Decision variables

g: number of production run in model [SISM]

R: number of production run in algorithm [SISM]

L½ � ikk : batch scheduled at position i in the kth production run from due date direction (backward approach), for ik = 1, 2, …, Nk, k = 1, 2, …, g

Q½ � ikk : batch size of L½ � ikk

N: possible total number of batch in a planning horizon

Nk: number of batch in kth production run, k = 1, 2, …, g

B½ � ikk : beginning time for batch L[ik]

C½ � ikk : completion time for batch L[ik]

BPM[k]: beginning time for kth PM

CPM[k]: completion time for kth PM

$$X\_{[i\_k k]} = \begin{cases} \mathbf{1}, \text{if} \\ \mathbf{0}, \text{if} \, \mathbf{Q}\_{[i\_k k]} = \mathbf{0}, \\ \mathbf{0}, \text{if} \, \mathbf{Q}\_{[i\_k k]} = \mathbf{0} \end{cases}, i = \mathbf{1}, \text{2, ..., } N\_{\text{be}} \text{ } k = \mathbf{1}, \text{2, ..., } \mathbf{g}$$

nCM: number of CM minimal repair (restoration)

R: total cost of CM (restoration)

M: number of nonconforming parts

Objective function TC: the total cost consisting of inventory cost in process and complete inventory costs, setup cost, preventive and corrective maintenance cost, and rework cost

The model has some assumptions in formulating the model, as follows:

Integrated Batch Production and Maintenance Scheduling to Minimize Total Production… DOI: http://dx.doi.org/10.5772/intechopen.85004

4.The same load force for machine in setup time and in processing time.

Using those defined notations and based on those assumptions, the integrating batch production and maintenance scheduling to minimize production and maintenance costs on a deteriorating machine in just in time environment (model [SISM]) can be expressed as mixed-integer nonlinear programming as follows:

Model [SISM]

3.4 Model formulation

Industrial Engineering

Parameters

cs: unit setup cost

Decision variables

Q½ � ikk : batch size of L½ � ikk

X½ � ikk ¼

and rework cost

machine.

approach).

36

(

t: unit processing time for a part

cPM: unit preventive maintenance cost cr: unit restoration cost (corrective cost)

q: number of parts to be processed

B½ � ikk : beginning time for batch L[ik] C½ � ikk : completion time for batch L[ik] BPM[k]: beginning time for kth PM CPM[k]: completion time for kth PM

> 1, ifQ½ � ikk 6¼ 0, 0, ifQ½ � ikk ¼ 0

R: total cost of CM (restoration) M: number of nonconforming parts

In order to formulate the integrating batch production and maintenance sched-

c2: unit inventory holding cost for the work in process part per unit per time unit

c1: unit inventory holding cost for finished part per unit per time unit

tPM: time interval for preventive maintenance (in constant assumption)

L½ � ikk : batch scheduled at position i in the kth production run from due date

,i= 1, 2, …, Nk,k= 1, 2, …, g

Objective function TC: the total cost consisting of inventory cost in process and complete inventory costs, setup cost, preventive and corrective maintenance cost,

The model has some assumptions in formulating the model, as follows:

1. This integrating model for single item processed on a single deteriorating

3. Batch position number and PM are counted from due date direction (backward

uling into a mathematical model, we use following notations.

cw: unit rework cost per part for nonconforming part

β: shape parameter for the Weibull distribution α: scale parameter for the Weibull distribution p1: probability of defect part on in-control state p2: probability of defect part on out-of-control state

d: an order delivery time (a common due date)

g: number of production run in model [SISM] R: number of production run in algorithm [SISM]

direction (backward approach), for ik = 1, 2, …, Nk, k = 1, 2, …, g

N: possible total number of batch in a planning horizon Nk: number of batch in kth production run, k = 1, 2, …, g

nCM: number of CM minimal repair (restoration)

