The final kefir grain mass concentration in the culture medium, ycc/f, daily kefir grain increase mass, mKG, di, and daily kefir grain increase mass fraction, wKG, di, experimentally determined under different conditions proposed by the DoE (Table 2), are presented in Table 3. Daily kefir grain increase mass fraction, wKG/i is the quotient between the kefir grain increase mass concentration (yG, f — 40 g/L) and the initial kefir grain mass concentration (ycG = 40 g/L).

Experiment	TKG, f (g/L)	mKG, di (g)	WKG, di (%)
1	40.40	0.40	1.00
2	45.83	5.83	14.58
3	46.51	6.51	16.28
4	45.44	5.44	13.60
5	43.39	3.39	8.48
6	45.55	5.55	13.88
7	42.06	2.06	5.15
8	53.10	13.10	32.75
9	50.14	10.14	25.35
10	60.62	20.62	51.55
11	41.70	1.70	4.25
12	41.90	1.90	4.75
13	52.60	12.60	31.50
14	58.06	18.06	45.15
15	55.93	15.93	39.83
16	52.56	12.56	31.40

Table 3. Experimental results — orthogonal array L16

Table 3 shows that the highest daily kefir grain increase mass fraction (wKG, i = 51.5 %) was found at the rotational frequency of the stirrer, fm = 90 (1/min), at culture medium temperature, 3 = 24 °C, with a glucose mass concentration, yG = 20 g/L, and without baker’s yeast (yy = 0 g/L).

Moreover, the average impacts of the bioprocess parameters along with interactions at the assigned levels on the daily kefir grain increase mass are shown on Fig. 1. The difference between levels of each bioprocess parameters indicates their relative impact (Prasad et al., 2005). The larger the difference, the stronger is the influence.

It can be observed from Fig.1 that among bioprocess parameters studied rotational frequency of stirrer showed the strongest influence and followed by glucose mass concentration, culture medium temperature and baker’s yeast mass concentration. However, the relative impact of the proposed influencing bioprocess parameters on daily kefir grain increase mass were estimated by ANOVA. The sum of squares or deviation, Sj, and the variance of individual bioprocess parameters, Vj, were calculated by equations (2) and (4), and the error value by equations (3) and (6), respectively. The variance ratio, Fj, is the ratio of variance due to the effect of an individual bioprocess parameter and variance due to the error term. It was calculated by equation (9). The results of ANOVA are shown in Table 4.

Fig. 1. Individual bioprocess parameters influence at different levels on daily kefir grain increase mass

The degrees of freedom of bioprocess parameter j and error variance equaled (f = fe = 3) in all cases. At 90 % confidence (level of importance 0.1), the value F3/3 = 5.3908 was determined through standardized tables of F-statistics. Table 5 shows that the variance ratio of all bioprocess parameters fell below F3,3. In accordance with the Taguchi’s method algorithm, we pooled baker’s yeast mass concentration from further statistical consideration as the least important bioprocess parameter, i. e., with the lowest variance ratio compared to F3/3.

Bioprocess parameter	Sj	fj	Vj	Fj
A:	£(°C)	102.52	3	34.17	1.893
B:	F (g/L)	29.18	3	9.73	0.539
C:	Fg (g/L)	156.58	3	52.19	2.891
D:	fm (1/min)	269.57	3	89.86	4.978
Error	54.16	3	18.05	1.000
Total	612.01	15	—	—

Table 4. Analysis of variance — orthogonal array L16

Pooling of the baker’s yeast as an insignificant bioprocess parameter requires a repeated variance analysis, whereby the sum of squares and the degree of freedom of the pooled bioprocess parameter are added to the error sum of squares and the degree of freedom of error variance, respectively. The results in Table 5 show that, consequently, the variance ratios of the remaining bioprocess parameters increase. In spite of this, a repeated comparison of variance ratio of each bioprocess parameter indicated in Table 5 with the F-statistics value, F3/6 = 3.2888, shows that culture media temperature does not meets the Fj > F3,8 condition. Nevertheless, regarding significant test criterion (Fj > Fm, n) and especially Taguchi’s recommendation, we pooled only baker’s yeast mass concentration as insignificant bioprocess parameter on daily kefir grain increase mass. The final results of ANOVA terms, which were modified after pooling baker’s yeast mass concentration, are shown in Table 5. The relative influences of the bioprocess parameter j and error on the daily kefir grain increase mass were calculated using equations (10) and (11), respectively.

