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18 Monitoring and C ontrolling in Continuous Manufacturing Process 329
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Fig. 18.5 Prediction results from Genetic Algorithm-based Wavelength Selection (GAWLS)-IOT
Fig. 18.6 PCA as preprocessing for GAWLS-IOT
mole fraction data and is effective in that it enables highly accurate prediction of
component concentrations while reducing the time and effort required to construct
the model [
11, 12
]. A synopsis of this is shown in Fig.
18.7.
330 K. Funatsu
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Fig. 18.7 Wavelength Selection based on Excess Absorption (WLSEA) method for IOT [12]
18.5 Control Using PAT
The purpose of real-time monitoring using PAT is to control for rapid correction of
deviations from the set values. The concept of control by PAT is introduced here. In
18.8, the concept of control is shown under the assumption that a calibration
Fig.
model has been built. Assume that a calibration model (here expressed as a soft
sensor) has been constructed between the operating variable and the control variable
(concentration) using the operating data so far. Suppose now that the control variable
is changed to a certain set value (or the control variable deviates from the set value
and the difference is returned to the set value). To realize the set point, assuming
that the operating conditions (O) are fixed, which value of the operating variable
U should be used, can be calculated immediately by inverse analysis of the soft
sensor. The question is how to vary the operating variable U. This is illustrated using
18.9. The upper left-hand side of Fig. 18.9 shows how the operating variable
Fig.
U can be changed empirically. What is important here is the process of changing
from U
at U
generating several patterns of U changes along this template and inputting them to
the soft sensor, the movement of the control variable corresponding to each pattern
can be quickly predicted in advance. The pattern that gives the most rapid control
can then be selected and executed. Apart from overshoot, here it is shown that rapid
control can be achieved by selecting the pattern with the smallest area, ISE (yellow
area), and executing the control [
to Uf. Once the variable is moved a little larger, it is then allowed to settle
o
. Such an operation can be represented by the template shown below left. By
f
13].
18 Monitoring and C ontrolling in Continuous Manufacturing Process 331
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Fig. 18.8 Inverse soft sensor-based Feed Forward control (ISFF)
Fig. 18.9 How to vary the operating variable U
18.6 Summary and Prospects
This chapter has provided an overview of the current status of research on PAT in
the context of the trend toward the introduction of continuous processes in the pharmaceutical industry. The current status and challenges for the mixing, granulation,
drying, transfer, and tableting processes have also been presented. Furthermore, IOT,
a calibration-free/minimum method for concentration prediction using NIRS, and its
extensions have been summarized: whereas IOT applied only to simple mixtures
without intermolecular interactions, the combination of latent variable modeling and
332 K. Funatsu
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wavelength-region selection methods PCA-GAWLS-IOT and WLSEA-IOT were
found to be capable of determining the end of mixing of multi-component powders
and predicting concentrations for solutions. However, IOT and related methods still
have problems in predicting the concentration of components in a solution. For
example, WLSEA-IOT cannot be used in multi-component systems where the NIRS
of the mixture is affected by intermolecular interactions over the entire measurement
range. In this respect, an example of non-linear IOT research was also presented,
albeit briefly. Further research is expected to make it possible to operate PAT
technology at a lower cost than before.
References
1. U.S. Department of Health and Human Services, Food and drug administration (2004)
Guideline for Industry.
2024.
2. Zhou GX et al (2006) Direct design of pharmaceutical antisolvent crystallization through
concentration control. Cryst. Growth Des 6(4):892-898.
3. Jolliffe HG, Gerogiorgis DI (2016) Process modelling and simulation for continuous pharmaceutical manufacturing of artemisinin. Chem Eng Res Des 112:310-325.
1016/j.cherd.2016.02.017
4. Roggo Y, Chalus P, Maurer L, Lema-Martinez C, Edmond A, Jent N (2007) A review of near
infrared spectroscopy and chemometrics in pharmaceutical technologies. J Pharm Biomed Anal
44:683-700.