2. Setup time is not depending on the size of batches.

s: setup time required for any batch processed

$$\text{Minimize TC} = c\_1 \sum\_{i=1}^{N\_1 - 1} \left\{ \sum\_{j\_i = 1}^{i\_1} \left( t Q\_{\left[i\_1 \right]} + s \right) \right\} Q\_{\left[ (i+1)\_1 \right]} + \frac{c\_1 + c\_2}{2} t \sum\_{i\_1 = 1}^{N\_1} Q\_{\left[ i\_1 \right]}^2 +$$

$$\frac{c\_2 - c\_1}{2} t \sum\_{i\_1 = 1}^{N\_1} Q\_{\left[ i\_1 \right]} + \sum\_{k=2}^{\mathcal{S}} \left[ c\_1 \sum\_{i\_1 = 1}^{N\_1 - 1} \left\{ \sum\_{j\_k = 1}^{i\_k} \left( t Q\_{\left[ i\_k k \right]} + s \right) \right\} Q\_{\left[ (i+1)\_k k \right]} + \frac{c\_1 + c\_2}{2} t \sum\_{i\_k = 1}^{N\_k} Q\_{\left[ i\_k k \right]}^2 +$$

$$\frac{c\_2 - c\_1}{2} t \sum\_{i\_k = 1}^{N\_k} Q\_{\left[ i\_k k \right]} + c\_1 \sum\_{i\_k = 1}^{N\_k} Q\_{\left[ i\_k k \right]} \left( (k - 1) t\_{PM} + \sum\_{j\_k = 1}^{N\_{\left[ k - 1\right]}} \left( t Q\_{\left[ j\_k k \right]} + s \right) \right) \right] + g c\_{PM} +$$

$$c\_i \sum\_{k=1}^{\mathcal{S}} N\_k + E(\mathcal{R}) + E(\mathcal{W}) \tag{14}$$

subject to

$$\sum\_{k=1}^{g} \sum\_{i\_k=1}^{N\_k} \mathbf{Q}\_{[i\_k k]} = q \tag{15}$$

$$B\_{\left[i\_1\mathbf{1}\right]} + \sum\_{j\_1=1}^{i\_1} \left( sX\_{\left[j\_1\mathbf{1}\right]} + tQ\_{\left[i\mathbf{1}\right]} \right) - s = d, i\_1 = \mathbf{1}, \dots, N\_1, k = \mathbf{1} \tag{16}$$

$$\begin{aligned} \mathbf{B}\_{[i\&k]} &+ \sum\_{l=2}^{k} \left[ \sum\_{j\_l=1}^{i\_l} \left( \mathbf{s} \mathbf{X}\_{[j\_l l]} + \mathbf{t} \mathbf{Q}\_{[j\_l l]} + (k-1) \mathbf{t}\_{\text{PM}} \right) \right] - \mathbf{s} + \mathbf{t} \\ &\dots & \dots \end{aligned}$$

$$d\sum\_{i\_1=1}^{N\_1} \left( \mathbf{s} \mathbf{X}\_{[i\_1 1]} + t \mathbf{Q}\_{[i\_1 1]} \right) = d, i\_k = \mathbf{1}, \mathbf{2}, \dots, N\_k \text{ and } k = \mathbf{2}, \mathbf{3}, \dots, \mathbf{g} \tag{17}$$

$$\sum\_{i\_k=1}^{N\_k} \left( t Q\_{[i\_k k]} + s \right) \le d,\\ k = 1 \tag{18}$$

$$\left(\sum\_{i\_k=1}^{N\_k} \left(tQ\_{[i\_k k]} + s\right) \le a, k = 2, 3, \dots, \mathbf{g}\right) \tag{19}$$

