000

**E2**

4000

*J*(**H2 O**)

6000

**E 2**

at 298.15 K. (a), dry-salt phase diagram; (b), water-phase diagram.

0.00 0.00 2.41 9.42 0.00 1.04 4.48 12.54 14.77 1.59 11.97 7.62 3.17 2.78 1.59 2.33 2.61 2.58 1.79 1.32 0.67 1.52 1.35

0.00 13.87 0.00 4.74 5.85 0.00 15.87 4.36 6.11 11.74 7.55 11.39 9.62 13.44 11.74 10.56 9.65 9.43 9.83 9.10 7.13 9.64 1.05

(b), the X-ray diffraction photograph and the analytical data for the invariant point (KCl + Borax + K2B4O7·4H2O)

Fig. 4. The X-ray diffraction data of the invariant points. (a), the invariant point (NaCl + KCl + Na2B4O7·10H2O); (b), the invariant point (Na2B4O7·10H2O + K2B4O7·4H2O + KCl).

#### **4.2 Stable phase equilibrium of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K**

The stable phase equilibrium experimental results of solubilities of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K were determined, and are listed in Table 3, respectively. On the basis of the Jänecke index (*J*B, *J*B/[mol/100 mol(2Na+ + 2K+)]) in Table 3, the stable equilibrium phase diagram of the system at 298.15 K was plotted and shown in Figure 5.

#### **4.3 Metastable phase equilibrium of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K**

The experimental results of the metastable solubilities and the physicochemical properties of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K were determined, and are listed in Tables 4 and 5, respectively. On the basis of the Jänecke index (*J*B, *J*B/[mol/100 mol(2Na+ + 2K+)]) in Table 4, the metastable equilibrium phase diagram of the system at 308.15 K was plotted (Figure 6).

No. Visible Ref. Code Chemical Formula Score Scale

KCl

(b), the X-ray diffraction photograph and the analytical data for the invariant point

Fig. 4. The X-ray diffraction data of the invariant points. (a), the invariant point

K2(B4O5(OH)4)(H2O)2 B4O5(OH)4(Na2(H2O)8

(NaCl + KCl + Na2B4O7·10H2O); (b), the invariant point (Na2B4O7·10H2O + K2B4O7·4H2O +

The stable phase equilibrium experimental results of solubilities of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K were determined, and are listed in Table 3, respectively. On the basis of the Jänecke index (*J*B, *J*B/[mol/100 mol(2Na+ + 2K+)]) in Table 3, the stable equilibrium phase diagram of the system at 298.15 K was plotted and shown in

The experimental results of the metastable solubilities and the physicochemical properties of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K were determined, and are listed in Tables 4 and 5, respectively. On the basis of the Jänecke index (*J*B, *J*B/[mol/100 mol(2Na+ + 2K+)]) in Table 4, the metastable equilibrium phase diagram of the

01-072-1540 01-076-0753 01-074-0339

**4.2 Stable phase equilibrium of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K**

**4.3 Metastable phase equilibrium of the quaternary system**

**(NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K**

system at 308.15 K was plotted (Figure 6).

1 2 3

KCl).

Figure 5.

True True True

(KCl + Borax + K2B4O7·4H2O)

Factor

0.650 0.011 0.004

39 37 10 Semi-Quant/%

72 22 5

\* *w*B is in mass fraction; \*\* K4, K2B4O7·4H2O; N10, Na2B4O7·10H2O.

Table 3. Stable solubilities of the system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K

(a) dry-salt phase diagram (b) water-phase diagram

Fig. 5. Stable phase diagram of the quaternary system (NaCl- KCl – Na2B4O7 - K2B4O7 - H2O) at 298.15 K. (a), dry-salt phase diagram; (b), water-phase diagram.

Stable and Metastable Phase Equilibria in the Salt-Water Systems 411

—\*\* — — — 5.63 7.29 7.72 7.81 — 8.22 8.66 9.21 8.51 9.55 9.43 — — 9.02 9.10 9.30 10.36 10.12 9.94 9.62 9.58 9.53 9.47 — 9.08 9.51 9.48 9.02 9.04 8.65 8.38

cm-3) pH Refractive index Viscosity

1.3405 1.3800 1.3742 1.3678 1.3869 1.3872 1.3880 1.3890 1.3802 1.3836 1.3860 1.3862 1.3879 1.3782 1.3798 — 1.3792 1.3814 1.3840 1.3863 1.3868 1.3868 1.3803 1.3823 1.3840 — 1.3856 — 1.3857 1.3842 1.3828 1.3827 1.3835 1.3841 1.3849 η/(mPa·s)

— — — — 1.1241 1.1452 1.1930 1.2620 — 1.3023 1.2865 1.2829 1.2729 0.8499 0.8443 — 0.8844 1.0625 1.0876 1.1963 2.8279 2.8032 1.5661 1.4548 — 1.3900 — — 1.1682 1.0812 1.0480 1.0252 1.0421 1.0809 1.0130

No.\* Density

ρ, /(g.

