Assessment and Prediction of Fish Freshness Using Mathematical Modelling: A Review

Citation: García, M.R.; Férez-Rubio, J.A.; Vilas, C. Assessment and Prediction of Fish Freshness Using Mathematical Modelling: A Review. Foods 2022,11, 2312. https:// doi.org/10.3390/foods11152312 Academic Editor: Robert L. Buchanan Received: 16 June 2022 Accepted: 25 July 2022 Published: 2 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). foods Review Assessment and Prediction of Fish Freshness Using Mathematical Modelling: A Review Míriam R. García 1, Jose Antonio Ferez-Rubio 1,2 and Carlos Vilas 1,* 1Research Group on Biosystems and Bioprocess Engineering (Bio2eng), IIM-CSIC, 36208 Vigo, Spain; [email protected] (M.R.G.); [email protected] (J.A.F.-R.) 2Research Group on Microbiology and Quality of Fruit and Vegetables, CEBAS-CSIC, 30100 Murcia, Spain *Correspondence: [email protected] Abstract: Fish freshness can be considered as the combination of different nutritional and organoleptic attributes that rapidly deteriorate after fish capture, i.e., during processing (cutting, gutting, packaging), storage, transport, distribution, and retail. The rate at which this degradation occurs is affected by several stress variables such as temperature, water activity, or pH, among others. The food industry is aware that fish freshness is a key feature influencing consumers’ willingness to pay for the product. Therefore, tools that allow rapid and reliable assessment and prediction of the attributes related to freshness are gaining relevance. The main objective of this work is to provide a comprehensive review of the mathematical models used to describe and predict the changes in the key quality indicators in fresh fish and shellfish during storage. The work also briefly describes such indicators, discusses the most relevant stress factors affecting the quality of fresh fish, and presents a bibliometric analysis of the results obtained from a systematic literature search on the subject. Keywords: mathematical modelling; fish quality; fish freshness; bibliometric analysis; predictive microbiology; stress variables; quality degradation 1. Introduction The main causes of food discarding among consumers and retailers are the food aspect, outdating, and safety uncertainty [ 1 ]. Damage and spoilage of foods lead to around 15% of waste, which increases to 35% if food is subject to inadequate storage and transport conditions [ 2 , 3 ]. Mathematical modelling describing the evolution of food quality indicators, under given storage and transport conditions, is central to minimising food waste [ 2 ]. Therefore, the prediction of fresh fish quality is a major challenge for the food industry, distributors and retailers to adjust prices and minimise food waste. Fresh fish and shellfish are highly perishable products due to their biological composition. Under normal handling chilled or refrigerated storage conditions, their shelf life is limited by enzymatic, chemical and microbiological spoilage. Fresh fish is stored, transported and distributed in boxes of high-density poly-ethylene filled with ice. Other common conservation methods for fresh fish are the transport and storage in tubs with water and ice or at superchilling temperatures [ 4 , 5 ]. From fish capture to consumer consumption, there are several factors affecting fish quality, being temperature the most relevant. The prediction of fish quality in all these cases is critical to determine the price of the product and sell it before it is not of sufficient quality, or even safety, for the consumer. Quality in fresh fish, and generally in food, is a broad concept that involves different attributes (chemical, physical, microbiological, sensory) which can be measured either directly or indirectly. In the last decades, several analytical techniques have arisen [ 6 ] including biosensors to measure microbial pathogens or biogenic amines [ 7 ]; electronic noses or electronic tongues for volatile compounds, K-value or TVB-N [ 8 , 9 ]; or hiperespectral imaging to determine moisture content or texture [ 10 , 11 ]; among other. The selection Foods 2022,11, 2312. https://doi.org/10.3390/foods11152312 https://www.mdpi.com/journal/foods Foods 2022,11, 2312 2 of 26 of the analytical method depends on the selected indicator, but also on properties such as accuracy, reliability, portability, rapidity, easiness to use and analyse the results, time consumption and price. Ideally, the methods should be also non-destructive and noninvasive [ 12 ]. Recent works [ 6 , 13 , 14 ] present exhaustive reviews regarding the different analytical methods considered in the literature to measure the most commonly used quality indicators for fish freshness assessment. Typically, assessment methods focus on fish quality at the moment of measurement but are unable to predict quality changes in the following days. Prediction requires the use of appropriate mathematical models. It is important to mention that some authors, for instance, ref. [ 15 – 17 ], use the term predictive model to denote models that correlate freshness indicators with experimental measurements (pH, TVB-N, hyperspectral imaging, Electronic nose data, etc.). Typically, some type of regression is used to obtain these models. Although these works are common and necessary, in this review, we will use the term predictive for those models able to forecast the future evolution of the freshness indicators. Otherwise, we will use the term assessment or estimation. Mathematical models for the prediction of fresh fish quality are diverse and difficult to classify. In this review, we propose the use of general features of the mathematical structure to organise the different modelling alternatives, as illustrated in Figure 1. The final objective of the model is either to estimate (using indirect online measurements) or to predict one or more chemical, physical, microbiological or sensory attributes that are indicators of the consumer’s perception. Such attributes (odour, texture, TVB-N, spoilage bacteria, etc.) are the output of the model (blue part of the figure). The input of the model (red part of the figure) can be any external factor (temperature, pH, fish feed, etc.) affecting the quality indicators. The model (orange part of the figure) provides a quantitative relationship between inputs and outputs either using empirical relationships or inspired by known mechanisms of fish quality degradation. Models Relationship factors/attributes (Section 4) Inputs Stress Factors (Section 3) Pre-slaughter and slaughter conditions Fish feed Fish origin Fish killing Handling, storage and distribution T pH CO 2 Outputs Quality attributes (Section 2) TVB-N, TMA-N Spoilage bacteria Texture ATP degradation Biogenic amines Sensory Analysis Lipid Oxidation Odour Colour Nutrients Water content Electrical properties Figure 1. Fish quality models are described attending to their Quality attributes (Section 2), Stress factors (Section 3) and models, i.e., mathematical relationships between attributes and stress factors (Section 4). This review is organised following the structure presented in Figure 1. It begins by summarising the results of the systematic literature review performed to investigate the