Mk ¼ p2xnumber of parts processed in interval

$$\left[B\_{\left[N\_11\right]} - s + a, C\_{\left[11\right]}\right], k = 1, 2, \dots, \text{g} \tag{20}$$

$$E(M) = M\_k, k = 1, 2, \dots, \text{g} \tag{21}$$

$$E(\mathbf{W}) = \mathbf{c}\_{\mathbf{w}} E(\mathbf{M}) \tag{22}$$

$$m\_{\rm CM} = \left\lfloor \left\{ \frac{d - \left( B\_{[N\_1 1]} - s \right)}{a} \right\}^{\beta} \right\rfloor \tag{23}$$

$$E(R) = c\_r n\_{\rm CM} \tag{24}$$

$$B\_{PM\ [I]} = d\_2$$

$$\mathcal{C}\_{\text{PM}[\mathbb{Z}]} = d + t\_{\text{PM}},$$

$$\mathcal{B}\_{\text{PM}[k]} = \mathcal{B}\_{[1\kappa k]} + t \mathcal{Q}\_{[1\kappa k]}, \ k = \mathbf{1}, \ \mathbf{2}, \ldots, \mathbf{g},$$

$$\mathcal{C}\_{\text{PM}[k]} = \mathcal{B}\_{\text{PM}[k]} + t\_{\text{PM}}, \ k = \mathbf{1}, \mathbf{2}, \ldots, \mathbf{g} \tag{25}$$

$$N = \left\lfloor \frac{d - \left\lceil \frac{d}{a} \right\rceil t\_{\rm PM} - tq}{s} \right\rfloor \tag{26}$$

$$\mathbf{g} = \lceil \mathbf{t}q/a \rceil \tag{27}$$

up to g production runs with g PMs. The best algorithm solution is the minimization of all the best total costs for k = 1, 2, …, g. Then, write all decision variables of single item single machine integration problem. Single item single machine integration

Integrated Batch Production and Maintenance Scheduling to Minimize Total Production…

Step-1. Set the length of the first failure time interval after PM as α. Go to Step -2. Step-2. A problem is said as feasible if and only if the total time of process with one setup doesn't exceed the due date of delivering d, otherwise the problem is unfeasible for a model or if s + tq ≤ d then the problem is feasible; continue to

Step-3. Compute g by Eq. (27), and set Nk = Nb c, being computed by Eq. (26),

Step-7. Substitute the values of g, Nk, p, q, t, s, d, tPM into the model and set Set X½ � ikk = 1 for ik=1 and k=1 dan set X½ � ikk = 0 for other ik and k. Go to Step-8. Step-8. Solve SISM Model without the constraint of Eqs. (20)-(24). Compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24),

=1,2,…,ik and l = 1,2,…,k, and X j

= 1,2, …, ik and l = 1,2,…,k+1, and set X j

Step-19. Solve SISM Model without the constraint of Eqs. (20)-(24). Compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24), and compute a total cost to find TC, write TC[i(k+1)] = TC. Go to Step-20.

Step-12. Solve SISM Model without the constraint of Eqs. (20)-(24). Compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24),

l ½ �k = 0 otherwise.

l ½ �l = 0 for other j

l , l.

and compute a total cost to find TC, write TC½ � 111 = TC. Go to Step-9.

and compute a total cost to find TC, write TC½ � ikk = TC. Go to Step-13.

Step-14. Write TC[k]\*= TC½ � ikk and writeall of TC\*-related decisionvariables, go to Step-15.

problem algorithm fully is as SISM algorithm.

DOI: http://dx.doi.org/10.5772/intechopen.85004

Step-4. For R = 1, 2, …, g. Go to Step-5.

Step-3. If s + tq> d, the problem is unfeasible, stop.

Algorithm [SISM]

k = 1, 2,…, g. Go to Step-4.

Step-5. Set R = 1. Go to Step-6. Step-6. Set g = R. Go to Step-7.

Step-9. Set k=1. Go to Step-10. Step-10. Set ik = 2.  Observe whether TC½ � ikk <TC ð Þ i�1 k ½ �k , - If TC½ � ikk <TC ð Þ i�1 k ½ �k , observe whether ik=Nk, - If ik=Nk, go to Step -14.

l

Step-20. Observe whether TC i½ � ð Þ kþ1 ð Þ kþ1 <TC[k]\*,

and writeall of TC[k]\* -related decision variables, go to Step-15.

