# Implementing Topological Data Analysis for Monitoring Mass Transfer during Vacuum-Assisted Osmotic Dehydration of Apples

## TL;DR

This study uses topological data analysis to monitor mass transfer during apple dehydration, revealing how different conditions affect water and solute diffusion.

## Contribution

The novel use of topological data analysis with Euler characteristic curves to monitor and quantify mass transfer in osmotic dehydration processes.

## Key findings

- ODVP treatment resulted in higher water diffusivity compared to OD.
- TDA revealed a double-peak structure in ECC, characteristic of diffusion processes.
- A topological metric correlated strongly with diffusion coefficients, varying by treatment and GJC concentration.

## Abstract

This study applies topological data analysis (TDA) to
real-time
experimental images of grape juice impregnation in apple samples with
the goal of monitoring and quantifying the evolution of mass transfer
under different processing conditions. We monitored the effective
diffusivity (D) of water, solutes, and biocompounds
during osmotic procedures using 40, 50, and 60 °Brix grape juice
concentrate (GJC) by computing a topological descriptor of the real-time
images known as the Euler characteristic curves (ECC). Osmotic procedures
were osmodehydration (OD, absolute pressure, P
abs = 598 mmHg) and OD assisted with vacuum (ODVP, P
abs = 498 mmHg/10 min). The modified slope method
for cubic geometry estimated D considering shrinkage
and time evolution with R
2 > 0.80.
Results
show that samples treated with OD have higher shrinkage (20–25%)
compared to those treated with ODVP. Water D was
greater with ODVP and increased (p ≤ 0.05)
at higher GJC concentrations. Solutes and total monomeric anthocyanins D were higher in OD and decreased with an increasing GJC
concentration. Our TDA of real-time images revealed a double-peak
structure of the ECC, which is characteristic of diffusion processes.
We also found a simple topological metric (the difference between
the maximum and minimum values of the ECC) that correlates positively
with the diffusion coefficient D (r
2 > 0.7858) in OD experiments and negatively (r
2 < −0.9567) in ODVP at 60 °Brix.
The TDA also indicated that the OD treatment at 40 °Brix resulted
in uniform impregnation and redistribution of solutes within the impregnated
samples after reaching osmotic equilibrium. The proposed TDA approach
opens the door to nonintrusive, image-based monitoring of impregnation
experiments, enabling high-throughput screening.