most typical quality attributes used to define fish quality, including a brief description Foods 2022,11, 2312 3 of 26 of the procedure followed to perform such a review. Secondly, it introduces the relevant stress factors affecting fish freshness. Such stress factors can be split into two groups: Pre-slaughter/slaughter conditions, and handling, storage and distribution conditions. In Section 4, we review the mathematical relationships or models that allow us to describe and predict fish quality attributes (outputs) as a function of the stress factors (inputs). As a final remark, we will discuss what we think are the main challenges for modelling fish quality and possible alternative solutions to consider in the future. As a general rule, we will denote by fish quality any positive attribute, either nutritional, organoleptic or a combination, in fresh fish, and therefore related to fish freshness. In this regard, issues not related to fresh fish were not considered in this review, such as processed fish (cooked, sterilised, etc.) or social aspects such as food security or production of added-value compounds. 2. Quality Attributes (Model Outputs) Food quality in fresh fish and fresh fishery products is a broad and complex concept defined by a set of attributes (quality attributes) that are either nutritional, organoleptic, or a combination of both. The levels (concentrations) of some chemical compounds describe nutritional quality attributes. Examples of nutrients include vitamins, bioactive forms of oligo-elements, essential amino acids, digestible proteins or unsaturated fatty acids, among others. On the other hand, colour, texture, flavours or aroma are attributes defining the organoleptic quality of a particular food product. Organoleptic variations in fish are caused by changes in chemical, microbiological and physical properties. Sometimes, quality attributes are defined by the level of a particular biological, chemical or biochemical factor (e.g., the concentration of a given vitamin, nucleotide, enzyme, or bacteria, among others), although usually, it is the result of a combination of different factors. For example, colour is the (observable) result of a certain combination of pigments on a given food matrix that have been produced or consumed under the action of many biochemical transformations. Other quality attributes, such as freshness, are defined by the combination of nutritional and organoleptic properties which deteriorate with time. Freshness can quantitatively be described using different sensory scores, such as the Quality Index Method (QIM), or other simpler indicators, such as the shelf life dating of a given food product, either to specify the last date when the product must be sold (“sell by date”), the “high-quality” period or the date when the product must be removed from the store [18]. We have analysed this diversity of quality attributes studied in the literature, and their interconnections, by conducting a systematic bibliographic review and bibliometric analysis of the articles (in the Web of Science Core Collection database, Food Science and Technology category). Figure 2summarises the procedure we have followed to perform the systematic literature search. Terms related to fish quality Terms related to fish names Terms related to off-topic issues NEAR/5 NOT Abstract, title and keywords analysis New terms Terms related to modelling 1636 works 33 works Full paper analysis 25 works Figure 2. General scheme of the procedure followed in this manuscript to perform the systematic literature search. Foods 2022,11, 2312 4 of 26 Inside the dashed rectangle, we represent the iterative part of the procedure. First, we constructed two lists. One of the lists contained terms related to fish quality, such as freshness, K-value, and lipid oxidation, among others. The other one contained general terms such as seafood or shellfish and fish species names. In the search, words from both lists must appear in a major field (abstract, title or author keywords). We have found many works that included words from both lists, in which the quality terms were not related to fish. To avoid these situations, we used a maximum separation of five words (NEAR/5) between the terms in both lists. This separation was chosen by the trial and error method with the objectives of avoiding the exclusion of manuscripts within the scope of this work (shorter separations) and minimising the number of off-topic manuscripts (larger separations). Since the focus of this review is on fresh fish, we have excluded from the search (NOT) those words related to off-topic issues such as processing (sterilisation, modified atmosphere, etc.), production of added-value compounds (essential oils, gelatin, etc.), food security or other social aspects, among others. The initial search still included works not related to fresh fish quality so we identified, new terms that should be avoided, and repeated the search. The list of terms included and excluded in the systematic search is presented in Appendix A. This iterative procedure resulted in 1636 works. Details about such works and a bibliometric analysis are available online in the repository [ 19 ]. In this material, the interested reader can access 2 types of reports: a PDF file that includes the main results of the general search, and 12 interactive reports for sub-collections defined as the group of works where one of the 12 selected quality attributes is mentioned in a major field. Table 1summarises the results of the systematic review for each of the 12 categories or groups. The table presents, for each category, the number of works, total citations, average citations per work, and the most cited works. Table 1. Most employed quality attributes in the literature. The number of total citations per year is used to obtain the most cited articles. The terminology used for each attribute was: Lipid oxidation (fatty acid*, lipid oxidation, TBA, TBARS, thiobarbituric), Sensory analysis (QIM, QSM, sensory analysis, sensory evaluation, sensory method, TVB-N/TMA-N (TVB-N/TMA-N), Spoilage bacteria (SSO, spoilage bacteria, spoilage microorganism*), Texture properties (texture, hardness, firmness), Biogenic amines (biogenic amine*), Odour (odour, odor), Colour (colour, color, chromatism), Nutrients (nutrient*, vitamin), Water content/activity (water content, water activity) and Electrical properties (electrical properties, conductance, conductivity). Quality Attribute Citation Counts No. Works Avg. Citations per Work Most Cited Works Lipid oxidation 10,875 474 22.9 Herrero [12], Richards and Hultin [20], Grigorakis et al. [21] Sensory analysis 5295 209 25.3 Ólafsdóttir et al. [22], Al Bulushi et al. [23], Olafsdottir et al. [24] TVB-N, TMA-N 4386 185 23.7 Pacquit et al. [25], Papadopoulos et al. [26], Ruiz-Capillas and Moral [27] Spoilage bacteria 3876 155 25.0 Al Bulushi et al. [23], Gram et al. [28], Dalgaard [29] Texture 3587 176 20.4 Herrero [12], Olafsdottir et al. [24], Alasalvar et al. [30] ATP degradation 3509 124 28.3 Ólafsdóttir et al. [22], Veciana-Nogués et al. [31], Jones et al. [32] Biogenic amines 3282 112 29.3 Al Bulushi et al. [23], Veciana-Nogués et al. [31], Kim et al. [33] Odour 3066 119 25.8 