Step-15. Observe whether k = g,

Step-16. Set k = k + 1, go to Step-17. Step-17. Set ik= 2, go to Step-18.

l ½ �l = 1 for j

Step-11. Set X j

Go to Step-12.

Step-18. Set X j

Go to Step-19.

39

$$X\_{[i\_k k]} = \begin{cases} \mathbf{1}, \text{if } \mathbf{Q}\_{[i\_k k]} \neq \mathbf{0},\\ \mathbf{0}, \text{if } \mathbf{Q}\_{[i\_k k]} = \mathbf{0} \end{cases}, i\_k = \mathbf{1}, \mathbf{2}, \dots, \mathbf{N}\_k, k = \mathbf{1}, \mathbf{2}, \dots, \mathbf{g} \tag{28}$$

$$Q\_{[i\_k k]} \ge 0, i\_k = 1, 2, \dots, N\_k, k = 1, 2, \dots, \mathbf{g} \tag{29}$$

$$Q\_{[i\_k k]} \le X\_{[i\_k k]} \mathbf{q}, i\_k = \mathbf{1}, \mathbf{2}, \dots, N\_k, k = \mathbf{1}, \mathbf{2}, \dots, \mathbf{g} \tag{30}$$

$$N\_k \ge \mathbf{1}, \mathbf{k} = \mathbf{1}, \mathbf{2}, \dots, \mathbf{g} \tag{31}$$

Eq. (14) declares an objective function to minimize total costs consisting of inventory costs, setup cost, preventive maintenance cost, corrective maintenance cost, and rework cost. Eq. (15) states the balance of the material in the shop, where the number of parts in all batches must be equal to the number of parts that will be scheduled. Eqs. (16) and (17) state the beginning time of each batch on the first run and the next runs, respectively. All batches are scheduled tight to a common due date d sequentially. Eqs. (18) and (19) state the length of first run and the next runs, respectively. Eq. (20) states the estimation of nonconforming parts for each run. Eqs. (21) and (22) state the estimation of total nonconforming parts and total rework cost for nonconforming parts, respectively. Eqs. (23) and (24) state the possible number of CM action with cumulative Weibull ROCOF and the expected cost of CM action, respectively. Eq. (25) represents a set of constraints for the beginning and the next of the PM times, with the assumption that first PM in schedule or the last PM in processing (backward approach) after all batches has been completed at a common due date d to ensure the machine in as good as new condition for the next order. Eq. (26) states the possible number of batches in a planning horizon. Eq. (27) states the possible number of production runs in a planning horizon. Equation (28) states a binary constraint that each batch will have: X½ � ikk ¼ 1 for non-empty batches and X½ � ikk ¼ 0 for empty batches. Eq. (29) states non-negativity of batch size. Eq. (30) states batch size less or equal with all parts that will be scheduled. Eq. (31) states the existence of the number of batches in each run.

#### 3.5 Algorithm

The algorithm developed begins with problem solving without involving restoration cost (CM) and rework cost for nonconforming parts or without the constraints of Eqs. (20)–(24). It begins with one batch in one production run with one PM. After having obtained a production schedule, estimate the number of nonconforming parts by Eq. (20) and the number of restoration (CM) by Eq. (23). Next, compute estimated rework cost by Eq. (22) and estimated restoration cost by Eq. (24), and then compute total cost. This step is done for two batches until an increased total cost is found. Write the best total cost for one production run and one PM. This process is carried out for two production runs with two PMs until the best total cost is found for two production runs with two PMs. Continue the process Integrated Batch Production and Maintenance Scheduling to Minimize Total Production… DOI: http://dx.doi.org/10.5772/intechopen.85004

up to g production runs with g PMs. The best algorithm solution is the minimization of all the best total costs for k = 1, 2, …, g. Then, write all decision variables of single item single machine integration problem. Single item single machine integration problem algorithm fully is as SISM algorithm.


