INTRODUCTION
Response surface methodology (RSM) is a collection
of statistical and mathematical techniques used in order
to design experiments for adequate response predictions,
fit a hypothesized (empirical) model to experimentally
obtained data under the chosen design, as well as to
optimize the conditions for the given process, i.e. to
ensure the appropriate selection of input variables that
lead to the desired response of a dependent variable [1].
There are several different options of the design of
experiments within RSM, and the options which are
used the most are Central Composite Design (CCD)
and Box-Behnken Design (BBD). When the analyzed
process requires adjustments to the experiment which
cannot be carried out using a standard design, some of
custom designs are used. In that regard, a particularly
interesting option is the Historical Data design option,
which uses data available from the experiments
which have already been conducted. Specifically,
Historical Data creates a blank design layout to accept
component and factor settings and responses from an
existing data set [2].
RSM was presented for the first time by Box and
Wilson in the 1950s, and this methodology is therefore
often called the Box-Wilson methodology. Detailed
information on response surface methodology is
described in [3]. In general, RSM enables testing
effects and interaction between different process
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parameters. It is successfully used to optimize or control
processes in various areas of production, research,
and engineering [4–8]. Some of the examples refer to
optimization of the medium composition and process
parameters for the control of different bioprocesses,
including the mead fermentation process [9–13].
Mead is an alcoholic beverage obtained by
fermentation of honey solution. Honey is a natural
food produced by honey bees from flower nectar
(blossom honey) or plant secretions (honeydew honey).
Honey is rich in carbohydrates (mainly glucose and
fructose), organic acids, and other components, however
concentrations of some components (assimilable
nitrogen) can be much lower than those considered
optimal for fermentation. High sugar contents and
low nitrogen concentration in honey slow down
fermentation. It means that the fermentation process
requires optimal pH, temperature, and growth
conditions. Therefore, various additives, such as pollen,
fruit pulps or juices, citric acid, etc., can be used to
improve alcohol yields, fermentation rates, sensory
characteristics of mead, etc. [14–18].
Fruits and their pulps are rich in carbohydrates,
fibers, minerals, vitamin C, carotenoids, as well as
phenolic and sulfuric substances. Also, their antioxidant
properties can help maintain balance between
production and elimination of reactive oxygen forms
and other related compounds, thereby attenuating
free radical-induced damage to cells [16–19]. Among
fruits, apples are a widely consumed, rich source
of phytochemicals (quercetin, catechin, phloridzin,
chlorogenic acid, etc.), all of which are strong
antioxidants [19]. Apples also contain water, sugars,
acids, pectin, tannins, dyed and aromatic substances,
mineral substances, starch, cellulose, vitamins, as
well as phenolic compounds and enzymes. All the
components give characteristic features to the fruit.
Available literature has not mentioned optimization
of honeydew honey as a substrate for obtaining mead.
Therefore, this research aimed to assess effects of
the concentration of added yeast, yeast energizer and
the dry matter content (independent variables) on
the ethanol yield and dry matter content in the final
product (dependent variables), with the development of
a corresponding mathematical model. The developed
mathematical model can enable better control of the
process in terms of optimum selection and setting of the
process parameters.
STUDY OBJECTS AND METHODS
Chemicals and equipment. All chemicals used in
this study were of analytical grade. In our experiments
we used scales (H54AR, Mettler-Toledo, Columbus,
USA and PFB 1200-2, KERN & SOHN, Balingen,
Germany), a magnetic stirrer (ARE, Velp Scientifica,
Usmate, Italy), a vortex (ZX3, Velp Scientifica, Usmate,
Italy), a spectrophotometer (Spectronic 1201, Milton
Roy, Ivyland, USA), a pH meter (HI-2211, Hanna
Instruments, Smithfield, USA), a waterbath (Wisecircu,
J.P. Selecta, Abrera, Barcelona, Spain), a refractometer
(Leica Abbe Mark II, Reichert Technologies, Depew,
USA), and a conductivity meter (HA-2315, Hanna
Instruments, Smithfield, USA).
Physicochemical analyses of honey. The study
object was honeydew honey from the territory of
the Republic of Srpska, Bosnia and Herzegovina.
