*2.3. HPP Treatment*

A QFP 2L-700 HPP unit (Avure Technologies, Columbus, OH, USA) was used to perform the combined pressure–heat treatments. The equipment hasa2L cylindrical stainless steel pressure treatment chamber with two internal thermocouples for monitoring the temperature. The system also includes a heating system, water circulation, and a pumping system, along with a computer-operated control system. Distilled water was used as a pressure transmission fluid, and isostatic pressure transmission resulted in a uniform pressure in all directions [35].

In HPP treatments, vacuum-packaged 15 mL samples were placed into the treatment chamber and immediately cooled in an ice water bath after treatment. HPP of 300 MPa (10 and 20 min), 400 MPa (10 and 20 min), 500 MPa (5 and 10 min), and 600 MPa (1 and 5 min) were applied at different temperatures, ranging from ambient temperature to ~40 ◦C. The treatment time refers to the duration of steady-state pressure conditions, as programmed in the operating system. The temperature increase was about 2.3 ◦C/100 MPa, due to the adiabatic heating during pressurization, and the decompression time was <20 s in all treatments.

However, similar to Evelyn and Silva [36], the temperature of the HPP chamber dropped steadily during the steady-state pressure phase of the HPP cycle, due to cooling followed by a rapid drop in temperature during decompression (Figure 1).

**Figure 1.** Temperature-pressure profile in alpha-lactalbumin (α-Lac)-added reconstituted infant milk formula (IMF): High pressure processing (HPP) applied at 40.4 ◦C/600 MPa for 5 min.

Transient temperature change significantly impacts all chemical and biological reactions, due to its exponential effect on them. The average temperature during the steady-state pressure phase does not represent the accurate representation of the treatment temperature. For instance, as shown in Figure 1, the pressure come-up time (100 s) prior to achieving the steady-state pressure condition is relatively long and must be accounted for. Considering this, Farid and Alkhafaji [37] provided an integrated value of processing temperature, named "effective treatment temperature (*T*eff)", to represent the entire treatment period (Equation (1)).

$$\mathcal{T}\_{\rm eff} = \frac{-E/R}{\ln(\sum\_{0}^{n} \mathbf{e}^{-E/RT}/n - 1)}\tag{1}$$

where *T* (K) is the absolute temperature recorded at a given time interval (t), *E* is the activation energy (kJ/mol) of the specific biological or chemical reaction, *R* is the gas constant (8.314 J/mol/K), and *n* is the number of temperature recording points measured at equal time intervals.

From now on, the temperature in HPP treatments referred to in this paper will be the *T*eff.