Bioprocess parameter	Sj	fj	Vj	Fj	Xj
A:	£(°C)	102.52	3	34.17	2.460	9.9
B:	F (g/L)	pooled
C:	Fg (g/L)	156.58	3	52.19	3.758	18.8
D:	fm (1/min)	269.57	3	89.86	6.469	37.3
Error	83.34	6	13.89	1.000	34.0
Total	612.01	15	—	—	100.0

Table 5. Final results of variance analysis — orthogonal array L16

The results, shown in Table 5, assign the highest relative influence on the daily kefir grain increase mass (37.3 %) during 24 h incubation to the rotational frequency of the stirrer. The impact of glucose mass contraction and culture medium temperature within the observed ranges (yG = (0-30) g/L and 3 = (20-26) °C) show the lower ones, 18.8 % and 9.9 %, respectively. The remaining fraction represents error influence.

It is well known that kefir grains are bulky and awkward to handle (Bylund, 1994). Despite extensive and careful kefir grain biomass activation, their variegated symbiotic microbial community makes it impossible to retain the constant viability over a long time period. This fact, together with neglecting of possible secondary interactions between bioprocess parameters, mainly explains the relatively high error influence on daily kefir grain increase mass (34.0 %).

2. Conclusion

Using the Taguchi’s fractional factorial design approach we analyzed the bioprocess parameters impacts on daily kefir grain increase mass during 24 h incubation in fresh high temperature pasteurized whole fat cow milk. Experiments proposed by the design of experiments (OA L16) were performed in an RC1 reactor system. We determined those conditions which assure the highest kefir grain increase mass fraction and, using analysis of variance, estimated the relative impact of the proposed bioprocess parameters on daily kefir grain increase mass. In the observed bioprocess parameters ranges, we established that the yeast mass concentration was insignificant compared to the other bioprocess parameters. The most influential bioprocess parameter is found to be the rotational frequency of the stirrer (37.3 %), followed by the glucose mass concentration (18.8 %), and the medium temperature (9.9 %), while the remaining share represents an error.

Summarily, this chapter deals with the experimental determination of the relative impacts of various significant bioprocess parameters, that influence one of the most difficult bioprocesses in the dairy industry. The presented results confirm and, even more importantly, upgrade well-known findings about influence of various bioprocess parameters on kefir grain increase mass. On the other side, the presented results also confirm the tremendous importance of optimal kefir grain biomass managements. In addition, the results also clearly verify the fact, that inadequate combination of different significant critical bioprocess parameters has a strong negative influence on daily kefir grain increase mass. For instance, in the worst case the kefir grains growth is almost totally stopped. Last but not least, the presented chapter presents important cutting-edge and, in scientific and commercial society, shortfall basic knowledge needed either for kefir grains mass growth kinetic studies or designing, optimization and commercialization of modern batch or continuous industrial kefir grains production processes.

3. Nomenclature

ALR Automatic Lab Reactor ANOVA ANalysis Of VAriance DoE Design of Experiments f degree of freedom of error variance (1)

Fj variance ratio of bioprocess parameter j (1)

fj degree of freedom of bioprocess parameter j (1)

fm rotational frequency of the stirrer (1/min)

Fm, n standardized value from the F tables at defined level of significance (1)

fT total degree of freedom of result (1)

HTP High Temperature Pasteurized

L number of levels (1)

M number of bioprocess parameters (1)

mKG, di daily kefir grain increase mass (g)

N total number of experiments (1)

Nk number of experiments on k level (1)

OA Orthogonal Array

Se error sum of squares (/)

Sj sum of squares of bioprocess parameter j (/)

ST total sum of squares (/)

Ve variance error (/)

Vj mean square (variance) of bioprocess parameter j (/)

wKG, di daily kefir grain increase mass fraction (%/d)

Xe relative impact of error on optimization criterion (%)

Xj relative impact of bioprocess parameter j on optimization criterion (%)

Yi i value of optimization criterion (/)

yG glucose mass concentration (g/L)

yKG kefir grain mass concentration (g/L)

ycG/f final kefir grain mass concentration in culture medium (g/L)

yY baker’s yeast mass concentration (g/L)

& temperature (°C)