The quality characteristics of honeydew honey was
assured by testing it for water content (18.5%), diastase
activity (47.67), HMF content (5.47 mg/kg), acidity
(50.67 mmol/kg), reducing sugars (68.16%), saccharose
(2.01%), and electrical conductivity (1.17 ms/cm) as
described by Ordinance on methods for control of honey
and other bee products (Official Gazette of BiH no
37/2009). The pH was measured with a pH meter (4.33).
Honey must preparation. Honeydew honey was
stirred with water in different ratios to obtain required
dry matter content (Tables 1 and 2). The resultant
must was pasteurized at 65°C for 10 min (with regular
stirring and skimming off the scum) and then cooled
and poured into fermentation flasks. Apple fruit was
pressed through a laboratory press to obtain juice that
was further used in the study to correct the acidity (pH
values of the must were adjusted to 3.7–4) and as a
source of additional nutrition for yeast.
The resultant juice was also pasteurized at 65°C for
10 min, cooled, and poured into fermentation flasks
in amount required for this study (10%). A total of
27 samples were prepared (Table 2) for the experiments.
Initial dry matter concentrations were measured
refractometrically. Different amounts of yeast energizer
VitaFerm® Ultra F3 (Erbslöh, Geisenheim, Germany)
were added into all the samples (Tables 1 and 2). Next,
commercial yeast Fermol® Associées (AEB, Italy) was
rehydrated in distilled water at 35–40°C during 30 min
and added into the samples in different amounts
(Tables 1 and 2).
The process of alcoholic fermentation was
conducted at 25°C for 20 days. All fermentations were
carried out in duplicate using a system that consisted
of 250 mL flasks containing 180 mL of must and
fitted with an airlock to release CO2 produced during
fermentation. Dynamics of the fermentation process
were controlled by weighing the flasks every 24 h
throughout alcoholic fermentation and expressed as
the cumulative mass of produced ethanol per hour.
The rate of fermentation depends on concentration
of such inhibitors as ethanol, acetic acid, fatty acids
(hexanoic, octanoic, decanoic acid), proteins (enzymes),
furfural, hydroxymethylfurfural, etc. The inhibitors
interact synergistically with high osmotic pressure
and the increasing concentration of ethanol during
fermentation [18].
General oenological parameters. At the end
of fermentations, oenological parameters of mead ‒
dry matter content, pH, and ethanol content ‒ were
determined according to standard methods [20].
Design of experiments and mathematical
modelling. The analysis and processing of previously
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obtained experimental data were carried out using the
Design-Expert 11 program (Stat-Ease, Inc. USA) and the
Historical Data Design option. The following variables
were used as independent variables: the initial content
of dry matter (Factor A), yeast (Factor B), and yeast
energizer (Factor C). As dependent (modelled) variables
we used maximum fermentation rate (R3), alcohol
content (R2), and dry matter content in the product (R1).
Table 1 shows the actual and coded values of the
above-mentioned variables, while Table 2 shows the
corresponding design of experiments.
The relation between the independent variables (A, B,
C) and the modelled variables (R1, R2, R3) is described
by a second-degree polynomial model, by fitting the
experimentally obtained data with the sum of squares.