**2.3. The study of atmospheric aerosols**

Atmospheric aerosol particles are a ubiquitous part of earth's atmosphere, present in very lungful of air breathed. They are produced in vast numbers by both human activity (anthropogenic) and natural sources and subsequently modified by a multitude processes. They are known to be crucially important in many issues that directly affect everyday life which include respiratory health, visibility, clouds, rainfall, atmospheric chemistry and global regional climate but they are also one of the more poorly understood aspects of the atmosphere. These shortcomings in understanding are partly due to their small size, which is typically of the order of microns or less, making them difficult to study and also the fact that the processes involved are complex. The description of the organic chemistry in atmospheric aerosol is by no means straightforward, but the addition of the solubility variables, aerosol thermodynamic, hygroscopic properties, deliquescence behaviour makes understanding the atmosphere and its effect is even more challenging, requiring the application of wide spectrum of scientific disciplines including chemistry, physics, mechanics, biology and medicine.


**5. References**

α*.*

Crystallization Kinetics of Metallic Glasses 125

Li, C.R. & Tang, T.B. (1999). A new method for analyzing non-isothermal thermoanalytical

Ligero, R.A.; Vazquez, J.; Villares, P. & Jimenez-Garay, R. (1990). Crystallization kinetics in the As-Se-Te system, *Thermochimica Acta*, Vol. 162, pp. 427-434; ISSN: 0040-6031 Matusita, K. & Sakka, S. (1979). Kinetic study of crystallization of glass by differential scanning calorimetry, *Physical Chemistry of Glasses*, Vol. 20, pp. 81-84; 0031-9090 Matusita, K. & Sakka, S. (1980). Kinetic study on Crystallization of glass by differential

Minic D.M. (2006). Synthesis, Characterization and Stability of Amorphous Alloys, *Science of*

Minic, D.M. & Adnadevic, B. (2008). Mechanism and kinetics of crystallization of α-Fe in

Minic, D.M.; Gavrilovic, A.; Angerer, P.; Minic, D.G. & Mariclc, A. (2009). Thermal stability

Moharram, A.H.; El-Oyoun, M.A. & Abu-Sehly, A.A. (2001). Calorimetric study of the

Ozawa, T. (1965). A New Method of Analyzing Thermogravimetric Data, *Bulletin of the*

Patel, A.T. & Pratap, A. (2012). Kinetics of crystallization of Zr52Cu18Ni14Al10Ti6 glass, *Journal*

Paulik, F. (1995). Ch. 10*, Special Trends in Thermal Analysis*, John Wiley & Sons, Chichester,

Pratap, A.; Shanker-Rao, T.L.; Lad, K.N. & Dhurandhar, H.D. (2007). Isoconversional vs.

Raval, K.G.; Lad, K.N.; Pratap, Arun; Awasthi, A.M. & Bhardwaj, S. (2005). Crystallization

Rotaru, A. & Gosa, M. (2009). Computational thermal and kinetic analysis Complete

Roura, P. & Farjas, J. (2009).Analytical solution for the Kissinger equaton, *Journal of Materials*

Rysava, N.; Spasov, T. & Tichy, L. (1987). Isothermal DSC methods for evaluation of the

Vol. 32, pp. 1015-1021; ISSN:1388-6150 (Print), 1572-894 (electronic version)

*Crystlline Solids*, Vol. 38-39, pp. 741-746; ISSN: 0022-3093

*Compound*, Vol. 482, pp. 502-507; ISSN: 0925-8388

2541-2546; ISSN 0022-3727 (Print) ISSN 1361-6463 (Online)

*Chemical Society of Japan*, Vol. 38, pp. 1881-1886; ISSN 0009-2673

*Sintering*, Vol. 38, pp. 83-92; 0350-820x

1572-894 (electronic version)

1572-894 (electronic version)

*Research,* Vol. 24, pp. 3095-3098;

6150 (Print), 1572-894 (electronic version)

6031

6031

UK

0040-6031

data from solid-state reactions, *Thermochimica Acta,* Vol. 325, pp. 43-46; ISSN:0040-

thermal analysis – criterion on application of Kissinger plot, *Journal of Non-*

amorphous Fe81B13Si4C2 alloy, *Thermochimica Acta.*, Vol. 474, pp. 41-46; ISSN: 0040-

and crystallization of Fe89.8Ni1.5Si5.2B3C0.5 amorphous alloy, *Journal of Alloys and*

chalcogenide Se72.5Te20Sb7.5 glass, *Journal of Physics D Applied Physics*, Vol. 34, pp.