Papadopoulos et al. [26], Ramanathan and Das [34], Kawai [35] Colour 2830 149 19.0 Pacquit et al. [25], Kuswandi et al. [36], Huang et al. [37] Nutrients 704 62 11.3 Chakraborty and Raj [38] , Moreda-Piñeiro et al. [39] , Palaniappan and Vijayasundaram [40] Water content/activity 573 32 17.9 Cakli et al. [41], Morzel et al. [42], Raju et al. [43] Electrical properties 381 11 34.6 Olafsdottir et al. [24], Vaz-Pires et al. [44], Yao et al. [45] Additionally, we have incorporated in the repository a PDF file that contains the information included in the interactive reports. All the reports, iterative or not, include a general analysis of the collection (including, for example, time span, collaboration index, Foods 2022,11, 2312 5 of 26 authors per article, citations per year), and analysis of the countries, authors, articles and journals. Networks of co-citations and keyword co-occurrences were also incorporated. Moreover, the collections can be downloaded as an Excel file and the graphs and tables can be manipulated to, for example, constrain the works to those where certain words, selected by the user, are mentioned in the abstract. Most of the manuscripts were research articles, dating back from 1949 and with citations increasing homogeneously since then, except for two jumps in publications in 1977 and 2002. Around 100 works were published in 2021, the last year considered in the review. The most cited works were written by Ólafsdóttir et al. [22] with a review on methods to evaluate fish freshness and by Ryder [46] with a method to measure ATP and its breakdown products to estimate the KI -value. The most productive countries have been China, USA and Spain. These are also the countries where the documents with the greatest impact (in terms of average article citations) were produced. Journal of Food Science (145 documents), Food Chemistry (140 documents) and Journal of Agricultural and Food Chemistry (72 documents) are the journals with the largest number of publications. The most productive authors were from the northwest of Spain (S. P. Aubourg, BarrosVelázquez), whereas the authors with the greatest impact were Ólafsdóttir and Dalgaard from Iceland and Denmark, respectively. After the iterative procedure was finished, we refined the search (see Figure 2) to find those works related to mathematical modelling. We read the resulting 33 manuscripts and kept those (25) that fitted within the scope of this review. In the next sections, we define each of the attributes with references to the main works in the area. For a deeper discussion about these quality attributes we recommend some recent comprehensive reviews [6,13,14]. 2.1. Lipid Oxidation Lipid oxidation is the attribute gathering the greatest attention, both in terms of the number of citation counts and of works, with a remarkable increase of publications during the first decade of the current century remaining almost invariant during recent years. The most cited researchers on this topic are M. P. Richards and Y. Ozogul. Although fatty acids are also nutrients (described in Section 2.10), we have decided to consider them separately because of the importance of lipid oxidation. Fish constitutes the main source of polyunsaturated fatty acids (PUFA), up to 40% of long chain fatty acids [ 47 ], with quantity and composition changing with the catching period and depending on whether the fish is wild or cultured [ 21 ]. PUFA are easily oxidised into aldehydes, responsible for changes in flavour, texture and odour, known as rancidity [ 6 , 12 , 20 , 22 , 48 ], and are highly affected in most of the cases by previous fish bleeding [ 20 ]. In addition, the oxidation reaction can decrease the nutritional quality of food and certain oxidative products are potentially toxic [ 48 ]. Primary lipid peroxidation products (peroxide value being its most common measure) include hydroperoxide that is unstable and decomposes to generate various secondary products, such as aldehydes that contribute to fish rancidity [ 12 ]. The most common method to measure aldehydes is the thiobarbituric acid-reactive substance (TBARS) test [22]. The main advantage of this indicator is that the oxidation of unsaturated lipids produces alterations in smell, taste, texture, colour, and nutritional value [22] . Therefore, it provides us with a global measure of fish freshness. However, analysis of PUFA is a destructive method so the fish sample analysed cannot be commercialised. 2.2. Sensory Analysis Despite being the second most relevant quality attribute in terms of publications (with G. Ólafsdóttir being to a large extent the most cited author), sensory analysis is the most used method to assess freshness, probably because it depends on a combination of the other quality attributes [ 22 ]. In this group, we include any form of measure or interpretation of fish freshness perceived by the senses of sight, smell, taste, or touch. They can be assessed Foods 2022,11, 2312 6 of 26 by a trained panel or by consumers’ subjective opinions about preferences. The most common method in Europe is the Quality Sensory Method (QSM) based on the Council Regulation (EC) No 2406/96 for marketing standards [ 49 ]. The output of this method is a discrete value that classifies fish in four levels of freshness (Extra, A, B, and Not Admitted). This method is based on shared characteristics in fresh fish and therefore is common to different fish species. For specific tests, the most common method is the Quality Index Method (QIM) [ 50 ]. The output of the QIM is also a discrete value ( 0,1,2, . . . , n) , where lower values correspond to fresher fish. The criteria to select the value and the number of levels (n) depend on the fish species considered. The main advantages of these methods are: (i) they are minimally invasive, and do not involve the destruction of the sample, since the sense of taste is not included; (ii) they can be used to estimate fish shelf life by agreeing from which level the food is not considered of sufficient quality to be sold to the consumer; (iii) instead of focusing on one particular feature, they provide a global evaluation of fresh fish. However, sensory analysis methods are highly subjective and depend, to a large extent, on the expertise of evaluators. The cost associated with the use of a panel of evaluators is another disadvantage. These disadvantages can be alleviated by using analytical techniques -colourimeters, electronic noses, hardness testersinstead of a panel of experts . Another alternative is the Global Stability Index (GSI), a score gathering the influence of many attributes, sensory or not. The GSI is computed using the following general expression [51]: GSI =1− n ∑ i=1 αi Ai−Ai,0 Li−Ai,0 (1) Ai and Ai,0 are, respectively, the values of a given attribute, for example, TVB-N or K-value, at assessment time t and at initial time t= 0. αi is the weight given to each attribute, n is the total number of attributes considered, and Liis the spoilage threshold for attribute Ai. 2.3. TVB-N/TMA-N The formation of volatile nitrogen bases, such as trimethylamine (TMA-N), dimethylamine (DMA), or ammonia, from the reduction of trimethylamine oxide (TMAO), is a widely investigated cause of fish odour. There was a substantial increase in interest during the 10 years after 1996, being Ruiz-Capillas the most cited author. The total amount of volatile bases (TVB-N), as well as individual methylamines, have been extensively used as indicators of quality degradation in postmortem fish [ 52 , 53 ]. The reduction reactions are catalysed by bacteria such as Shewanella spp. or Pseusomonas spp., during fish spoilage [ 54 ]. Some authors [ 17 , 26 , 52 ] have argued that these volatile bases are poor freshness indicators for some fish species because of the low content, or even absence, of TMAO. However, the FAO specified a maximum allowable level in international trading of 10 mg of TMAnitrogen per 100 g fish muscle [55]. 