1.0441 1.1935 1.1857 1.2003 1.2300 1.2414 1.2433 1.2524 1.2060 1.2172 1.2274 1.2313 1.2398 1.2270 1.2347 — — 1.2433 1.2536 1.2700 1.3040 1.3206 1.2533 1.2600 1.2636 1.2764 1.2784 — 1.2555 1.2484 1.2409 1.2348 1.2366 1.2404 1.2381

\* Corresponding to the no. column in Table 4; \*\* not determined.

(NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K

Table 5. Physicochemical properties of the metastable reciprocal quaternary system

\* K4, K2B4O7·4H2O; N10, Na2B4O7·10H2O; *w*B, in mass fraction.

Table 4. Metastable solubilities of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K

0.00 100.00 100 0.00 100 98.54 97.6 94.98 96.47 95.63 95.33 95.22 94.92 85.66 85.99 86.66 87.60 85.56 81.57 77.34 0.00 15.03 39.58 49.49 62.43 65.66 72.68 75.94 80.09 85.45 87.64 89.98 90.62 91.80 93.91

Jänecke index

2- *J*(2Cl-) *J*(2K+) *J*(H2O)

0.00 0.00 100 100 32.94 32.89 33.09 32.89 0.00 8.25 15.27 18.97 27.96 100 94.61 94.16 86.86 80.30 73.39 71.90 71.66 75.41 76.36 79.22 79.81 79.97 76.57 72.72 69.15 67.31 63.8 60.17 57.36 50.79 43.95

*J*B, /[mol/100mol(2Na++2K+)] Equilibrium

2090.17 1788.31 18468.05 4311.59 1471.69 1469.10 1456.10 1445.77 1736.76 1684.84 1612.49 1566.69 1532.30 1955.76 1899.70 1894.74 1893.49 1844.98 1699.85 1641.11 2346.01 2134.79 2000.89 2160.56 1906.21 1773.28 1712.53 1838.60 1664.48 1723.59 1717.14 1699.65 1652.70 1604.93 1562.35

solid phase\*

N10 NaCl KCl K4 NaCl+KCl NaCl+KCl NaCl+KCl NaCl+KCl+N10 NaCl +N10 NaCl +N10 NaCl +N10 NaCl +N10 NaCl+N10 KCl+K4 KCl+K4 KCl+K4 KCl+K4 KCl+K4 KCl+K4 KCl+K4+N10 N10+K4 N10+K4 N10+K4 N10+K4 N10+K4 N10+K4 N10+K4 N10+K4 N10+KCl N10+KCl N10+KCl N10+KCl N10+KCl N10+KCl N10+KCl

No.

1.30 10.47 0.00 0.00 7.85 7.84 7.85 7.87 10.62 9.88 9.36 9.10 8.15 0.00 0.49 0.54 1.22 1.86 2.65 2.84 2.01 1.89 1.74 1.66 1.79 1.87 2.28 2.78 3.11 3.26 3.64 4.06 4.45 5.27 6.17

Composition of the solution 100*w*B

Na+ K+ Cl- B4O7

0.00 16.15 13.49 0.00 18.06 17.76 17.66 17.17 15.80 15.89 16.24 16.50 16.57 11.83 12.16 12.29 12.51 12.45 12.51 12.06 0.00 1.78 4.49 6.11 8.55 9.48 10.89 8.30 12.46 13.13 13.59 14.15 14.57 15.16 15.94

\* K4, K2B4O7·4H2O; N10, Na2B4O7·10H2O; *w*B, in mass fraction. Table 4. Metastable solubilities of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K

4.40 0.00 0.00 19.26 0.00 0.58 0.95 1.99 1.28 1.59 1.74 1.81 1.94 4.34 4.34 4.15 3.88 4.60 6.19 7.74 24.00 22.09 15.01 13.66 11.27 10.86 8.97 11.95 6.78 4.90 4.20 3.45 3.30 2.97 2.27

0.00 0.00 14.87 3.87 6.56 6.54 6.60 6.56 0.00 1.51 2.87 3.62 5.38 15.22 14.75 14.73 13.68 12.88 12.41 12.36 8.65 9.86 9.55 10.78 12.05 12.73 12.65 12.61 11.86 11.41 10.91 10.43 10.17 9.25 8.23

\* Corresponding to the no. column in Table 4; \*\* not determined.