*of Thermal Analysis and Calorimetry*, Vol. 107, pp. 159-165; ISSN:1388-6150 (Print),

Model fitting methods A case study of crystallization kinetics of a Fe-based metallic glass, *Journal of Thermal Analysis and Calorimetry*, Vol. 89, pp. 399-405; ISSN:1388-

kinetics of a multicomponent Fe-based amorphous alloy using modulated differential scanning calorimetry, *Thermochimica Acta*, Vol. 425, pp. 47-57; ISSN:

standard procedure to evaluate the kinetic triplet form non-isothermal data, *Journal of Thermal Analysis and Calorimetry*, Vol. 97, pp. 421-426; ISSN:1388-6150 (Print),

kinetics of crystallization in the Ge-Sb-S glassy system, *Journal of Thermal Analysis*,

Coats, A.W. & Redfern J.P. (1964). Kinetic Parameters from Thermogravimetric Data, *Nature (London)*, Vol. 201, pp. 68-69; ISSN: 0028-0836 (Print), EISSN: 1476-4687 Criado, J.M.; Sanchez-Jimenez, P.E. & Perez-Maqueda, L.A. (2008). *Journal of Thermal*

Dhurandhar, H.; Patel, A.T.; Shanker-Rao, T.L.; Lad, K.N. & Pratap, A. (2010). Kinetics of

Doyle, C.D. (1961). Kinetic Analysis of Thermogravimetric Data, *Journal of Applied Polymer*

Doyle, C.D. (1962). Estimating Isothermal Life from Thermogravimetric Data, *Journal of*

Doyle, C.D. (1965). Series Approximations to the Equation of Thermogravimetric Data, *Nature (London)*, Vol. 207, pp. 290-291; ISSN: 0028-0836 (Print), EISSN: 1476-4687 Flynn, J.H. & Wall, L.A. (1966). General Treatment of the Thermogravimetry of Polymers,

Friedman, H.L. (1964). Kinetics of thermal degradation of char-forming plastics from

Galwey, A.K. (2003). Eradicating erroneous Arrhenius arithmetic, *Thermochimica Acta*, Vol.

Gao, Y.Q. & Wang, W. (1986). On the activation energy of crystallization in metallic glasses, *Journal of Non-Crystalline Solids*, Vol. 81, pp. 129-134; ISSN: 0022-3093 Giridhar, A. & Mahadevan, S. (1982). Studies on the As-Sb-Se glass system, *Journal of Non*

Gupta, A.K.; Jena, A.K. & Chaturvedi, M.C. (1988). A differential technique for the

Hsiao, A.; McHenry, M.E.; Luaghlin, D.E.; Kramer, M.J.; Ashe, C. & Ohkubo, T. (2002). The

Jones, G.A.; Bonnett, P. & Parker, S.F.H. (1986). Crystallilzation kinetics of the amorphous

Kissinger, H.E. (1957). Reaction kinetics in differential thermal analysis, *Analytical Chemistry*,

Lad, K.N.; Savalia, R.T.; Pratap, A., Dey, G.K. & Banerjee, S. (2008). Isokinetic and

Lesz, S. & Szewieczek, D. (2005). *Proceedings of the Worldwide Congress on Materials and*

determination of the activation energy of precipitation reactions from Differential Scanning Calorimetric data, *Scripta Metallurgica*, Vol. 22, pp. 369-371; ISSN: 0036-