2.4. Spoilage Bacteria Research works regarding this quality attribute have increased since 1994 without any deceleration in the last years as previously described attributes. Dalgaard, Gram and Bulushi, are, markedly, the most cited authors. Fish freshness deteriorates rapidly with the growth of Gram negative psychrophilic or psychrotrophic bacteria, named spoilage bacteria (SSO), due to their ability to reduce TMAO and to produce hydrogen sulphide [ 28 ]. Common spoilage bacteria of fish at chilled temperatures are: (1) Shewanella putrefaciens for being H2S -producing bacteria and with acceptability limits around 10 7 CFU/g [ 56 ] or even slightly higher 10 7.02 CFU/g [ 57 ], (2) Pseudomonas spp. with the same acceptability limits [ 56 – 58 ], or larger when analysing for example Pseudomonas psychrofila (10 8.5 CFU/g [ 59 ]), and (3) broad measurements such as Total Viable Counts (TVC) with a limit of 106CFU/g [16]. More information can be found in [28,60,61]. Foods 2022,11, 2312 7 of 26 Since microbial growth and metabolism is the major cause of food spoilage [62] , spoilage bacteria is a key indicator of fish freshness and shelf life. The main disadvantage is that the procedure to determine bacterial concentration is tedious and time consuming. 2.5. Texture Properties Bibliometric analysis for texture attributes reveals that many works mentioned this attribute without being the focus of the work. Among the works considering texture as a relevant focus, we would like to highlight the review on fish texture [ 63 ] and a research article assessing texture, among other chemical and sensory characteristics, of sea bream [30]. Texture can be evaluated using minimally invasive techniques. However, contrary to other food matrices, such as beef, texture in fish is not usually regarded as a relevant freshness indicator, particularly when considering fresh fish. As mentioned in [64] , it should be considered in combination with other indicators, such as colour and odour. Use of texture as a fish quality indicator limits to either cooked or frozen fish stored for long periods, where an increase in toughness and dryness of the tissues can be observed [ 63 ]. After cooking, the taste of fresh fish is associated with firm meat that goes to dry, crumbly with short, tough fibres for deteriorated fish. However, raw fish maximum toughness commonly occurs after 1–2 days of storage, corresponding to the minimum pH and rigor mortis [63]. Texture properties are typically considered in the evaluation of the QIM [65]. 2.6. ATP Degradation Although the number of citations places this attribute in the sixth position, it is the third one in average citations per work. Most of the works were published in the nineties and during the past 10 years, with G. Ólafsdóttir being the most cited author . After fish death, ATP transforms, within the first 24-48 h , into inosine 5 0 -monophosphate (IMP) in three steps, producing adenosine diphosphate (ADP) and adenosine monophosphate (AMP) [ 66 , 67 ]. IMP degradation continues on a cascade of reactions that produces Inosine 5 0 -monophosphate (Ino) and hypoxanthine (Hx), which is further decomposed in other compounds such as xanthine and uric acid [ 52 , 67 ]. This cascade of reactions occurs in the order of days to weeks, depending on the storage temperature and bacterial concentration [ 68 ]. IMP is related to the pleasant sweet and meaty flavors in fresh fish, umami flavour [ 69 , 70 ], whereas Hx is responsible of unpleasant bitterness [ 71 , 72 ]. The K-value and K I -value are two of the most widely employed indicators to evaluate freshness. They are defined as the following function of the ATP degradation products [68,73–76]: K-value =Ino +Hx ATP +ADP +AMP +IMP +Ino +Hx ·100 (2) KI-value =Ino +Hx IMP +Ino +Hx ·100 (3) The K-value has been also correlated with the freshness of different fish species [ 73 ]. The authors found that very high grade corresponded with K-value lower than 10%. High grade individuals had K-values lower than 20% or 30%, depending on the fish species. Fishes with K-value up to 50% correlated with medium grade. Finally, K-value larger than 50–70% was obtained for low grade samples. The main advantages of indexes based on the degradation of ATP (K-value, KI-value ) are their reliability [66] and, as mentioned above, their direct connection with fish flavor. The main disadvantages are that the evaluation of K-value or KI-value requires the destruction of the sample and their usefulness depends on the fish species being examined [64]. 2.7. Biogenic Amines Works studying the correlation between spoilage and biogenic amines are homogeneously increasing since the nineties, being the most cited articles by Bulushi, Ruiz-Capillas and Vecianogues. Biogenic amines here are non-volatile amines (histamine, cadaverine Foods 2022,11, 2312 8 of 26 and putrescine) formed by decarboxylation of amino acids (histidine, lysine and ornithine, respectively). Although TMA-N and TMAO are also biogenic amines, they are not considered in this group because TMA-N is volatile and it is a result of the degradation of TMAO, therefore being one of the main contributors to the formation of TVB-N, as discussed in Section 2.3. Within non-volatile biogenic amines, histamine is the most studied due to its toxicity and allergic potential, but it is unable to correlate with the level of spoilage for different fish and conditions [ 23 ]. Cadaverine is the biogenic amine that can be used as a spoilage indicator (for example, for salmonid fish, values less than 10 mg/kg indicate good quality [ 77 ]). Putrescine, however, is not a good spoilage index because its amine, ornithine, is not present in all fish species (for example, it is missing in tuna). Alternatively, there are amine indexes combining different biogenic amines such as the amine index (AI): AI =putrescine +cadaverine +histamine Total amines ·100 Total amines =putrescine +cadaverine +histamine +tyramine+ tryptamine +methylamine +spermidine +spermine or the chemical index: Chemical index =putrescine +cadaverine +histamine 1+spermidine +spermine For relationships between amine content and spoilage level for different fish species, the reader is referred to Table 2 in [23]. 