## 1 Introduction  
Harvested lettuce heads should be stored at 0\({}^{\circ}\)C until marketed or used [1]. Research has shown that the shelf life of lettuce stored at 0\({}^{\circ}\)C is 21 - 28 days, but only about 14 days when stored at 5\({}^{\circ}\)C [2]. Pre-cooling and maintaining lettuce at low temperatures, without interruption, is one of the most important factors for prolonging post-harvest shelf life and quality. Shelf life of field-grown lettuce was prolonged by rapid (vacuum) cooling immediately following harvest [3]. If pre-cooled lettuce is left outdoors at an air temperature of approximately 21\({}^{\circ}\)C, the core temperature can go from 0.6\({}^{\circ}\)C to 10\({}^{\circ}\)C within the same day [4]. Greenhouse-grown butterhead lettuce is more perishable than field-grown iceberg lettuce [5]. Our preliminary results indicated that vacuum cooling improved the shelf life of commercially harvested greenhouse lettuce [6].  
Temperature fluctuations during post-harvest handling and storage also influence shelf life, and it is desirable to be able to predict the remaining shelf life (RSL) for a box of lettuce. For this reason, some type of device was necessary to record temperatures after harvest. There are two general approaches. First, time-temperature indicators (TTI) may be used to monitor temperatures and to predict shelf life. Three types of TTI for temperature-sensitive foods [7] were available based on; the melting point of a chemical mixture (e.g. 3M Monitor Mark), an enzymatic reaction (e.g. Vitsab TTI tags), or a polymerization reaction (e.g. LifeLines FreshCheck indicators). Some of these consumer readable TTI tags were evaluated with greenhouse-grown lettuce in a previous study, and Vitsab was found to be most suitable for lettuce [8]. There are certain problems that need to be corrected before TTI can be used [9]. For example, manual activation of the TTIs may cause variability in the mixing of the lipid substrate and the enzyme. A machine was designed to activate the TTIs automatically and uniformly in large-scale applications. Even more critical, the activation energy of food and the TTI must be identical, often requiring thorough experimentation. Secondly, a recording device such as a portable data logger can be placed inside a box of lettuce, and temperature records of shipping conditions can be retrieved at various points along the distribution chain. The total shelf life (TSL) of a lettuce head consists of the total number of remaining marketable days: the number of days in storage until the present, plus the RSL which consists of a sum of unknown days into the future. If the overall response of a product to variable storage temperature scenarios can be modeled, it should be possible to use measurements to a given date during the storage period to predict what will occur under assumed future conditions. However, the interactions of temperature and time are complex and difficult to model.  
Methods to model and predict biological functions are often difficult due to non-linear responses and complicated interactions among input factors. A new approach, neural network (NN) modeling, has been applied to predict biological functions. NN models have been used for different predictions: canopy photosynthesis [10], shelf life of meat products [11], pepper fruit coloration [12], and pepper weekly yields [13]. There is no literature reporting the use of NNs to predict shelf life of greenhouse-grown lettuce. The objective of this study was to develop models for predicting RSL of greenhouse-grown lettuce. The data used were from experimental and commercial harvests involving a wide range of pre-harvest conditions and post-harvest temperature fluctuation. Several NN models were established and validated against observed shelf lives. Regression analysis was also used as a comparison.