Thermal, Magnetic, and Structural Characterization of the Crystallization Kinetics of Fe88Zr7B4Cu1, An Amorphous Soft Magnetic Ribbon, *IEEE Transactions on*

magnetic material 2605 Co (Fe67Co18B14Si1), *Journal of Magnetism & Magnetic*

isoconversional study of crystallization kinetics of a Zr-based metallic glass,

*Manufacturing Engineering and Technology COMMENT'2005*, Poland, Gliwice-Wisla

*International*, Vol. 7, pp. 1-15; 978-0-8031-7516-7

*Applied Polymer Science*, Vol. 6, pp. 693-642; ISSN:1097-4628

*Science*, Vol. 5, pp. 285–292; ISSN: 1097-4628

*Chemistry,* Vol. 70A, pp. 487-523; 0022-4332

*Crystalline Solids,* Vol. 51, pp. 305-315; ISSN: 0022-3093

*Magnetics*, Vol. 38, No. 5, pp. 3039-3044; ISSN:0018-9464

*Thermochimica Acta,* Vol. 473, pp. 74-80; ISSN: 0040-6031

*Materials*, Vol. 58, pp. 216-226; ISSN:0304-8843

Vol. 29, pp. 1702-1706; ISSN:0003-2700

(CD-ROM), Vol. 637, May 16-19, 2005

Vol. 6, pp. 183-195; ISSN: 0449-2994

399, pp. 1-29; ISSN: 0040-6031

9748

(electronic version)

*Analysis and Calorimetry,* Vol. 92, pp. 199-203; ISSN:1388-6150 (Print), 1572-894

crystallization of Co-based multi-component amorphous alloy, *Journal of ASTM*

*Journal of Research of the National Bureau of Standards. Section- A. Physics and*

thermogravimetry. Application to phenolic plastic, *Journal of Polymer Science Part C*,

**6**

*Turkey*

*Istanbul Technical University*

**Crystallization Kinetics of Amorphous Materials**

Amorphous (non-crystalline) materials have no crystal structure where the atoms appear to have a random distribution (Omar, 1993). There are different classes of amorphous materials. Glasses, inorganic materials which have no long-range order (<10 Å) and high viscosity greater than 1013 Poise, are the most typical amorphous materials (Doremus, 1973; Jackson, 2004; Park, 2009). The regular arrangement resulting from the distribution over long distances of a repeating atomic arrangement, which is characteristic of a crystal, is missing in glasses (see Fig. 1). However, there is often evidence of a short-range order in glasses, which corresponds to the atomic arrangement in the immediate vicinity of any

(a) (b)

Fig. 1. Schematic two-dimensional illustration of the atomic arrangement in (a) crystal and

Glass can be formed by cooling from a liquid state without a change in its specific volume, which delays crystallization and assist to reach the glass transition temperature before the crystallization occurs (Jackson, 2004; Park, 2009). This is why amorphous materials, such as

In a liquid, the atoms or molecules move around much more rapidly than in a crystal. They are constantly in motion, jiggling around relative to each other, unlike in a crystal, where the

glasses, are sometimes referred to as supercooled liquids (Omar, 1993).

**1. Introduction**

selected atom (Carter & Norton, 2007).

(b) glass (Carter & Norton, 2007)

Miray Çelikbilek, Ali Erçin Ersundu and Süheyla Aydn


**6. The prospect of treatment of AD**

For a long time, it is considered that Aβ accumulation is the central and initial event in the pathological process of AD. The famous amyloid cascade hypothesis thinks that the increase of Aβ levels leads to the pathological events of AD [124, 125]. Extensive clinical medicine trials of Aβ finally come to an end, and results showed that reduced Aβ load does not affect the cognitive ability of patients with AD [126, 127]. So, finding a new target rather than Aβ may be our priority. Microglia play pivotal roles in the pathological process, and interfering with their detrimental process in AD can become our next focus.