2.8. Odour The number of citations, works, and average citations per work, regarding this attribute, are similar to ATP degradation and Biogenic amines but with a homogeneous distribution of the number of articles per year. X. Y. Huang and V. Papadopoulos are the authors with the largest number of citations regarding this attribute. Same as texture and colour, this quality attribute is usually studied in the literature together (or even correlated) with other attributes. The major aromatic compounds identified related to spoilage levels are fatty acids profiles, aldehydes, ketones, trimethyl amine (TMA), and volatile organic compounds [ 78 ]. Typically, studies focus on assessing odour following one standard sensory index (see, for example, ref. [ 26 ], for sea bass assessment). Commonly, freshness is associated with iodine shellfish and seaweed smell, and spoiled fish with muddy, putrid, faecal, pungent, smell to ammonia or ink smell in cephalopods and acidic in shrimps. Odour can be evaluated using non-invasive methods. However, using a panel of evaluators to assess this indicator is subjective and expensive. Analytical methods could be used to analyse aromatic compounds. However, in most cases, this would involve the destruction of the sample. Although, if electronic noses are properly calibrated and validated odour can be a very interesting quality indicator . 2.9. Colour Despite being an important indicator for consumers, it is one of the attributes with the lowest number of citations and average citations per work. However, the interest of the scientific community seems to increase during the last 15 years. The most cited author in this field is A. Pacquit. Colour changes have been also used as an indicator for quality degradation in combination with other attributes or as a part of sensory analysis. Colour degradation kinetics are the result of changes in the pigments due to some biochemical transformations. For example, the oxidation of myoglobin and haemoglobin turns the flesh colour from red to brown. As pointed out by [ 6 ], some compounds present in fish, such as amines or ammonia, may react with the oxidised liquid causing serious browning. The main advantage of using this feature to assess quality is that, as mentioned above, it is an important indicator for consumers. Besides, colour measurements can be obtained Foods 2022,11, 2312 9 of 26 using non-invasive or minimally invasive techniques. However, fish skin is heterogeneous in many species. Therefore, the results provided by devices to measure colour, such as colourimeters, will vary depending on the regions of the skin being measured. A trained panel of experts could be used to globally evaluate the colour of fish skin. However, this alternative has the same disadvantages mentioned for sensory analysis and odour, i.e., it is expensive and subjective. 2.10. Nutrients Fish is highly appreciated as a healthy food product [ 16 , 79 , 80 ] mainly because it is rich in nutrients such as high-quality proteins, fatty acids, and vitamins, among others. However, despite its importance, nutrients are not usually considered as a factor for determining fish freshness, except for the study of fatty acids, already considered in Section 2.1. This is the attribute with lower average citations per work, being the most cited author K. Chakraborty with48citations. Mostofthehighlycitedmanuscriptsfoundin thesystematicsearch regarding nutrients focused on different aspects [ 38 – 40 , 81 ], such as the characterisation of vitamin compounds; the use of fish oil; correlations between arsenic bioavailability and nutrient content; among others, not directly related to fish freshness. This is probably because the rate of degradation of most nutrients is slower than other indicators such as the QIM and when changes are noticeable, fish is already spoiled. Another disadvantage is that the assessment of nutrient content requires destructive methods. 2.11. Water Content/Activity The number of citation counts and the average citations per work for this attribute are the second lowest in the list, after nutrients. This is probably because it is usually considered a stress factor and not a quality indicator itself. The most cited author is S. Cakli. Water content is related and can be described from water activity using the moisture sorption isotherm curve. Although this relationship is a non-linear function, water content increases with water activity and vice versa, and therefore both are essential quality parameters related to important textural attributes such as juiciness [ 12 ], mainly related to texture and flavour. However, as in the case of other indicators, destructive methods are used for the assessment of water content. 2.12. Electrical Properties This attribute has gained the lowest attention in terms of the number of works. However, works focusing on this attribute are highly cited, with a review of different multisensors gathering most of the citations [24] . In fact, the average number of citations per work is the largest of all attributes considered in this review. Enzymatic and bacterial decomposition of proteins and lipids after fish death results in the formation of charged molecules which increase the electrical conductance (EC) of the muscle [ 6 , 82 ]. The loss of this kind of nutrients can be, therefore, correlated with the increase of EC. Autolytic spoilage is also responsible for cell membrane disruption, which allows the liquids to pour out increasing the EC [24,45]. The main advantage of this indicator is that it can be measured using minimally invasive techniques, avoiding the destruction of the sample. However, the correlation between EC increase and freshness degradation must be performed for the different fish species. 3. Stress Factors and Their Usual Models (Additionally, Named Secondary Models) Food quality attributes are conditioned by the food matrix microstructure and composition as well as by several stress or environmental variables [ 18 ]. Chronologically, those factors modifying fish quality can be classified attending to the origin and slaughter conditions of the fish (pre-slaughter and slaughter) and due to handling, storage and distribution. Fish composition and matrix microstructure depend on many factors such as the fish species, its size, age, and gender, whether it is lean or fat, fresh or saltwater fish, the fish feed, catching period (seasonal variability), geographical area or temperature of Foods 2022,11, 2312 16 of 26 where a0represents the parameter determining the duration of the delay (mathematically equivalent to the expression used by [ 113 ] for lag phase in bacterial growth, a0= 1 indicates no delay), K is the growth rate due to psychrotrophic bacteria ( N ). Interestingly, years after this work, a simpler exponential model was used to model TVB in rohu fish stored at 0 and 5 °C [ 80 ], claiming that TVB formation was a primary function of microbial action and suggesting the necessity to model TVB as a function of the microbial population as already carried out in the literature [97]. Table 4. Works in the systematic search, including modelling of spoilage bacteria. The following acronyms are used: TVA for total viable counts, TMAB for total mesophilic aerobic bacteria, TPAB for total psychrophilic aerobic bacteria and LAB for lactic bacteria. Output Matrix Secondary Model Primary Model References Pseudomonas & Shewanella Bogue µmax(T)Arrhenius & Ratkowsky Baranyi’s model Taoukis et al. [56] Pseudomonas & Shewanella Gilt-head seabream