Fish freshness is one of those issues that concerns both consumers and businesses, but it's often assessed by feel: we look at the brightness of the eyes, smell it, touch it… and decide if it's good or not. The problem is that these methods are subjective, depend on the experience of the person looking at the product, and, moreover, don't always detect the internal changes already occurring in the fish's muscle.
In a context where seafood travels thousands of kilometers from the point of capture to the plate, relying solely on sight and smell falls short. Therefore, in recent years, mathematical models have been developed that can predict freshness based on real biochemical processes that occur after the fish dies. One of the most interesting advances comes from Hokkaido University, where a predictive model based on ATP degradation has been designed. This model allows for the estimation of not only current but also future freshness with great accuracy and clear applications in the industry.
Why is fish freshness such a delicate issue?
Fish deterioration begins immediately after the animal dies , even if it appears perfectly fine externally. Internally, a series of transformations occur in the muscle tissue that affect nutritional quality, aroma, flavor, and texture, but these changes are not always evident without specific analyses.
Traditionally, the industry has relied on sensory inspection and microbial counting to assess freshness: the overall appearance, gills, eyes, and odor are observed, and the bacterial load is measured in the laboratory. These methods have several significant limitations: they depend heavily on the inspector's experience, require time and equipment, and the results can vary from one technician to another.
This variability in assessment can lead to serious errors: fish that is discarded prematurely (food waste and economic losses) or products that are kept on sale when they have already begun an advanced stage of deterioration, impacting food safety and consumer confidence.
To address this problem, food science has established the use of the K value as an objective indicator of freshness. This index is based on the chemical degradation of energy compounds in fish muscle, allowing for the quantification of the fish's stage of deterioration without relying so heavily on subjective judgment.
ATP and muscle breakdown: the biochemical basis of the K value
While alive, the fish's muscle cells use ATP (adenosine triphosphate) as their energy currency. At the time of death, this ATP ceases to be regenerated, and a well-known and sequential chain of degradation reactions begins, resulting in various intermediate and final compounds.
ATP is first transformed into ADP and AMP, and subsequently into IMP (inosinate), which is further degraded into inosine (HxR) and hypoxanthine (Hx). Each step in this chain is linked to noticeable changes in the taste and smell of fish. IMP, for example, is related to the pleasant umami flavor we associate with tasty, fresh fish, while the final compounds, such as hypoxanthine, contribute bitter notes and increasingly strong and unpleasant odors.
The K value is constructed precisely from this sequence of reactions. It is defined as the percentage that inosine (HxR) and hypoxanthine (Hx) represent with respect to the total ATP-derived compounds present in the muscle:
K(t) = (HxR + Hx) / (ATP + ADP + AMP + IMP + HxR + Hx) × 100
The higher this percentage, the greater the degree of degradation of the muscle's energy system and, therefore, the lower the freshness. When the K value is low, ATP and its early derivatives predominate, and the product is considered very fresh; as the value increases, deterioration compounds take over the system and the fish enters advanced stages of quality loss.
One of the key findings from the studies is that the final stage leading to spoilage compounds (especially the formation of hypoxanthine) has a much greater impact on the overall outcome than the initial stages of the chain. In practical terms, the rate at which the fish "crosses the line" into these end products is what truly distinguishes acceptable fish from questionable fish from clearly spoiled fish.
From laboratory index to predictive mathematical model
Although the K value was proposed more than 60 years ago at Hokkaido University itself and is now an international benchmark indicator, its traditional application has an obvious drawback: to measure it, muscle samples must be taken, processed and analyzed in the laboratory using chemical techniques, in a procedure that is slow, destructive and expensive.
To overcome these limitations, researchers in Hokkaido, led by Associate Professor Naoto Tsubouchi , have developed a mathematical model that describes ATP degradation as a chain of first-order reactions. In this type of process, the conversion rate of each compound depends on the amount present at that moment, allowing the use of relatively simple differential equations to describe the evolution of the system.
The new model does not simply calculate a static K value, but simulates how the concentrations of ATP, ADP, AMP, IMP, HxR, and Hx in muscle change over time under specific storage conditions. From these theoretical concentrations at any given time, the K(t) value is obtained using the previous equation, making it easier to estimate current and future freshness.
In experimental tests with different marine species, the model has shown correlations greater than 0,96 between the K values ​​calculated by the equations and those measured in the laboratory. This high level of agreement suggests that the tool is robust and applicable beyond purely experimental settings, approaching real-world market and distribution situations.
One of the great advantages of this approach is that it uses relatively simple information: species, storage time, and temperature . With this data, it's possible to predict freshness without needing to take tissue samples at every point in the chain, opening the door to non-destructive, near-real-time control systems.
A nearly universal model for different species of fish
A major challenge in modeling fish freshness is the enormous diversity of species. Although the ATP degradation pathway is basically the same in many marine fish, reaction rates and certain nuances can vary from one species to another, which traditionally required the design of species-specific models, impractical for an industry that handles a multitude of different products.
The work of Tsubouchi and his team proposes a common model structure for several species, maintaining the same chain of reactions and adjusting only some kinetic parameters for each type of fish. This approach allows the model to have a unique mathematical framework into which the specific values ​​of the species in question are "plugged in."
The trials included, among others, different varieties of mackerel , a species of great importance both in Japan and in other markets. The model's predictions were compared with laboratory K-value measurements, and a very high degree of agreement was observed, with error margins of around 30% or less, a range considered reasonably adequate for industrial applications.
This ability to generalize to multiple species is key to the model's practical implementation. Instead of developing a separate mathematical system for each fish, a common, adaptable foundation is used, reducing costs, complexity, and development time. Furthermore, other studies applied to species such as sardines, salmon, gilthead seabream, and hake have also generated predictive equations based on physicochemical parameters, achieving accuracies exceeding 90% in estimating freshness, ice storage time, and microbial load.