5. Muteki K, Blackwood DO, Maranzano B, Zhou Y, Liu YA, Leeman KR (2013) Mixture
component prediction using iterative optimization technology (Calibration-Free/Minimum
Approach). Ind Eng Chem Res 52:12258-12268.
6. Azzouz T, Tauler R (2008) Application of multivariate curve resolution alternating least squares
(MCR-ALS) ot he quantitative analysis of pharmaceutical and agricultural samples. Talanta
74:1201-1210.
7. Kriesten E, Alsmeyer F, Bardow A, Marquardt W (2008) Fully automated indirect hard
modeling of mixture spectra. Chemom Intell Lab Syst 91:181-193.
j.chemolab.2007.11.004
8. Minnich C, Helmdach L, Ulrich J, Feth MP (2015) Model-Based recognition of mid-infrared
sensor fouling in paracetamol crystallization. Chem Eng Technol 38(8):1303-1307.
org/10.1002/ceat.201400585
9. Kaneko H, Muteki K, Funatsu K (2015) Improvement of iterative optimization technology
(for process analytical technology calibration-free/minimum approach) with dimensionality
reduction and wavelength selection of spectra. Chemometr Intell Lab Sys 147:176-184.
doi.org/10.1016/j.chemolab.2015.08.017
10. Arakawa M, Yamashita Y, Funatsu K (2011) Genetic algorithm-based wavelength selection
method for spectral calibration. J Chemom 25:10-19.
11. Shibayama S, Kaneko H, Funatsu K (2016) A novel calibration-minimum method for prediction
of mole fraction in non-ideal mixture. AAPS PharmSciTech 18:595-604.
1208/s12249-016-0547-6
https://doi.org/10.1016/j.jpba.2007.03.023
https://doi.org/10.1016/j.talanta.2007.08.024
https://www.fda.gov/media/71026/download. Accessed 11 February
https://doi.org/10.1021/cg0504049
https://doi.org/10.
https://doi.org/10.1021/ie3034587
https://doi.org/10.1016/
https://doi.
https://
https://doi.org/10.1002/cem.1339
https://doi.org/10.
18 Monitoring and C ontrolling in Continuous Manufacturing Process 333
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12. Shibayama S, Kaneko H, Funatsu K (2016) Iterative optimization technology combined with
wavelength selection based on excess absorption for a process analytical technology calibration–minimum approach. Chemometr Intell Lab Sys 156:137-147.
chemolab.2016.06.001
13. Kimura I, Kaneko H, Funatsu K (2015) Development of a novel feedforward control method
using soft sensors and its inverse analysis. J Chem Eng 41(1):29-37.
kakoronbunshu.41.29
https://doi.org/10.1016/j.
https://doi.org/10.1252/
Chapter 19
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Formulation Using Hansen Solubility
Parameters
Hiroshi Yamamoto
19.1 Introduction
The concept of Solubility Parameter (SP) value was derived by Hildebrand. The
Gibbs mixed free energy is expressed by Eq. (
ΔG =ΔH − ΔS · T (19.1)
where G is Gibbs free energy, H is enthalpy, S is entropy, and T is temperature.
Mixing occurs when ΔG is zero or negative. –ΔS · T is generally negative, so if ΔH
is small enough, ΔG will be zero or negative and mixing will proceed. Hildebrand
defined this ΔH by Eq. (
19.2)[1].
19.1).
where ϕ is the volume fraction, V is the molecular volume, and δ is the SP value. This
is where the concept of SP value first arose. When the SP values of two substances are
close, the ΔH becomes smaller and easier to mix. The energy required to remove one
solvent molecule and create a void is measured as the latent heat of evaporation. The
energy required to return another molecule to the void is observed as the solvation
energy. This is usually sufficiently small compared to the latent heat of evaporation
to be ignored (Fig.
So, the SP value of the low-molecular-weight solvent system is defined by
19.3).