µmax(T)&λ(T) Arrhenius & Ratkowsky Mod. logistic model Koutsoumanis and Nychas [57] Sulphide producers & non-producers Gilt-head seabream µmax(T)(not clearly defined) Baranyi’s model Giuffrida et al. [92] Pseudomonas & Carnobacterium Tropical shrimp µmax(T)Arrhenius & Ratkowsky Baranyi’s model Rep. Gompertz Model Dabadé et al. [59] Pseudomonas & Shewanella Hake µmax(T)Ratkowsky Baranyi’s model García et al. [95] TVC Grass carp – Rep. Gompertz Model Ying et al. [16] Psychrotrophic counts Cod – Baranyi’s Model García et al. [97] Pseudomonas, Enterobacteriaceae, TMAB, TPAB & LAB Rainbox trout µmax(T)Ratkowsky Mod. Logistic Model Genç and Diler [99] Pseudomonas Gilt-head seabream – Mod. Logistic Model Correia Peres Costa et al. [58] Biomass Rohu fish – Mod. Logistic Model Gompertz Model Prabhakar et al. [80] 4.3.3. Texture Properties As mentioned above, no predictive models were found in the systematic search for texture properties. It must be highlighted that the works [ 89 , 93 ] describe the models they develop as predictive. However, as mentioned in the introduction, we use the term predictive to indicate the ability of the model to forecast the evolution of the quality indicators. The models developed in [ 89 , 93 ] are built using partial least squares regression or least-squares support vector machines to assess texture indicators using nuclear magnetic resonance (NMR) or hyperspectral imaging (HSI) measurements. In other words, these models provide a non-invasive estimation of the texture properties at the NMR or HSI measurement time, but they do not predict the future evolution of such indicators. A predictive model to describe the viscoelastic behaviour of rohu fish (Labeo rohita) was developed in [ 115 ], although this work was not present in the systematic search. The authors used the modified Maxwell model to relate skin hardness and compression time for iced fish: F(t) = C0+Cexp t trel  Foods 2022,11, 2312 17 of 26 where F(t) is the force at any time, C0 corresponds with the force at equilibrium, C is the decay force, and trel is the relaxation time. Experimental data was used to fit coefficients C0,Cand trel. Further research is required regarding the mathematical description of the evolution of texture in fresh fish. 4.3.4. ATP Degradation As mentioned in Section 2.6, ATP degradation occurs in a series of steps represented as: ATP →ADP →AMP →IMP →Ino →Hx →Xa →Uric acid The first three steps occur relatively fast after slaughter so, when fish samples are analysed they contain low (or zero) concentrations of ATP, ADP and AMP. On the other hand, the degradation from Hx to Xa and uric acid is usually slow and when such products are formed, the fish is already spoiled. Therefore, in general, ad hoc models only consider the part of the scheme involving IMP, Ino and Hx. The KI -value, Equation (3), can be obtained from these compounds. Table 5summarises the main features of the models derived in the different works of the systematic search. In particular, ref. [52,67] considered the reaction scheme: IMP K1Ino K2 Kbac Hx where K1 and K2 are, respectively, the reaction rates for the conversion of IMP into Ino, and Ino into Hx. Bacterial conversion of Ino into Hx ( Kbac ) was also taken into account. In these works, first-order kinetics are considered. Arrhenius expressions were used to account for the dependency of reaction rates on the temperature. Bacterial growth was modelled using an exponential model of the form of Equation (7). In [ 52 ], the possibility of a loss of nucleotides by leaching (diffusion through muscle and skin) was also considered. Another interesting issue about this work is that the author presented and discussed the results obtained from data of forty-five different fish species. Reliable results were obtained for most of the considered species. In [ 68 , 96 ], the authors found, by fitting the models to experimental data, that alternative nucleotide degradation paths might occur in European hake (Merluccius merluccius). In particular, the direct conversion of IMP to Hx and other products should be considered. Leaching of nucleotides and the effect of bacteria, namely Pseudomonas spp. and Shewanella spp., on the conversion of IMP to Ino and Ino to Hx, were also considered. The standard square-root model [ 85 ] was used to represent the bacterial growth rates. Table 5. Ad-hoc models found in the systematic search to describe the degradation of IMP, Ino and Hx. The KI -value is obtained from the concentration of these components. All these models consider a cascade of first-order reactions. Output Matrix Secondary Model Primary Model References IMP, Ino, Hx Rainbow trout Ki(T)Arrhenius Exponential model, Bacterial catalysis Howgate [67] IMP, Ino, Hx Forty-five species Ki(T)Arrhenius Exponential model, Bacterial catalysis, leaching Howgate [52] IMP, Ino, Hx Hake Ki(T)Arrhenius First-order reaction model Vilas et al. [96] IMP, Ino, Hx Hake Ki(T)Arrhenius First-order reaction model, Bacterial catalysis, leaching Vilas et al. [68] 4.4. Sensory or Shelf Life Models Quality ad hoc models are usually a tool, more than the final aim, to assess or predict shelf life or different grades of fish quality. For example, modelling of spoilage bacteria in Table 4is commonly used to estimate shelf life by specifying a concentration of bacterial Foods 2022,11, 2312 18 of 26 counts at which the quality is considered not sufficient. Shelf life date, for example, is estimated using spoilage bacteria in bogue fish (Boops boops) and gilt-head seabream (Sparus aurata) for numbers greater than 7 logs ( N> 10 7 CFU/g) [ 56 , 57 ] or even N> 10 8.5 CFU/g for Pseudomonas psychrofila in tropical shrimp [59]. There are models in the literature that are used to estimate different grades of freshness, not only shelf life or a given quality indicator. These models are summarised in Table 6. As shown in the Table, works following this approach and the number of species considered are scarce. The main challenge is to find a mathematical relationship between the outputs of the ad hoc models and different quality levels. The first attempt consisted of dividing the QIM into three indexes ( QIMS for skin, QIMG for gills, and QIMF for flesh), and finding their relationship with non-producers ( Nw ) and producers ( Nb ) of sulphide, present in those specific parts for the fish [ 92 ]. However, for an estimation of a final QIM index, not only models of spoilage bacteria but also of TVB-N are required [ 97 ]. In this work, a simple ANN was developed to obtain the relationship between QIM and the model variables (TVB-N and bacterial count). A logistic model was used to describe the bacterial evolution. Other works focused on using models of spoilage bacteria to find ranges of standard sensory methods. Such methods considered fewer freshness grades than the QIM. That is the case in [ 16 ], where cod freshness, in terms of a three-level standard (SC/T 3108-1986), was correlated with the TVC value. The work by [ 95 ] used a nonlinear function of Pseudomonas and Shewanella counts to determine a four-level QSM value in European hake. This work is the only one that considers a secondary model, and therefore, it is the only one that provides the final relationship