Mathematical modelling of Hass avocado firmness by using destructive and non-destructive devices at different maturity stages and under two storage conditions

Avocado is rich in fatty acids and has high economic and health importance globally (Dreher and Davenport, 2013; Pedreschi et al., 2019). Fruit firmness is an important quality attribute which is used to assess the ripeness stage of the fruit during storage (Penchaya et al., 2015). It is the most reliable parameter for determining if the fruit is ripe to eat and plays a critical role in controlling postharvest shelf-life. The firmness at which fruit is consumed or assessed for quality is also very important since rots and internal disorders of Hass avocado develop rapidly during the later stages of fruit ripening (White et al., 1999; Zhang et al., 2019). Firmness can be measured by conventional destructive (fruit penetrometers) and recently by non-destructive texture analysers. Comparison of non-destructive methods indicates that each method is probably assessing different textural attributes; hence, the softening patterns may also differ (Goldberg et al., 2019). Fruit firmness and the rate of softening vary greatly, both between and within fruit batches, especially during shelf-life. Since the conventional methods for assessing the progress of fruit ripening with a penetrometer are destructive, they require many fruits (Goldberg et al., 2019). Knowledge of textural properties is important for stakeholders in the food value chain including producers, postharvest handlers, processors, marketers and consumers (Chen and Opara, 2013).

The fruit penetrometer is used to monitor the ripeness stage and to check the consistency of the inner fruit flesh. It is very useful in the field for determining the best harvest time. Moreover, it can be used for quality control during storage or after transport. First, the fruit skin and flesh are removed, and the penetrometer is then pushed into the exposed fruit flesh (Khalaj et al., 2016; Souri and Dehnavard, 2017). Usually, each fruit is measured twice at the equator, with measurements made at 90° to each other. The average value is then taken as the firmness of that fruit (Li et al., 2016). Non-destructive devices allow repeated measurements of the same fruit or even the possibility of all fruit being assessed on a grading line. A key aspect of non-destructive measurement is that the whole fruit is assessed, although the particular technology applied will determine whether a specific part of the fruit has a large impact on the measurement made (Li et al., 2016).

There are significant amounts of studies in the literature comparing firmness by a penetrometer and nondestructive devices in different fruit such as in mango (Penchaiya et al., 2015), apple (Peleg, 1993), kiwifruit (Li et al., 2016; Goldberg et al., 2019), blueberries (Giongo et al., 2013) and watermelon (Abbaszadeh et al., 2015). Significant heterogeneity of maturities is frequently observed in Hass avocado fruit depending on the harvest season, environmental and agronomic factors (Fuentealba et al., 2017; Hernandez et al., 2016, 2017). It would be advantageous to have a reliable non-destructive method for measuring Hass avocado fruit firmness. Such a tool will be optimal for determining optimal harvest, monitoring periodic firmness in controlled atmosphere (CA) storage and regular air (RA). If a higher positive relationship is found, then non-destructive measurement can be used in the routine laboratory to assess Hass avocado firmness. The main goals of this study were to study the relationships between the Hass avocado fruit firmness measured by destructive (fruit penetrometer) and non-destructive devices (texture analyser) from harvest to ready-to-eat (RTE) stage and in two storage conditions (CA and RA).

The results of normality tests (i.e., normal Q-Q plots and histograms with normal curves of fruit firmness measured by non-destructive and destructive devices for fruit stored in RA and CA of Quilhuica and Bartolillo orchards) are summarised in Supplementary Figures 1–4. Independently of the storage technique, all variables tested (firmness by a penetrometer and firmness by a texture analyser) did not follow a Gaussian distribution, and the variances tested by Levene's test (p < 0.05) between the groups were different (not homogeneous). Supplementary Figures 1 and 2 present the normal Q-Q plot of fruit firmness measured by non-destructive and destructive devices for fruit stored in RA and CA for Quilhuica and Bartolillo orchards, respectively. Supplementary Figures 3 and 4 show a histogram with a curve of normal distribution for Quilhuica and Bartolillo orchards, respectively. As it can be observed, the variables tested did not follow a normal distribution, confirming previous results of Shapiro–Wilk test (p < 0.05). Spearman correlation was then chosen as the normality assumptions were not satisfied and the rho was calculated using Equation 1 below: {rho=∑(x−mx)(y−my)∑(x−mx)2∑(y−my)2} \left\{{rho = {{\sum {\left({x - {m_x}} \right)\left({y - {m_y}} \right)}} \over {\sqrt {{{\sum {\left({x - {m_x}} \right)}}^2}{{\sum {\left({y - {m_y}} \right)}}^2}}}}} \right\} where x = rank (x) and y = rank(y).

Results of spearman correlations (Figure 1) showed a positive moderate association between the firmness measured by penetrometer (destructive device) with non-destructive fruit firmness in all storage conditions and orchards. Higher positive association (rho = 0.51) was found for Bartolillo orchard (Figure 1C) fruits stored in RA, while for those fruits stored in CA (Figure 1D), a coefficient of 0.46 was observed. The lowest coefficients found were 0.41 (Figure 1B) and 0.45 (Figure 1A) for Quilhuica fruit stored in CA and RA, respectively.