The general form of a second-degree polynomial is
given using the following equation:
Table 1 Coded values of experimental data
Factor Parameter Minimum Maximum Coded low Coded high Mean* SD
A Dry matter content, % 16.30 24.40 –1 ↔ 16.30 +1 ↔ 24.40 20.30 (20.20) 3.37
B Yeast content, mg/L 150.00 600.00 –1 ↔ 150.00 +1 ↔ 600.00 350.00 (300.00) 190.65
C Yeast energizer, mg/L 140.00 500.00 –1 ↔ 140.00 +1 ↔ 500.00 302.33 (267.00) 151.92
* The specified mean values represent the arithmetic mean of the lowest and the highest values (the actual, i.e. the used mean values
of experimental data are given in brackets)
Table 2 Historical Data Experimental Design
Factor 1 Factor 2 Factor 3 Response 1 Response 2 Response 3
Run A: Dry matter
content, %
B: Yeast
content, mg/L
C: Yeast
energizer, mg/L
R1: dry matter after
fermentation, %
R2: Alcohol
content, vol.%
R3: Maximum
fermentation rate, g/h
pH
1 16.3 150 140 6.15 8.64 1.16 3.23
2 16.3 150 267 6.10 8.40 1.20 3.23
3 16.3 150 500 6.25 8.15 1.34 3.29
4 16.3 300 140 6.40 8.24 1.27 3.34
5 16.3 300 267 6.55 7.83 1.24 3.34
6 16.3 300 500 6.35 8.40 1.28 3.22
7 16.3 600 140 6.60 8.56 1.03 3.29
8 16.3 600 267 6.50 8.24 1.11 3.33
9 16.3 600 500 6.25 7.51 1.45 3.27
10 20.2 150 140 6.90 10.62 1.33 3.18
11 20.2 150 267 7.85 10.45 2.84 3.36
12 20.2 150 500 7.20 10.62 1.47 3.35
13 20.2 300 140 7.70 10.20 1.20 3.21
14 20.2 300 267 7.60 10.79 2.50 3.37
15 20.2 300 500 7.45 10.71 1.44 3.33
16 20.2 600 140 7.30 11.13 1.17 3.31
17 20.2 600 267 6.70 11.22 2.80 3.41
18 20.2 600 500 7.35 10.96 1.93 3.34
19 24.4 150 140 11.80 10.88 0.83 3.07
20 24.4 150 267 10.45 11.30 1.33 3.10
21 24.4 150 500 10.70 11.39 0.88 3.18
22 24.4 300 140 10.70 12.24 1.03 3.11
23 24.4 300 267 10.00 11.90 1.15 3.14
24 24.4 300 500 10.20 11.56 1.15 3.13
25 24.4 600 140 10.20 11.73 1.03 3.14
26 24.4 600 267 10.45 11.30 1.34 3.14
27 24.4 600 500 10.15 11.64 1.73 3.17
(1)
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where Yi is the response of interest (R1, R2, R3); Xi refers
to independent variables (A, B, C); β0 is the constant
coefficient; β1, β2, and β3 are linear coefficients; β12,
β13, and β23 are coefficients of interaction between the
variables; β11, β22, and β33 are quadratic coefficients;
and e is the model error.
The statistical analysis of the developed
mathematical models, i.e. the determination of their
statistical significance, was conducted using the analysis
of variance (ANOVA), i.e. the Fisher’s exact test (F-test).
The analysis of variance determined the significance of
the effect of each model parameter on the variance of the
outcome, in comparison with the total variance of all the
observed model parameters.
Optimization. In order to determine the initial
content of dry matter, yeast, and yeast energizer
resulting in the maximum alcohol content, with the
fermentation rate as consistent as possible, we carried
out the numerical optimization of the developed
mathematical models using the Design-Expert 11
program (Stat-Ease, Inc.). Prior to the optimization,
we selected the objective – the range of numeric values
within which we looked for solutions and the level of
significance of reaching the set optimization objective,
i.e. we selected the corresponding optimization
criteria (Table 3).
RESULTS AND DISCUSSION
We studied effects of the analyzed independent
variables on the values of dry matter content (R1) and
alcohol yield (R2) in the finished product – mead, as well
as on the maximum fermentation rate (R3). Apart from
the determined design of experiments, Table 2 shows the
corresponding numeric values of the response of interest
(R1, R2, and R3) and the measured pH values.
The results from Table 2 show that the lowest
residual dry matter content was measured in the
samples which had the lowest dry matter content before
fermentation (samples 1–9), while the samples with
the highest dry matter content before fermentation
(samples 19–27) had the highest content of residual
dry matter after fermentation. That is related to the
duration of the fermentation process (20 days for all the
samples), which means that the dry matter content could
decrease, and the ethanol content could increase if the
fermentation process was extended.