between the effect of temperature changes in the four levels of quality in QSM. Table 6. Modelling of sensory scores using ad hoc models. QIM stands for Quality index specific for gilt-head seabream [ 65 ] or cod [ 50 ] method. S,G and F for Skin, Gills, Flesh, Nw , Nb , Np , Ns , Npsy for sulphide and non-sulphide produces, Pseudomonas,Shewanella and psychrotrophic counts. Output Matrix Secondary Model Primary Model References QIMS,QIMG,QIMF(15 levels) Gilt-head seabream Not clearly defined QIM(Nw,Nb)Giuffrida et al. [92] Council Regulation(EC) No 2406/96 (1996) Standard method (4 levels) Hake µmax(T)Ratkowsky SM(Np,Ns)García et al. [95] SC/T 3108-1986 Standard method (3 levels) Cod – SM(NTVC)Ying et al. [16] QIM (23 levels) Cod – QIM(TVBN,Npsy)García et al. [97] 5. Modelling Challenges and New Directions In this review, we have described, classified and established connections for the different types of mathematical models to describe and predict fish quality. We have mainly focused on those works within the systematic search described in Appendix A, although other relevant contributions, not included in such search, were considered in this review. First of all, we should stress that the literature is larger, particularly in the case of spoilage bacteria using predictive microbiology. However, there are many comprehensive reviews regarding predictive microbiology [ 60 , 116 , 117 ], and the focus of this review was, instead, on providing connections between models that describe different fish quality attributes, and on identifying those topics that require more research attention. For example, there are still relevant quality attributes for which it was not possible to find mathematical models. The most illustrative example is lipid oxidation, the most studied attribute in the literature from the experimental point of view. Other attributes lacking modelling approaches are non-volatile biogenic amines, nutrients, odour and water activity (although this is considered as an input in several models in the literature). Other attributes, such as colour, have been modelled only for processed fish. Foods 2022,11, 2312 19 of 26 We need to stress that, in addition to the lack of modelling for certain quality attributes, there are major limitations in some of the models we found. Generic models, named in this review software sensors or multi-sensors, are particularly advantageous to compare results from different studies but, in this comparison, it is clearly observed that there are many inconsistencies between works. For example, both linear and exponential functions have been used to model the same attribute (see Table 3). However, whereas linear functions may approximate a short time window of an exponential model, differences between both approaches are considerable for wide prediction windows. There is a need to compare those modelling structures and detect which ones are more appropriate for the different quality outputs. Ad-hoc predictive microbiology models, that have been studied in detail, still present limitations, mainly due to the uncertainty of the estimated parameters and the initial bacterial fish load (or model initial conditions). Microbial models require a known starting state, but measuring bacterial load takes time and involves the destruction of the sample. Some partial solutions have been considered such as (1) using the worst-case scenario [ 116 ], (2) estimating the initial conditions variability [ 95 ], or (3) estimating the numbers using indirect measurements of other variables (such as conductance measurements) that are non-invasive and fast to obtain [ 118 ]. However, taking into account that bacteria grow exponentially between lag and stationary phase, model prediction is highly affected (very sensitive) by its initial conditions. More research on this topic is required to find confidence models of spoilage bacteria. Another challenge, still only partially addressed in the literature, is the derivation of expressions that allow the inference of sensory attributes or shelf life from the growth of spoilage bacteria. In this regard, some works derived models describing two or several attributes, for instance, shelf life and growth of Pseudomonas, but such attributes were only connected through the stress variables, typically temperature (see examples in Table 4). Ideally, the model should provide a final quality index, as a function of different quality attributes that depend on the stress variables, as the examples provided in Table 6. In addition, only a few works validate the predictive capability of the models proposed, i.e., the ability of the model to describe data outside of the set used for model development and parameter estimation. Most of them use constant temperature or temperature oscillating at a high frequency, as compared with the model dynamics time-scale (using such oscillating temperature would be equivalent to using a mean constant temperature). For example, in the work by [ 56 ] two non-isothermal profiles are used for the validation. In one profile, temperature oscillates at high frequency and the change in the output signal was smaller than the experimental error of the measurement. On the other hand, the model was validated using a temperature profile with wider oscillations, that provided a change in data trend and model dynamics. Only a few works consider dynamic temperature profiles, computed using an optimal experimental design, to reduce the uncertainty of the predictive model [95]. To advance in this area, reproducibility of published works is a key aspect, particularly for ad hoc models, usually more complex and with many different mathematical structures. Currently, comparison among works is extremely difficult, not only because of the variability between fish species and conditions before and after the capture (for example in food structure [119] ) but also because the proposed measure of fish quality is sometimes specifically developed for the study [ 118 , 120 ]. We think that for the advance of modelling of fresh fish quality, research should be focused on reproducing and predicting established sensory indexes, such as QIM [95,97,121], allowing comparison between approaches. Finally, the community should invest in better exploitation of the available models and towards their integration into software systems for online quality prediction, as is already the case in food safety [ 122 ], or even for optimisation-based determination of the best conditions to maximise shelf life in different processes. In this regard, an ambitious objective would be the derivation of a digital twin [ 123 ] for fresh fish degradation. Let us here use an illustrative example of the potential of these models in a study developed in Foods 2022,11, 2312 20 of 26 our group, namely [ 124 ]. In this work, existing models were used to find the best active package configuration (including the type of packaging and concentration of antimicrobial) that maximises food quality while ensuring food safety. In addition, the model was used to predict, at any moment, the expected food quality for the expected stress variables along the food chain. Author Contributions: M.R.G. and C.V. designed the original idea, drafted and review the manuscript. J.A.F.