Eq. (
H. Yamamoto (B)
Pirika.Com, 53-61 Enokigaoka, Aoba-Ku, Yokohama City, Kanagawa, Japan
e-mail: yamahiro@pirika.com
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024
H. Satoh et al. (eds.), Drug Development Supported by Informatics,
https://doi.org/10.1007/978-981-97-4828-0_19
19.1).
ΔH = φ1φ2V (δ1 − δ
ΔH
SP value =
(
− RT
v
V
2
)
2
)
(19.2)
(19.3)
335
336 H. Yamamoto
https://t.me/med1917
Fig. 19.1 Concept of solvent-based SP values for small molecules
where Hv is the latent heat of evaporation, V is the molecular volume, R is the gas
constant, and T is the temperature. Hildebrand’s SP value was an excellent pioneering
study, but it did not do enough for practical problems. The reason is that the latent heat
of evaporation of a substance is determined by various types of intermolecular forces,
but they are reduced to a single SP value. Hansen divided the energy of evaporation
into a dispersion term (δD), a polarity term (δP), and a hydrogen bonding term
2], and the relationship between Hildebrand’s SP value and Hansen’s HSP is
(δH )[
established as shown in Fig.
19.2.
When Hansen Solubility Parameters (HSP) are considered as a 3-dimensional
vector, the length of the vector corresponds to the Hildebrand SP value. The theory
of HSP, including the length and direction of the vectors, is that “solvents with similar
vectors dissolve solutes with similar vectors”.
Fig. 19.2 Relationship between Hildebrand and Hansen SP values
19 Formulation Using Hansen Solubility Parameters 337
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Fig. 19.3 HSP distance between solute and solvent
The distance between HSP vectors (Fig. 19.3) differs from the usual Euclidean
distance as shown in Eq. (
19.4), with a factor of 4 before the difference in the δD
term.
HSP distance =
4(δD1 − δD
2
+ (δP1 − δP
)
2
2
+ (δH1 − δDH
)
2
2
(19.4)
)
2
The HSP of the drug itself is obtained from a solubility test. The solubility test is
performed using a solvent with a known HSP. Based on the results of this test, the
solvent is divided into “good” and “poor” solvents. The boundary is determined by
the researcher who performed the solubility test. If a compound is poorly soluble,
even 10 mg/100 ml may be a good solvent. On the other hand, 10 g/100 ml may be
the boundary. This ambiguity is a characteristic of HSP. Since the solvents used in
the test have known HSP, they are placed on the 3-dimensional coordinates as shown
19.2. However, the δD axis is scaled twice as large as the δP and δH axes. This
in Fig.
is called Hansen Space. Solvents marked as good solvents gather at similar positions
in Hansen space and form a sphere. This is called the Hansen Solubility Sphere. The
center coordinates of this sphere are the [δD, δP, δH]ofthe solute.Ifthe HSPof
an unexamined solvent or solvent mixture falls inside the sphere, they will dissolve
the solute as well as a “good solvent” as defined by the researcher. The HSP values
themselves are beginning to be used as identifiers for machine learning to predict
drug substance performance. Considering that the closer the HSP of the receptor is
to the HSP of the drug, the more likely it is to dissolve the drug, it is reasonable to
use it as an identifier. Various machine learning methodologies are described in this
book. It is easy to try such methods by simply adding three columns as HSPs.
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19.2 Selection of Extraction Solvents Using HSP
When manufacturing pharmaceuticals, purification of drugs is an important issue.
This is because no synthesis reaction is completely free of by-products. In addition,
pharmaceuticals are often solids with relatively large molecular sizes. In addition,
they often have low thermal stability and cannot be subjected to high temperatures.
Therefore, the distillation methods commonly used in chemical engineering cannot
be used.