According to Pereira et al., residual dry matter
consists of a high number of different compounds:
sucrose, maltose, isomaltose, trisaccharides, tetrasaccharides,
glycerol, etc [12]. In the research conducted by
Savić et al., the dry matter content ranged between 5.2
and 11.85% [21]. In our work, the highest ethanol content
was obtained in samples 19–27, which had the highest
dry matter content before fermentation, while the lowest
ethanol content was in samples 1–9. In the research
conducted by Martínez et al., the ethanol content was
10.11 vol. % after day 18 day of fermentation, and it was
12.52 vol. % after 26 days [22].
The obtained pH values (Table 2) were lower than
those of the honey solution, most probably due to acids
produced by yeast during fermentation [23, 24]. The
pH value is a very important parameter for alcoholic
fermentation, because yeast cannot ferment under acidic
conditions. In this research, the lowest pH value of mead
was 3.07 (sample 19). A low pH value can slow down
or even stop the fermentation process, as well as cause
incomplete sugar breakdown due to acetic and succinic
acid formation, which cause an increase in the content
of undissociated fatty acids [23]. Ammonium ion uptake,
which is part of yeast energizer, is associated with the
excretion of proton ions into the medium, thereby
decreasing extracellular pH [25].
By fitting the data from Table 2 within the regression
analysis, the corresponding coefficients were determined
in Eq. (1), and the following empirical models were
developed:
Table 3 Optimization criteria
Optimization objective Range of numeric values Level of significance of the objective (from 1 to 5)
Factor A in range 16.3–24.4% not applicable
Factor B minimize 150–600 mg/L 3
Factor C minimize 140–500 mg/L 4
Response R1 none not applicable
Response R2 maximize 7.51–15.00 vol. % 5
Response R3 minimize 0.83–2.84 5
(2)
(3)
(4)
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The equations given above are written in the form of
the actual values of the factors (A, B, C), and they may
be used to predict the corresponding response, simply
by inserting the values of A, B, C in the given units. The
given equations are normalized and may not be used to
determine the significance of the factors A, B, and C.
When analyzing equations where +1 and –1 correspond
to the largest and least factor values, respectively, the
relative effect of individual factors of the process under
study may be identified by comparing the coefficients
in front of the corresponding factor. Apart from that,
equations written in a coded form may be used to
predict the response for the given factor level. The
above-mentioned equations, written in a coded form,
are given below:
Table 4 ANOVA for quadratic models in terms of coded factor (equations 5, 6, and 7)
R1, % R2, vol. % R3, g/h
F-value P-value F-value P-value F-value P-value
Model 64.67 < 0.0001 44.43 < 0.0001 3.84 0.0082
A-Dry matter content 493.60 < 0.0001 360.36 < 0.0001 0.0592 0.8107
B-Yeast 1.31 0.2676 1.10 0.3089 0.8737 0.3630
C-Yeast energizer 1.19 0.2900 0.9048 0.3548 3.34 0.0852
AB 3.92 0.0640 1.35 0.2615 0.9202 0.3509
AC 0.7242 0.4066 0.6884 0.4182 0.0097 0.9226
BC 0.1031 0.7521 1.24 0.2817 1.87 0.1888
A² 41.78 < 0.0001 37.02 < 0.0001 18.63 0.0005
B² 0.0162 0.9003 0.3373 0.5690 0.1417 0.7113
C² 0.3903 0.5404 0.0645 0.8025 10.73 0.0045
Figure 1 Diagnostics plots
Dry matter content Yeast content Yeast energizer
(5)
(6)
(7)
The conducted analysis of variance (ANOVA) of the
data (Table 2) proved their statistical significance as a
whole, as well as the statistical significance of individual
members of Eqs. (5)–(7). Table 4 demonstrates the
ANOVA values for the developed models related to
the effect of the process parameters on the dry matter
content after fermentation (Eq. (5)), the alcohol content
(Eq. (6)) and the maximum fermentation rate (Eq. (7)).
The ANOVA was carried out for the equations written
in a coded form. All the conclusions drawn for the
equations written in a coded form apply to the equations
in an actual form as well.
