## 3 Results and Discussion
### Evolution of VOC Profiles During Successive Kefir Grain Passages
The VOCs identified in both the unfermented substrate and the kefirs obtained during the first three passages included organic acids (11 compounds), alcohols (19), aldehydes (10), ketones (4), esters (22), hydrocarbons (8), and other compounds (7). The concentrations of organic acids, alcohols, aldehydes, ketones, and esters detected in the milk kefirs produced during the first three 24 h batch fermentations [25] were consistently lower than those found in the fermented kiwi-based drinks (Tables S1-S3). A comparison of key VOCs in both types of fermented beverages during the first kefir grain passage reveals notable differences. The number of organic acids found in the fermented kiwi-based drinks (0-1; Table S1) was lower than that found in fermented UHT milk (4 compounds; [25]). The numbers of alcohols (9) and aldehydes (3) in the milk kefir fell within the ranges observed in the fermented kiwi-based beverages (alcohols: 4-11;aldehydes: 0-6). However, the number of ketones (4) and esters (14) in the milk kefir [25] exceeded those detected in the fruit-based drinks (ketones: 1-2; esters: 2-8) (Table S1). During the second kefir grain passage, the milk kefir contained higher numbers of organic acids (6), aldehydes (6), and esters (11) [25], compared to the kiwi-based beverages, which exhibited values of 0, 0-5, and 3-12, respectively (Table S2). In contrast, the numbers of alcohols (10) and ketones (2) in the dairy beverage fell within the respective ranges observed in the fruit-based drinks (alcohols: 3-13; ketones: 1-2). In the third kefir grain passage, the dairy beverage contained higher numbers of organic acids (10) and aldehydes (7) [25] compared to the fermented kiwi-based beverages (Table S3). However, the numbers of alcohols (10), ketones (2), and esters (13) in the milk kefir fell within the respective ranges observed in the fruit-based beverages (alcohols: 4-15, ketones: 1-2, and esters: 2-13). Effect of Shaking Rate and Inoculum Percentage on the Production of VOCs in the Kiwi-Based Drinks During Successive Kefir Grain Passages  
The primary objective of employing response surface methodology (RSM) in this study was to structure the experimental design for producing kefir-like beverages based on kiwifruit [11], rather than to develop empirical models describing the relationship between the production of volatile organic compounds (VOCs) and variations in the shaking rate (SR) and the proportion of milk kefir grains (PMKG). As previously mentioned, a total of 82 VOCs were identified across the 27 fermented beverage samples, making it both impractical and labor-intensive to evaluate the effects of the two independent variables on the concentrations of each individual compound. Furthermore, the application of RSM to evaluate the effects of the SR and PMKG on specific VOC families--such as total organic acids, alcohols, aldehydes, ketones, esters, furrans, and others--resulted in empirical models that were not consistently statistically significant (see Tables S4-S21). In fact, only the total concentration of volatile compounds ([TVOCs]) in each beverage, measured across successive kefir grain passages, could be reliably modeled as a function of the two independent variables. The resulting empirical models for [TVOCs] obtained at 24, 48, and 72 h were as follows:  
\[\text{[TVOCs]}\ (24\ \text{h})=13.92-3.25\cdot\text{SR}+2.04\cdot\text{PMKG}-2.59 \cdot\text{PMKG}^{2} \tag{1}\]  
\[\text{[TVOCs]}\ (48\ \text{h})=13.86-1.61\cdot\text{SR}+1.40\cdot\text{PMKG}-3.25 \cdot\text{PMKG}^{2} \tag{2}\]  
\[\text{[TVOCs]}\ (72\ \text{h})=24.60-1.93\cdot\text{SR}+1.48\cdot\text{PMKG}-4.87 \cdot\text{PMKG}^{2} \tag{3}\]  
The three empirical models and their parameter values demonstrated a consistently good fit, as confirmed by both [PERSON]'s \(t\)-test and [PERSON]'s \(F\)-test (see Tables S22-S24 in the Supplementary Materials). A general trend observed across models 1-3 is that the coefficients for the linear terms of SR and PMKG consistently exhibited negative and positive signs, respectively.