In the specific case of these commonly consumed species in Spain, approximate sensory shelf lives have been defined as 10 days for gilthead seabream and 12 days for salmon and hake, provided that adequate cold storage conditions are maintained. Sardines, due to their nature and greater sensitivity to temperature fluctuations, are more problematic and require special attention.
Relationship between freshness, flavor and consumer perception
The mathematical model's value extends beyond safety and shelf life, providing information on sensory quality and flavor . The same biochemical pathway of ATP degradation used to define the K value largely determines whether the fish will have a pleasant (umami) flavor profile or begin to develop undesirable tastes and odors.
During the early stages, when inosinic acid (IMP) predominates , the umami flavor is intense and characteristic; the fish is perceived as savory and fresh. As inosine and hypoxanthine accumulate, the sensory profile shifts towards bitter undertones and more aggressive aromas, even though the overall appearance may still be acceptable to an untrained eye.
Studies conducted across the agri-food chain have shown that consumers consider freshness the most important attribute of fish, even above price. This priority is observed in both wild-caught and farmed fish, such as gilthead seabream. Retailers generally agree with this assessment, while producers sometimes place more emphasis on other factors, although they acknowledge the critical importance of offering the freshest possible fish.
Detailed analyses of freshness attributes have shown that gills and eyes are the elements that show the earliest signs of deterioration during ice storage, a finding consistent with everyday experience in fishmongers and markets. However, models based on physicochemical parameters (such as nitrogen compounds, pH, K value, etc.) allow for the anticipation of internal changes before they become visible to the naked eye, providing an objective basis that complements sensory evaluation.
Furthermore, the use of multivariate analysis and mathematical modeling has shown enormous potential for integrating objective and subjective dimensions of fish quality: on the one hand, measurable and reproducible data; on the other, perceptions, preferences and expectations of the different links in the chain (producers, distributors, retailers and final consumers).
From theory to real time: sensors and the Internet of Things
The practical utility of the mathematical model based on ATP degradation increases when combined with real-time monitoring technologies . Currently, tools such as hyperspectral imaging, chemical sensors, and electronic systems exist that can detect variations in fish composition without destroying the sample.
On their own, these devices typically offer point measurements, but lack predictive capabilities . The approach developed in Hokkaido proposes using the model as a "brain" that interprets the sensor signals, translates them into parameters of the reaction system, and from there, estimates the current K value and its future evolution.
In an Internet of Things (IoT) scenario , where fish boxes, cold storage rooms, trucks, and logistics centers can be equipped with connected sensors, the model would act as an automated decision-making tool: it feeds on data about temperature, species, and storage time, calculates freshness and remaining shelf life, and issues alerts or recommendations on which batches should be sold first, which ones are better to lower in price, or when it is advisable to remove product from the chain.
Researchers have filed patents in several countries related to this technology, envisioning its integration into sensor devices and automated freshness control systems. For an increasingly globalized fishing industry, where supply chains are lengthening and becoming more complex, tools like these can make the difference between efficient logistics and one plagued by losses and claims.
In parallel, established predictive models, such as the Food Spoilage & Safety Predictor (FSSP) program from DTU Aqua, are used as a benchmark for comparing new equations. Recent work has developed up to 15 predictive equations based on physicochemical parameters, demonstrating over 90% accuracy against real-world data and FSSP results, confirming that the combination of sensors, modeling, and sensory evaluation is a powerful tool for the industry.
Impact on industry and quality management
Fish is a staple food in the global diet , with a very high percentage of global production destined directly for human consumption, and fresh fish surpassing other forms in popularity. In the European Union, per capita consumption is very high, and countries like Spain are among the top in the ranking, with more than 40 kg per person per year.
This importance translates into enormous pressure on the management of seafood quality and safety . Companies must offer fish that meets the freshness expectations of an increasingly demanding consumer, while controlling costs, reducing waste, and complying with strict health regulations.
Objective quality studies have shown that temperature fluctuations during storage and transport have a direct impact on spoilage, especially in sensitive species like sardines. Small variations in the cold chain can significantly shorten shelf life, increase the K value, and accelerate the appearance of sensory defects.
At the same time, the heterogeneity of the raw material (size, physiological state, post-capture handling, etc.) introduces additional variability. Modeling allows for the incorporation of some of this variability through adjustable parameters and confidence ranges, helping the company to better understand and control the risks associated with each batch.
In assessments of compliance with freshness and quality requirements, it has been observed that producers typically meet technical specifications at a high rate (around 87%), retailers fall slightly short (around 79%), and consumers perceive compliance as lower (around 50%). This gap highlights the difference between "measured" and "perceived" quality and reinforces the role of objective tools in supporting transparency and communication throughout the supply chain.
In practice, having mathematical models of freshness that integrate laboratory data, sensory evaluation, and process parameters allows the industry to make faster and more reliable decisions: better define the declared shelf life, adjust pricing strategies according to the actual state of the product, plan transport based on the expected freshness, or identify critical points in the chain where the most days of shelf life are lost.
This whole approach fits with a clear trend towards more efficient and sustainable food systems , where the goal is no longer just to ensure that the fish "is not bad", but also to reduce avoidable waste and offer consistent quality over time and across markets.
Looking at the body of evidence, models based on ATP degradation and K value transform invisible processes into a quantitative tool that helps us understand how fish freshness evolves from the moment of capture until it reaches the plate. By combining sensory inspection, physicochemical analysis, predictive equations, and sensor and IoT technologies, a much more refined system is achieved for quality control, improving decision-making in the fishing industry and offering consumers a safer, tastier product that is more consistent with what they expect when they simply ask for truly fresh fish.