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By analyzing the F-values and the P-values for
the quadratic equation (5), i.e. the response R1, it can
be concluded that the developed model is statistically
significant as a whole taking into consideration that the
F-value of the model is 64.47 and that there is only 0.01%
of probability for such a high F-value to occur due to
noise. The P-values below 0.05 indicate that a particular
member of the analyzed equation, to which the given
value refers, has a statistically significant effect. In the
analyzed equation, those are the members A and A2. The
P-values above 0.1000 indicate that the given member
of the equation does not have a statistically significant
effect, and in this case, those are B, C, AB, AC,
BC, B2, and C2.
The quadratic models related to the effect of the
process parameters on the response R2, i.e. the alcohol
content (Eq. (6)), have the F-values of 44.43, and there
is only 0.01% of probability for such a high F-value to
occur due to noise. Therefore, it can be concluded that
the developed model is statistically significant. Like
in the previously analyzed equation, the P-values
of the members A and A2 are below 0.0001, which
means that they are statistically significant members
of the given model.
The quadratic models related to the effect of
the process parameters on R3, i.e. the maximum
fermentation rate (Eq. (7)), have the F-value of 3.84 and
the P-value of 0.0082, i.e. there is 0.82% of probability
for such a high F-value to occur due to noise. Therefore,
it can be concluded that the given model is statistically
significant. By analyzing the P-values of the individual
members of Eq. (7), it can be concluded that only the
members A2 and C2 are statistically significant members
of the model, because their P-values are below 0.05 (the
P-value of the member A2 is 0.0005, and the P-value of
the member C2 is 0.0045).
The validation of the developed models was
conducted by comparing the experimentally obtained
data with the corresponding values obtained by using the
model (Fig. 1), and by analyzing the fit statistics from
Table 5. First of all, it is necessary to notice that in all
the experiments there is a satisfactory relation between
the measurement signal (response) and noise, which is
expressed by the values of the Adeq Precision parameter
above 4 (Table 5).
Figure 1 shows that the actual values in all three
cases approximate to the values foreseen by the model,
i.e. that the individual values are in the vicinity of the
ideal line (y = x), and that they are randomly distributed
on both sides of the line y = x. This indicates that there
is a correlation between the actual values and the values
foreseen by the model. This is verified by the high values
of the determination coefficient (R2), given in Table 5.
The table shows that the R2 values for fitted Eqs. (5)
and (6) are higher in comparison with the R2 values of
fitted Eq. (7).
However, since all three R2 values are above 0.5, only
by observing this indicator, it could be concluded that all
three models realistically explain the dependence of the
observed responses (R1, R2, and R3) on the independent
variables (A, B, C). However, that only applies to
Eqs. (6) and (7). The further analysis of the fit statistics
from Table 5 shows that a reasonable agreement between
the adjusted R2 and the predicted R2 only exists for the
case of fitted Eqs. (5) and (6), while it is not the case for
Eq. (7), where there is a significant difference between
the two parameters.
Specifically, the predicted R2 value (0.2785) is
not close enough to the adjusted R2 value (0.4955),
i.e. it is higher than 0.2. This indicates the possibility
of occurrence of a blocking effect as a result of the
conduct of experiments in several blocks (a group of
experimental conditions) or a possible problem with
the model itself and/or individual data. Given the fact
that ANOVA showed for this empirical model that only
the members A2 and C2 are statistically significant, it is
assumed that the presence of the other members in the
model contributes to the above-mentioned problem,
and the equation is therefore reduced by excluding
the member B, and the members of the interaction AB,
AC and BC. The repeated fitting of data from Table 2
resulted in the following equation written in the actual
and in the coded form respectively:
(8)
(9)
The ANOVA values for the fitted equation (9) in
the coded form show that the equation reduced in such
a manner is also statistically significant as a whole,
because the F-value of the model is 8.21, and there is
only 0.03% of probability that such a high value is a
result of noise. Apart from that, the members A2 and
C2 are also statistically significant with the P-values
Table 5 Fit statistics
Dry matter content R1 Yeast content R2 Yeast energizer R3 *Yeast energizer R3
R² 0.9716 0.9592 0.6701 0.5988
Adjusted R² 0.9566 0.9376 0.4955 0.5259
Predicted R² 0.9299 0.9005 0.2785 0.3957
Adeq Precision 20.6715 17.7830 6.3645 8.3653
*Reduced model
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of 0.0002 and 0.0027, respectively. The comparison
between the experimentally obtained values of the
maximum fermentation rate and the values obtained by
using the empirical model described by Eq. (8) or (9)
gives the value of the determination coefficient R2 of
0.5988, which means that there is a correlation between
the values obtained in such a manner. Apart from that,
the values of adjusted R2 of 0.5259 and predicted R2
of 0.3957, which differ by less than 0.2, indicate the
presence of the given correlation. All this indicates
that the model reduced in such a manner may be used
for determining the maximum fermentation rate (R3) in
the given designed space (the tested range of the change
of values of the independent variables). The reduction
of the other two models, i.e. fitted Eqs. (2) and (3), and
Eqs. (5) and (6), was not carried out, because the given
equations have satisfactory values of all the statistical
parameters tested (Fig. 1, Tables 4 and 5).
