*3.2. Modeling Probiotics Viability Loss as a Function of Temperature and Pressure*

A single multi-parameter model was developed to describe the effect of pressure and temperature process conditions only on the D-value of Bifidobacteria;

$$D = D\_0 \cdot \left\{ \exp\left\{-\frac{2.303 \cdot T \cdot T\_{ref}}{Z\_T} \cdot \exp\left[-A\left(P - P\_{ref}\right)\right] \cdot \left(\frac{1}{T} - \frac{1}{T\_{ref}}\right) + \frac{2.303}{Z\_P} \cdot \left(P - P\_{ref}\right) \right\} \right\}^{-1} \tag{3}$$

where *D0* (min) is the decimal reduction time at the reference conditions of pressure (Pref, MPa) and temperature (Tref, ◦C), *A* is a constant parameter of the proposed model (MPa−1) and *zT* ( ◦C) and *zP* (MPa) are the thermal and pressure resistance constants, respectively.

This equation takes into account the effect of pressure on the zT value, while the zP value found not to be dependent on the process temperature. The parameters of the model were estimated (Table 2) using non-linear regression and, results indicated that the predicted D-values from the model were

well correlated with the corresponding D-values obtained from the experimental data (Figure 2, R2 0.97−0.99).


**Table 2.** Viability loss kinetic parameters of *Bifidobacterium bifidum.*

Values are means ± standard error of regression.

As detailed described above, considering that the survivability of *B. bifidum* was more sensitive to pressure and temperature conditions contrary to this of *L. casei*, we presumably deduce that the specific model can be a useful tool for estimating the survival of single or symbiotic bacterial cultures, comprising strains of the Bifidobacteria and Lactobacilli species, when exposed to HP processing conditions.

**Figure 2.** Correlation of experimental and predicted from the proposed model decimal reduction times (D) of *B. bifidum* tested in growth media of different pH values (Solid and dashed black lines represent the linear correlation of the data at pH of 4.8 and 6.5 respectively, while grey solid and dashed lines represent the corresponding 95% prediction bands).

### *3.3. Selection of Optimal HP Conditions-Application in Yoghurt Production*

Given that the application of HP processing at the pressure range of 100−300 MPa and temperature range of 20−25 ◦C for 10−15 min did not induce any significant lethality to the probiotic cells population under acidic conditions, we decided to assess the feasibility of these processing conditions when applied to a fermented probiotic dairy food. Treatment of yoghurt samples was also performed at 400 MPa, to explore possible positive effect on the rheological parameters at this higher pressure. The physicochemical, rheological and sensory properties as well as the probiotics cells survivability over a 28 days storage period were monitored.