Microglia are shown to maintain the function of neurons by clearing toxic damage in the early stage of AD [128]. Consequently, interfering with the activation of microglia to lengthen the period of anti-inflammatory seems to be a therapy for AD [129]. Other anti-inflammatory cytokines such as IL-2, IL-4, and IL-33 have

### *Microglia, TREM2, and Therapeutic Methods of Alzheimer's Disease DOI: http://dx.doi.org/10.5772/intechopen.100203*

the potential to ameliorate AD pathology by regulating microglial activation [128], despite its results are not decisive [130].

Moreover, TREM2 is shown to be a positive target for treating AD. Recently, AL002c, an anti-human TREM2 agonistic monoclonal antibody (mAb), gives a positive outcome in 5xFAD mice expressing both the R47H variant and the common variant (CV). Prolonged administration of AL002c ameliorates filamentous plaques, causes neurodystrophy, and regulates microglial inflammation. AL002 is a derivative product of AL002c, which is modified for clinical use. AL002 is proven safe and well-tolerated in a first-in-human phase I clinical trial [131]. Overexpression of TREM2 can attenuate the pro-inflammatory effect caused by LPS, which can contribute to the increase of NO, LDH, TNF-α, IL-1b, and the activation of AKT [132]. Thus, relative experiments can be conducted in CNS.

Another way to increase TREM2 expression in microglia is by preventing ADAM10/17 family proteases from shedding extracellular domain [133, 134]. To stabilize TREM2 on the cell surface and enhance its activity, a specific mAb against TREM2 called 4D9 was screened to selectively compete for α-secretase-mediated shedding [133]. Shedding is considered to end cell-autonomous TREM2 signaling, and data show an increased phagocytic capacity of cells that express TREM2 by inhibiting ADAM proteases [135]. Combined with another research, Aβ clearance is TREM2-dependant [136], and future treatments can combine anti-Aβ antibodies with microglia-stimulating antibodies (4D9). This view opens a new door to the treatment of AD. Another study evaluated aducanumab as another antibody that may treat AD, but clinical trial results are still unsatisfactory [137]. In addition to cross-linking and activating the TREM2-DAP12 signal, 4D9 also inhibits the shedding of TREM2, resulting in the decrease of soluble TREM2 *in vitro* and the increase of total TREM2 in the brain [133]. This research may consider the role of sTREM2 in AD [91]. Since TREM2 is expressed in peripheral myeloid cells, any effects of treatment for TREM2 should be evaluated for peripheral adipose tissue in liver, lung, bone, and spleen. However, this has not been thoroughly investigated [91].

A novel property, cyclocreatine, the creatine analog, which can generate a supply chain for ATP demand regardless of the TREM2-mTOR pathway [138], is found to ameliorate autophagy, induce microglia around Aβ, and decrease neuronal dystrophy during dietary administration in 5xFAD mice [63]. Based on metabolism, this is a new era for treating AD.

Another research provides a creative angle in treating AD. It is known that meningeal lymphatic vessels drain macromolecular substances from the brain into the deep cervical lymph nodes [139], in which meningeal lymphatic serves as a channel to transport substances such as an antibody. But ablation of meningeal lymphatic vessels in 5xFAD mice can lead to a switch of microglia from homeostasis to DAM [140] and inhibit the transportation of antibodies to specific locations, thus exacerbating the cognitive ability of AD patients. It may bring unexpected clinical effects to patients with AD, if the treatment is placed in the early stage, thus enhancing the meningeal lymphatic function and combined with immunotherapy, to better play the role of meningeal lymphatic vessels.

Recently, tau pathology is the study focus. Tau hyperphosphorylation causes abnormal aggregation and neurodegeneration in AD brains [141], and protein phosphatase 2A (PP2A) has the most robust dephosphorylation activity to tau protein *in vitro* and *in vivo* [142]. A novel DEPho-sphorylation Targeting Chimaera (DEPTAC) was designed to enhance the combination of tau and PP2A-Bα, which shows high efficiency in preventing tau accumulation *in vitro* and *in vivo* [143]. Further studies showed that DEPAC significantly improved the microtubule assembly, neurite plasticity, and hippocampus-dependent learning and memory in transgenic mice [143].