Figure 2 shows the response surface plots which
enable an insight into the behavior of the observed
dependent variables (responses R1, R2, and R3) to change
the independent variables and their possible interaction.
The plot A (Fig. 2) shows the effect of different
combinations of the initial content of dry matter and
yeast on the dry matter content after fermentation at
the fixed value of yeast energizer of 320 mg/L. The dry
matter content after fermentation increased from 6.4 to
10.1% with an increase in the initial dry matter content
from 16.3 to 24.4% at the value of the yeast content of
600 mg/L.
An almost identical increase in the dry matter
content after fermentation from 6.2 to 10.7% with the
same amount of increase in the dry matter content in the
initial raw material was noticed at the value of the yeast
content of 150 mg/L. Therefore, it can be concluded
that the effect of the yeast content in the initial raw
material on the dry matter content after fermentation
was negligible in comparison with the dominant effect of
the dry matter content in the initial raw material, in the
tested range of values of the independent variables.
The plot B (Fig. 2) shows the effect of different
combinations of the dry matter content and yeast
energizer on the dry matter content after fermentation at
the fixed value of the yeast content of 375 mg/L. The dry
matter content after fermentation increased from 6.4 to
10.3% with an increase in the initial dry matter content
from 16.3 to 24.4% at the value of yeast energizer of
500 mg/L. A similar increase in the dry matter content
after fermentation from 6.4 to 10.7% with the same
amount of increase in the dry matter content in the
initial raw material was noticed at the value of yeast
energizer of 140 mg/L. Therefore, it is clear that the
effect of yeast energizer in the initial raw material on the
dry matter content after fermentation was negligible in
comparison with the dominant effect of the dry matter
content in the initial raw material, in the tested range of
values of the independent variables.
Taking into consideration the previous conclusions
on the negligible effect of the content of yeast and yeast
energizer in the initial raw material on the dry matter
content after fermentation, it is expected that different
combinations of the two given independent variables do
not have an effect on the value of the observed response.
This is confirmed by the plot F (Fig. 2), which shows
that there is almost no change in the dry matter content
after fermentation at different combinations of the given
independent variables and at the fixed dry matter content
in the initial raw material of 20.35%.
The plot C (Fig. 2) demonstrates the effect of
different combinations of the content of dry matter and
yeast on the alcohol content after fermentation at the
fixed value of yeast energizer of 320 mg/L. The alcohol
content after fermentation increased from 8.14 to 11.73%
with an increase in the dry matter content from 16.3 to
24.4% at the value of the yeast content of 600 mg/L in
the initial raw material. An almost identical increase
in the dry matter content after fermentation from 8.21
to 11.31% with the same amount of increase in the dry
matter content in the initial raw material was noticed at
the value of the yeast content of 150 mg/L. Therefore,
it can be concluded that the effect of the yeast content
in the initial raw material on the alcohol content after
fermentation was negligible in comparison with the
dominant effect of the dry matter content in the initial
raw material, in the tested range of values of the
independent variables.