Table 5. Physicochemical properties of the metastable reciprocal quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K

Stable and Metastable Phase Equilibria in the Salt-Water Systems 413

**0.0 0.5 1.0 1.5 2.0 2.5 3.0**

**E3**

**E2 E1 F E**

**0 5 10 15 20 25**

100*W*(**B4O7**

**F E**

**KCl**

**F'**

**E3**

**E'**

**E1**

**NaCl**

**E2**

**2-**)

**E4**

**E4**

**pH η/(mPa·s)**

**0 5 10 15 20 25**

quaternary system (NaCl- KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K

**2-**)

Fig. 7. Diagram of physicochemical properties versus composition for the metastable

**K2B4O7**·**4H2O**

**4.3 Comparison of the stable and metastable phase diagram of the quaternary system**

A comparison of the dry-salt diagrams of the metastable phase equilibrium at 308.15 K and the stable phase equilibrium at 298.15 K for the same system is shown in Figure 8. The metastable crystallization regions of borax and potassium chloride are both enlarged while the crystallized area of other minerals existed is decreased. When compared with the stable system, the solubility of borax in water in the metastable system is increased from 3.13 % to 5.70 %. The metastable phenomenon of borax is obvious in this reciprocal quaternary

**K2B4O7 2KCl**

**0 20 40 60 80 100**

*J*( **2Cl- Na2B4O7** ) **2NaCl**

Fig. 8. Comparison of the metastable phase diagram at 308.15 K in solid line and the stable phase diagram at 298.15 K in dashed line for the quaternary system (NaCl - KCl – Na2B4O7 -

K2B4O7 - H2O). --, metastable experimental points; -○-, stable experimental points.

**Na2B4O7**·**10H2O**

**100***W*(**B4O7**

**E1**

**(NaCl - KCl – Na2B4O7 - K2B4O7 - H2O)**

**0**

**20**

**40**

*J*( **2K+** )

**60**

**E4**

**80**

**100**

system.

**E3**

**F**

**E E2**

Fig. 6. Metastable phase diagram of the quaternary system (NaCl- KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K. (a), dry-salt phase diagram; (b), water-phase diagram.

On the basis of physicochemical property data of the metastable system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K in Table 5, the diagram of physicochemical properties versus composition was drawn and shows in Figure 7. The physicochemical properties of the metastable equilibrium solution vary regularly with the composition of borate mass fraction. The singular point on every curve of the composition versus property diagram corresponds to the same invariant point and on the metastable solubility.

0 20 40 60 80 100 0

*J*( **2Cl-** ) **2NaCl Na2B4O7**

**Na2B4O7**·**10H2O**

**K2B4O7 2KCl**

**K2B4O7**·**4H2O**

**F'**

**E'**

**E'3**

**KCl**

**E'1**

**NaCl**

(a) dry-salt phase diagram (b) water-phase diagram

Fig. 6. Metastable phase diagram of the quaternary system (NaCl- KCl – Na2B4O7 - K2B4O7 -

On the basis of physicochemical property data of the metastable system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K in Table 5, the diagram of physicochemical properties versus composition was drawn and shows in Figure 7. The physicochemical properties of the metastable equilibrium solution vary regularly with the composition of borate mass fraction. The singular point on every curve of the composition versus property diagram

**E4**

**1.375**

**1.380**

**E2**

**1.385**

**E1**

**1.390** *n***35**

**E**

**F**

**0**

**2-**) **0 5 10 15 20 25**

**E3**

**W**(**B4O7**

**2-**)**,/%**

**E4**

**500**

**1000**

**1500**

**E'1**

**E'2**

**E'**

**E'3**

**F'**

**2000**

**2500** *J*( **H2O**)

**0 20 40 60 80 100**

**E'4**

*J*(**B4O7 2-** )

**E'2**

H2O) at 308.15 K. (a), dry-salt phase diagram; (b), water-phase diagram.

corresponds to the same invariant point and on the metastable solubility.