-R. conducted the bibliometric analysis. All authors have read and agreed to the published version of the manuscript. Funding: We thanks the grants RTI2018-093560-J-I00 funded by MCIN/AEI/10.13039/501100011033, “ERDF A way of making Europe”, the CSIC grant 20213AT001 and Project Pescando4.0 (ref. 202178002) funded by NextGenerationEU funds in the framework of the Plan de Recuperación, Transformación y Resiliencia (PRTR) managed by the Ministerio de Agricultura, Pesca y Alimentación through the RD 685/2021. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: All bibliometric analysis is shared in the repository [ 19 ], with link doi:10.5281/zenodo.6414360. Acknowledgments: Authors M.R.G. and C.V. would like to express their gratitude and dedicate this contribution to Antonio A. Alonso, the researcher that inspired this work, which unfortunately left us prematurely. We thank their endless support and continuous guidance. Conflicts of Interest: The authors declare no conflict of interest. Appendix A. Systematic Literature Search Table A1. Terms of the search performed on the web of science. The search was limited to the Web of Science Core Collection database and to the Food Science and Technology category. All years until end 2021 are considered. Set Search Records #1 (TI OR AB OR AK) = ( (“quality” OR “freshness” OR “shelf life” OR “shelf-life” OR “K-value” OR “KI-value” OR “ATP” OR “adenosine triphosphate” OR “IMP” OR “inosine monophosphate” OR “hypoxanthine” OR “colour” OR “color” OR “chromatism” OR “fatty acid*” OR “lipid oxidation” OR “tba” OR “electrical properties” OR “electrical conductance” OR “electrical conductivity” OR “texture” OR “hardness” OR “firmness” OR “odour” OR “odor” OR “nutrient*” OR “vitamin” OR “biogenic amine*” OR “water content” OR “water activity” OR “tvb-n” OR “tma-n” OR “qim” OR “qsm” OR “sensory analysis” OR “sensory evaluation” OR “sensory method” OR “sso” OR “spoilage bacteria” OR “spoilage microorganism*") NEAR/5 ("fish” OR “fishes” OR “shellfish” OR “seafood*” OR “albacore” OR “amberjack” OR “anchovy” OR “angler” OR “barbel” OR “barracuda*” OR “sea bass” OR “beluga” OR “bigeye” OR “blackfish” OR “bluefish” OR “blue runner” OR “blue shark” OR “branzino” OR “seabream” OR “sea bream” OR “butterfish” OR “carp” OR “catfish” OR “catshark” OR “comber” OR “conger” OR “cutlassfish” OR “danubian wels” OR “dogfish” OR “eel” OR “eels” OR “flounder” OR “flying fish” OR “forkbeard” OR “garfish” OR “garrick” OR “guitarfish” OR “gunard” OR “haddock” OR “hake” OR “halibut” OR “hammerhead” OR “herring” OR “icefish” OR “John dory” OR “lamprey” OR “lanternfish” OR “leerfish” OR “little tunny” OR “mackerel” OR “mahi mahi” OR “marlin” OR “megrim” OR “melva” OR “monkfish” OR “moonfish” OR “needlefish” OR “pandoras” OR “panga” OR “pangasius” OR “parrotfish” OR “parrot fish” OR “perch” OR “pike fish” OR “pilchard” OR “pilotfish” OR “pilot fish” OR “plaice” OR “pollack” OR “pollock” OR “ponyfish” OR “porbeagle” OR “rainbow trout” OR “cownose ray” OR “devilray” OR “butterfly ray” OR “softnose skate” OR “legskate” OR “sawfish” OR “ribbonfish” OR “rockfish” OR “rosefish” OR “sablefish” OR “sailfish” OR “salmon” OR “sardine” OR “sardinella” OR “scabbardfish” OR “scorpionfish” OR “sheatfish” OR “shi drum” OR “sillago” OR “skipjack” OR “smooth hound” OR “smooth-hound” OR “spearfish” OR “St Peter’s fish” OR “stargazer” OR “stingray” OR “sturgeon” OR “surgeon fish” OR “swordfish” OR “tilapia” OR “threadfin” OR “triggerfish” OR “trout” OR “tubefish” OR “tuna” OR “turbot” OR “walleye” OR “whitebait” OR “whiting” OR “yellowtail” OR “octopus” OR “squid*” OR “crab” OR “lobster*” OR “prawn*” OR “shrimp*” OR “cuttlefish*” OR “crayfish*” OR “langoustine*” OR “scampi*” OR “urchin”) ) 6429 Foods 2022,11, 2312 21 of 26 Table A1. Cont. Set Search Records #2 ( TI OR AB OR AK ) = ("high pressure” OR “atmospheric cold plasma” OR “modified atmosphere*” OR “sterilization” OR “sterilisation” OR “frozen” OR “thawed” OR “pH-shift processing” OR “cross-processing” OR “fillet*” OR “slice*” OR “fish oil*” OR “quality of water” OR “water quality” OR “frying” OR “garlic” OR “canned fish*” OR “surimi” OR “fish sauce” OR “nugget” OR “chitosan” OR “x-ray*” OR “farming” OR “farm-level” OR “antibacterial” OR “antimicrobial” OR “electronarcosis” OR “immun*” OR “Fluorescence in situ hybridization” OR “cooking” OR “microplastic*” OR “embryo*” OR “rice” OR “drying” OR “dried” OR “nursery” OR “fishmeal” OR “plastic” OR “irradiation” OR “larva*” OR “feed*” OR “coating” OR “diet” OR “dietary” OR “reproductive” OR “ibuprofen” OR “fertilizer*” OR “valorization” OR “catch damage” OR “thermal process*” OR “non-thermal process*” OR “non thermal process*” OR “children” OR “gear design” OR “additive” OR “mimicry” OR “seed quality” OR “sodium alginate” OR “edible film*” OR “TYRP1 gene*” OR “transgene” OR “antioxida* peptide*” OR “antioxida* capacity” OR “antioxida* solution” OR “antioxida* effect*” OR “anti-oxida* activity” OR “antioxida* activity” OR “rearing” OR “algae” OR “collagen expression” OR “genomic*” OR “proteomic*” OR “s-potential*” OR “fish meal” OR “synthesis” OR “egg quality” OR “carotenogenesis” OR “nutrient requirement*” OR “maternal” OR “oily fish” OR “gelatin” OR “polychlorinated” OR “nutrition of salmonoid” OR “fish retina” OR “color picture*” OR “elderly” OR “inheritance of color” OR “short read mapping program” OR “tea polyphenol” OR “fish consumption” OR “inter-specific hybrids” OR “extracellular lipase” OR “pathology” OR “metabolic polymorphisms” OR “transgenic” OR “eco-label” OR “lethality” OR “micro-squid” OR “emulsion*” OR “vegetable production” OR “source of nutrient*” OR “hydrolyzate*” OR “epiphitic” OR “bilirubin” OR “essential oil*” OR “histology” OR “egg-yolk” OR “chd” OR “silver toxicity” OR “biomanipulation” OR “hormonal-control” OR “protein crosslinking” OR “food security” OR “high hydrostatic pressure” OR “red tide*” OR “intake” OR “digestibility” OR “nutrient absorption” OR “nutrition” OR “docking” OR “egg” OR “diet” OR “nutrient recycling” OR “farm effluents” OR “fish behavior” OR “smoked” OR “chromatophore*” OR “hydroponic” OR “recovery of fish” OR “fish recovery” OR “fish-odor syndrome” OR “fish-odour syndrome” OR “water chemistry” OR “natural preservatives” OR “mince” OR “epiphytic” OR “phosphorus” OR “omega3” OR “hemolysate” OR “hemolysis” OR “availability of nutrients” OR “biosynthesis” OR “health” OR “globalization” OR “inhibition of polyphenoloxidase” OR “species identification” OR “virus” OR “norovirus” OR “ferment*” OR “bread” OR “plant extract*” OR “nanoencapsulate*” OR “starch” OR “edible compound*” OR “edible natural compound*” OR “fish burger*” OR “wafer*” OR “bromelain” OR “fish ball*” OR “fish cake*” OR “dehydrat*” OR “grill*” OR “4-hexylresorcinol” OR “freezing” OR “freezing-point” OR “restructure*” OR “squid oil” OR “molecular distilation”) 332,851 #3 #1 NOT #2 1636 #4 (TI OR AB OR AK) = (“mathematical model*” OR “predictive model*” OR “dynamic model*” OR “growth model*” OR “predictive microbiology” OR “model”) 922,980 #5 #3 AND #4 33 The use of the term ID (keywords plus) in our search caused the selection of many spurious publications. 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