The plot D (Fig. 2) shows the effect of different
combinations of the content of dry matter and yeast
energizer on the alcohol content after fermentation at the
fixed value of the yeast content of 375 mg/L. The alcohol
content after fermentation increased from 8.13 to 11.66%
with an increase in the dry matter content from 16.3 to
24.4% at the value of yeast energizer of 500 mg/L in the
initial raw material. A similar increase in the alcohol
content after fermentation from 8.47 to 11.66% with
the same amount of increase in the dry matter content
in the initial raw material was noticed at the value
of yeast energizer of 140 mg/L. Therefore, it can be
concluded that the effect of yeast energizer in the initial
raw material on the alcohol content after fermentation
was negligible in comparison with the dominant effect
of the dry matter content in the initial raw material.
Taking into consideration this conclusion, as well as the
conclusion drawn from the analysis of the plot C, it can
be concluded that different combinations of the content
of yeast and yeast energizer do not have a significant
effect on the alcohol content after fermentation either,
similar to the effect on the dry matter content after
fermentation as shown in the plot F. To ensure visibility
of the work, the corresponding plot is not given in Fig. 2.
The plot E (Fig. 2) shows the effect of different
combinations of the yeast content and the dry matter
content in the initial raw material on the maximum
fermentation rate at the fixed value of yeast energizer of
375 mg/L. Unlike the previous plots, the effect of both
observed independent variables can be clearly noticed
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Figure 2 Response surface plots for dry matter content after fermentation (plots A, B, F), Alcohol content (plots C, D) and maximum
fermentation rate (plot E). Plots A and C at the fixed content of yeast energizer of 320 mg/L. Plots B, D, and E at the fixed content
of yeast energizer of 375 mg/L. Plot F at the fixed dry matter content in the initial raw material of 20.35%
a b
c d
e f
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here, which was in accordance with the developed
model (Eq. (8)), which had two quadratic members. The
maximum fermentation rate increased, went through the
maximum, and then decreased, at a particular value of
yeast energizer in the initial raw material.
A similar trend of a change in the maximum
fermentation rate was noticed with a change in the
value of yeast energizer in the initial raw material, at a
particular value of the dry matter content in the initial
raw material. It is obvious that it is possible to select
particular combinations of the content of dry matter and
yeast energizer in the initial raw material, which would
give the maximum alcohol content at the corresponding,
i.e. desired values of the fermentation rate and the
dry matter content, which was the subject of the
optimization study.
Figure 3 shows the results of numerical optimization
of the developed mathematical models. According to
the defined optimization criteria (Table 3), the optimum
conditions were the dry matter content of 24.4%, the
content of yeast of 150 mg/L, and yeast energizer of
140 mg/L in the initial raw material. Under such
conditions, the alcohol content obtained after
fermentation was 11.22% with a moderate fermentation
rate of 0.86 g/h.
The above-mentioned solution had the highest
level of desirability (0.809) among a total of 65 offered
solutions. That means that it is possible to select a series
of combinations of the minimum content of yeast and
yeast energizer in the initial raw material which would
enable the maximum yield of alcohol at a moderate
fermentation rate, with the dry matter content within the
range of the analyzed numeric values.
Figure 3 Optimum conditions and the corresponding responses
CONCLUSION
Response surface methodology allowed us to
develop empirical mathematical models in the form of
second-degree polynomials. The models describe the
effect of the initial content of dry matter, yeast, and
yeast energizer on the maximum fermentation rate, the
alcohol yield, and the dry matter content in the finished
product – mead.
The statistical analysis has proved that the initial
dry matter content had the statistically significant effect
on the content of alcohol and dry mater in the final
product. The initial content of yeast and yeast energizer
in the tested range of values of the given variable was
negligible. The developed mathematical models were
used to select optimum fermentation conditions: the dry
matter content of 24.4%, the yeast content of 150 mg/L,
and the content of yeast energizer of 140 mg/L, in the
initial raw material. Under such conditions, the alcohol
yield obtained after 20 days of fermentation was 11.22%
at a moderate fermentation rate of 0.86 g/h.
CONTRIBUTION
Saša Papuga, Igor Pećanac, Maja Stojković,
Aleksandar Savić, and Ana Velemir conceived and
designed the experiments; performed the experiments;
contributed reagents, materials, and analytical tools;
and wrote the paper. Saša Papuga analyzed the data,
developed mathematical models, and performed
parameter optimisation.
CONFLICT OF INTEREST
The authors declare no conflict of interest.

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