**0 5 10 15 20 25**

**100***W*(**B4O7**

**1.15**

**1.20**

**1.25**

**E1**

**E**

**E2 E3** **F**

*ρ***,/(g·cm-3)**

**1.30**

**1.35**

20

40

*J*( **2K+** )

60

**E'4**

80

100

Fig. 7. Diagram of physicochemical properties versus composition for the metastable quaternary system (NaCl- KCl – Na2B4O7 - K2B4O7 - H2O) at 308.15 K

#### **4.3 Comparison of the stable and metastable phase diagram of the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O)**

A comparison of the dry-salt diagrams of the metastable phase equilibrium at 308.15 K and the stable phase equilibrium at 298.15 K for the same system is shown in Figure 8. The metastable crystallization regions of borax and potassium chloride are both enlarged while the crystallized area of other minerals existed is decreased. When compared with the stable system, the solubility of borax in water in the metastable system is increased from 3.13 % to 5.70 %. The metastable phenomenon of borax is obvious in this reciprocal quaternary system.

Fig. 8. Comparison of the metastable phase diagram at 308.15 K in solid line and the stable phase diagram at 298.15 K in dashed line for the quaternary system (NaCl - KCl – Na2B4O7 - K2B4O7 - H2O). --, metastable experimental points; -○-, stable experimental points.

Stable and Metastable Phase Equilibria in the Salt-Water Systems 415

*φ* is the osmotic coefficient; *ZM* and *ZX* are the charges of anions and cautions in the solution. *m* is the molality of solute; υM, υX, and υ (υ = υM + υX) represent the stiochiometric

In equation (1), *fφ, B*φMX and CφMX are defined as following equations. In equation (1a), here *b*

*A I f bI* φ

*MX MX MX B e*

*MX MX MX MX B ee*

ββ

3 1000

π ρ=

β

For non 2-2 type of electrolytes, such as several 1-1-,2-1-, and 1-2-type pure salts, the best

φ

1 2 1 2 1 */ /*

*() () I* 0 1

1 2 *() () I () I* 01 2

3 2 1 2 2 1 2 0

*/ / N e W A*

*Aφ* is the Debye-Hückel coefficient for the osmotic coefficient and equal to 0.3915 at 298.15 K. Where, *N*0 is Avogadro's number, *dw* and *D* are the density and static dielectric constant of the solvent (water in this case) at temperature and e is the electronic charge. *k* is Boltzmann's constant. In equation (1b), *β*(0) *MX*, *β*(1)*MX*, *CφMX* are specific to the salt MX, and are the singleelectrolyte parameters of MX. The universal parameters α = 2.0 kg1/2·mol-1/2 and omit *β*(2)*MX* for several 1-1-,2-1-, and 1-2-type salts at 298.15 K. As salts of other valence types, the values α1 = 1.4 kg1/2·mol-1/2, and α2 = 12 kg1/2·mol-1/2 were satisfactory for all 2-2 or higher valence pairs electrolytes at 298.15 K. The parameter *β*(2)*MX* is negative and is related to the

*v v (v v ) ln z z f m B m C*

12 12 1 2 1 21 */ / / f A [I / ( bI ) ( / b)ln( bI )]*

γγ

γ

*MX MX MX B* =+ +

 βα  β

For 2-2 type of electrolytes, such as several 3-1- and even 4-1-type pure salts, an additional

 α

αα

*DkT*

3 2 2 2 2 */ M X M X M X MX MX*

± =+ + (3)

= − ++ + (3a)

 α

2 *g(x) [ ( x)ex* = −+ − 21 1 *p( x) / x ]* (3d)

*v v*

 φ

> β

0 1 12 2 12 *MX* 1 2 *() () / () /*

 β

− − =+ + (2c)

= − + (2a)

− = + (2b)

 γ

= + (3b)

*g(I ) g( I )]* (3c)

(2d)

coefficients of the anion, cation, and the total ions on the electrolyte MX.

φ

is a universal empirical constant to be equal 1.2 kg1/2·mol-1/2.

φ

φ

form of *B*φ*MX* is following (Pitzer, 1973):

term is added (Pizter, 1977):

association equilibrium constant.

The mean activity coefficient *γ±* is defined as:

γ

γ

 φ

β

*MX MX MX BBB*


**Assessing Complexity in Physiological Systems through Biomedical Signals Analysis**

Editors

**Paolo Castiglioni Luca Faes Gaetano Valenza**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editors* Paolo Castiglioni IRCCS Fondazione Don Carlo Gnocchi Italy

Luca Faes Department of Engineering, University of Palermo Italy

Gaetano Valenza Department of Information Engineering and Research Center "E. Piaggio", University of Pisa Italy

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

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