Figure 1

Figure 2

Regression analysis was also performed, and models were built. Four models were built for Quilhuica and Bartolillo for samples stored in RA and CA conditions, respectively. The accuracy of the first model (Q_RA) was 0.79, and the variance explained by the model (coefficient of determination) was 0.63. The second model (Q_CA) expressed a variance of 0.61 with model accuracy of 0.78, the third model expressed a variance of 0.53 with accuracy of 0.73 and finally the fourth model expressed a variance of 0.57 with accuracy of 0.76. All tested models were statistically significant (p < 0.05). Table 1 presents the prediction intervals of all tested models with 95% confidence intervals. As it can be observed, the fitted values of firmness by a penetrometer were within the range of the confidence intervals, and according to the model equations, it is possible to predict firmness by a penetrometer using a non-destructive device in Hass avocado fruit.

[F_PE = 50.66 + 2.09F_TA ](Q_RA)

Analysis of variance (ANOVA) by Kruskal–Wallis (non-parametric ANOVA) was also performed to assess if there were significant differences in firmness changes during the storage period. For Quilhuica fruit stored in RA storage and measured by a non-destructive device (Table 2), Dunn's test revealed significant statistical differences of firmness during the storage time. No differences from harvest until day 20 were observed using the penetrometer. For Bartolillo orchard (Table 2) and using non-destructive devices, firmness at day 0 and 10 differed from day 20 and 30 and RTE, whereas significant differences at each day of sampling were observed when using a penetrometer. Significant differences during the sampling time were also observed for samples stored in CA storage (Table 3).

Results presented in this study agree with those reported by Li et al. (2016) in kiwifruit. A decline in firmness during storage was also observed, and a good relationship between standard penetrometer and nondestructive device was reported. The firmness change depended on the storage technique and while measuring by penetrometer depends also by the speed approach measurement. Higher speed tends to give higher values of firmness. Peleg (1993) found positive association while comparing destructive and non-destructive firmness in apple fruit but claimed that linear regression and correlation coefficients depended strongly on the firmness range of the inspected sample. As the firmness may vary from sample to sample, correlation coefficient is not suitable for comparisons of firmness measurement methods. The results of our study are also in agreement with those reported by Plocharski et al. (2000) who found positive association between destructive and nondestructive firmness in pear and apple fruit stored in CA and RA conditions. They concluded that correlation coefficient varies with cultivar and growing season; these results that corroborate with those of our study. Significant correlations in firmness measurement methods were also found according to fruit type in peaches, nectarines and plums (Valero et al., 2007). As it was observed in our study, the rugosity of the peel and its characteristics also influence the results of the measurement. How might it affect the correlations between these two devices is a matter to be considered.

The technique of CA can provide different concentrations of gas, such as low O₂ and high CO₂ levels, which are always used with the appropriate temperature and relative humidity (RH) for fruit storage. Ma et al. (2019) reported that CA storage with the suitable conditions proves to be better than RA as a storage regimen to keep the quality of fruit. In their research, they found that fruit stored under CA showed lower contents of weight loss and malondialdehyde (an indicator of lipid peroxidation, membrane injury and cellular oxidation) and a higher content of total soluble solids, titratable acidity, total phenolic contents and vitamin C, and in contrast, the alcohols, malondialdehyde and esters displayed elevated levels in RA conditions of stored lemon fruit (Ma et al., 2019). McDonald and Harman (1982) also reported that CA conditions delay the rate of kiwifruit softening and increased storage life up to 3–4 months beyond normal air-storage life (RA). Enhancement of quality attributes (firmness and weight loss) in mango fruit by CA technology was also found by Hailu et al. (2016) and by Santana et al. (2011) in peaches. Ethylene production was also found to be lower in CA storage conditions (Golias et al., 2016) in pear fruits. Recently, a study by Hernandez et al. (2021) using mechanistic models clearly showed that CA storage retains the firmness of the fruit when compared to RA. Different non-destructive firmness measurements have been previously reported in other fruits such as in apples (Osinenko et al., 2021), in tomato (Alenazi et al., 2020), in peach fruit (Minas et al., 2021) and in avocado (Landahl and Terry, 2020), and this was recently extensively reviewed by Arunkumar et al. (2021). The results presented here are important, and the models built can be used in the routine laboratory to rapidly measure the firmness, thus contributing to decrease fruit discards commonly observed while using destructive devices.

The results prompt us to conclude that there is positive association between firmness measured by the destructive method (fruit penetrometer) and non-destructive measurement by a texture analyser during the maturity stages and under different storage conditions. The rho coefficient was dependent on the orchard and storage technique. There was less loss of firmness in fruit stored in CA than that stored in RA. The models built are robust and can be used to predict penetrometer firmness from non-destructive measurement. The models were built from sufficient data and can be extended to model firmness of any Hass avocado fruit via non-destructive measurements. In addition, using non-destructive methods to account for quality parameters contributes to decrease fruit discards while firmness by penetrometer depends on the penetration speed and the trigger force at which the penetration measurements commence.