19.2.1 How to Determine HSPs for Pharmaceuticals
The solubility parameter is calculated from the energy of evaporation and molecular
volume, as defined in Eq. (
evaporation at room temperature is not available. Therefore, the HSP of pharmaceuticals is determined by the Squeeze theorem using solvents with known HSP. The
method of HSP determination is explained using Paracetamol as an example. Solubility of Paracetamol in solvents was collected from the literature [
in Table
ware (ver. 5.4.06). These solvents are then divided into good and poor solvents. The
division can be subjective. Here, the solvents with log(solubility) greater than 2.0
are considered as good solvents. The HSP is considered as a vector and plotted on
a 3-dimensional coordinate. This coordinate is expanded by a factor of 2 in the δD
direction. This is because there is a factor of 4 before the difference in δD when
calculating the distance of the Hansen vector. The solvents used in the dissolution
test are plotted in this 3-dimensional space in Fig.
set as poor solvent. Then, Hansen’s solubility sphere is calculated using HSPiP
software. The Hansen solubility sphere is the sphere with the smallest radius where
the good solvent is placed inside the sphere and the poor solvent is placed outside
the sphere. The center of the Hansen solubility sphere is defined as the HSP of the
solute (paracetamol). In this case, [δD, δP, δH ] = [17.7, 14.0, 17.5]. The radius of
Hansen’s solubility sphere is called the interaction radius. Here it was calculated to
be 9.1. When the HSP value of a new solvent is known, if its vector falls inside the
sphere with center [17.7, 14.0, 17.5] and radius 9.1, the solvent is expected to dissolve
the solute to the same degree as a “good solvent, log(Solubility) > 2” as defined by the
researchers. The exception in this system was THF. There are many intermolecular
forces at work. In particular, a solvent such as THF, which has the characteristics of
both polar and non-polar solvents, is likely to be an exception. Although there can
be exceptions, it is possible to select solvents from the HSP database that can easily
dissolve the solute.
19.1.
Hansen Solubility Parameters (HSP) of solvents were collected from HSPiP soft-
The blue sphere is the solvent set as good solvent and the red sphere is the solvent
19.3). However, for many pharmaceuticals, the energy of
3] and summarized
19.4 (a).
19 Formulation Using Hansen Solubility Parameters 339
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Table 19.1 Solubility of Paracetamol in various solvents
CAS Solvent g/Litter Log(Solubility) δD δP δ H
67-68-5 DMSO 1087.1 3.04 18.4 16.4 10.2
68-12-2 DMF 962.2 2.98 17.4 13.7 11.3
67-56-1 Methanol 292.6 2.47 14.7 12.3 22.3
64-17-5 Ethanol 185.0 2.27 15.8 8.8 19.4
109-99-9 THF 145.8 2.16 16.8 5.7 8
107-21-1 Ethylene Glycol 160.4 2.21 17 11 26
67-63-0 Isopropanol 105.6 2.02 15.8 6.1 16.4
71-23-8 1-Propanol 105.6 2.02 16 6.8 17.4
67-64-1 Acetone 89.8 1.95 15.5 10.4 7
71-36-3 1-Butanol 74.9 1.87 16 5.7 15.8
64-19-7 Acetic Acid 86.4 1.94 14.5 8 13.5
78-93-3 MEK 56.4 1.75 16 9 5.1
71-41-0 1-Pentanol 55.1 1.74 15.9 5.9 13.9
111-27-3 1-Hexanol 40.5 1.61 15.9 5.8 12.5
111-70-6 1-Heptanol 30.7 1.49 16 5.3 11.7
75-05-8 Acetonitrile 25.2 1.40 15.3 18 6.1
111-87-5 1-Octanol 22.6 1.35 16 5 11.2
108-10-1 MIBK 14.3 1.15 15.3 6.1 4.1
7732-18-5 Water 17.4 1.24 15.5 16 42.3
123-91-1 1,4-Dioxane 17.7 1.25 17.5 1.8 9
141-78-6 Ethyl Acetate 9.7 0.99 15.8 5.3 7.2
67-66-3 Chloroform 2.4 0.38 17.8 3.1 5.7
Fig. 19.4 Placement of solvent in Hansen space (a), Determination of Hansen’s solubility sphere
(b)
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