GR1009084B - A non-destructive method for the direct evaluation of the fish flesh mechanical features - Google Patents

Abstract

Novelty: there is disclosed a method enabling the direct evaluation of the mechanical features and, thereby, the quality level of the flesh of the caught fish via analytic mathematical expressions derived from the experimental non-destructive dynamic action of a load exerting pressure to the fish flesh. Evaluation process: the entire fish or portion thereof consisted of muscle tissues is placed on a steady or moving base for being subjected to a non-destructive sinusoidal, pulse, impulse or step-type pressure exerted to a defined point of the fish flesh. The subsequent reaction of the base -in terms of resistance, displacement, velocity or acceleration force- is registered in real time. It has been demonstrated that the reaction is associated to the mechanical features of the fish flesh via analytic mathematic expression describing the elasticity and toughness of this last; so, the use of the data resulted from a number of experimental cycles conducts to the evaluation of the mechanical features of the fish flesh, in an automated “algorithmic” manner. For the comparative evaluation of the quality level of the fish flesh mechanical features, the evaluation data can be compared to the respective values of other related fish via statistical decision-making processes.

Description

P E R I G R A F H

Non-destructive method for direct calculation - evaluation of mechanical characteristics of fish flesh

The present invention refers to a method that allows the direct calculation - evaluation through analytical mathematical expressions of the mechanical characteristics (and therefore the quality) of the flesh of caught fish, through a non-destructive experimental process for the fish.

One of the main characteristics of fish quality is the mechanical characteristics of their flesh. These vary depending on many endogenous or exogenous factors. Endogenous factors include fish species, sex, genetic background and stage of maturity. Extrinsic parameters include its nutritional history (Grigorakis, 2010), handling for farmed fish (exercise, handling stress), its degree of freshness, the handling it has undergone during extirpation (mortality stress) and after it (Coppes- Petricorena, 2010). Based on the above, it is understood that a direct calculation - assessment with analytical mathematical expressions of the mechanical characteristics of fish flesh can provide information about its quality and mainly about key parameters in determining it, their freshness (freshness) and traceability them (traceability).

The non-destructive evaluation of the quality of fish concerns, mainly, the part of their freshness and is implemented by numerous provisions, which, however, are not based on the mechanical characteristics of their flesh but on the evaluation of visual changes (e.g. EP2189789 A1, WO2014053679A) or in the evaluation of electrochemical changes related to freshness (eg EP0137677 B1, US5288613 A, US 4980294 A). Regarding the evaluation of the mechanical characteristics of fish flesh and food in general, the relevant methods can be distinguished into two types. In the organoleptic evaluation methods of the mechanical characteristics of the flesh, i.e. the evaluation based on the human senses and their analysis in an analytical way with the use of a relevant analysis device (texture profile analyzer-TPA). The first always involves the issue of the human factor and the subjectivity of human perception, while the validity of its results requires the organization and training of a group of people who will evaluate the characteristics of the fish flesh through specialized organoleptic tests (texture analysis). Therefore, it is time-consuming and involves technical difficulties, since it requires the coordination of a group of people, specific space and conditions. In addition, it requires the destruction of test samples, i.e. the fish evaluated by the testers. Analyzers, on the other hand, are analytical instruments with high costs and space limitations, while the majority of these tests destroy the sample.

Furthermore, there are a number of patents that make robotic assessment of flesh characteristics by reproducing the processes of chewing and processing food in the mouth (e.g. JP4089301B2, CN201340359Y, CN201754138U), with devices simulating the oral cavity (test chamber) of the tongue ( suction cup) or the jaws (upper and lower moving surfaces) The aforementioned methods also recommend destructive testing of the samples. In addition, methodologies have been developed to measure the "physicality" (physicality) and therefore the mechanical properties of agricultural foods, by using a clamp on the food and reading the produced vibration spectrum or acoustic spectrum which is then analyzed by Fourier analysis into its basic elements to provide information on the mechanical properties of the food (US6857317B2). Patents that describe the penetration of a piston into food and convert the produced electrical vibration signal into textural properties of the food (US2013/0228016) are of a similar philosophy. These methods constitute on the one hand destructive control and on the other hand refer to agricultural products (fruits, vegetables) or food vaguely, without making any allusion to the possibility of application to meat products (such as fish).

The use of vibration spectra after prior excitation in the context of the interpretation of the mechanical properties, has also been done in semi-liquid or liquid foods, as a non-destructive method of their evaluation (US2009/0217758). US2007/0104840 is a method for evaluating the acceptability of muscle foods, including fish, in terms of firmness, juiciness and aroma, using electrical stimulation and converting the signal into a scale of degree of acceptance (palatability index). This particular method, although non-destructive, is an indirect way of approaching some mechanical properties. The same logic applies to EP0290540B1, which has a scope of application in fish fillets whose mechanical properties are evaluated non-destructively using lighting and image analysis of the light signal, in order to identify breaks on the surface of the fillet, related based on size and depth to destruction of the tissue (hence degradation of its mechanical properties).

In the fish industry, the most common empirical, non-destructive method for assessing the mechanical properties of fish is the so-called finger pressure method, where a person presses the flesh of the fish and empirically assesses its hardness and elasticity (Coppes-Petricorena , 2010). Therefore, any method that includes non-destructive measurement of these properties in a direct way and without involving the subjectivity of the human factor is particularly applicable and useful in industry.

In the past there has been a method with commercial application (Zwick hardness tester) for non-destructive measurement of hardness and counting its changes based on the change of freshness of the fish (Schubring 2002). Fish freshness has also been assessed (Grigorakis, & Dimogianopoulos, 2010) on the basis of indirect assessment of changes in their mechanical properties, through a non-destructive method. In this method there was no analytical mathematical expression describing the response of the fish to stimulation as a function of its mechanical characteristics, so the latter were evaluated from the response signal in an indirect way. At the same time, a stochastic methodology was used to model the response of the fish to non-destructive loading with the aim of connecting it with freshness (Dimogianopoulos & Grigorakis, 2011), as well as with their nutritional history (Grigorakis & Dimogianopoulos, 2012), while subsequent improvements of this methodology they acted so that there was no effect of the body weight of the fish (Dimogianopoulos & Grigorakis, 2014). In the last three cases, the evaluation of the mechanical characteristics was done in an indirect way based on the calculation of a stochastic model of the response of the fish and the examination of some of its characteristic properties.

The purpose of direct calculation - evaluation of the mechanical characteristics of fish flesh in a non-destructive manner is achieved by the method having the characteristics defined in claim 1. The method comprises the application of non-destructive dynamic loading to a given point of a whole fish or part thereof containing muscle tissue (piece, fillet, fillet) called "fish flesh" and is placed on a firm or endogenic base, called "substrate". By performing non-destructive loading, it is ensured that the product under test can be used either for consumption or for further controls after the test in the context of the application of the present method, thus taking advantage of the corresponding methods as well as the TPA that require destruction of the sample and mentioned above. Although TPA can potentially do non-destructive testing, the present method is superior based on the fact that it does not require bulky, expensive, and specialized infrastructure (equipment). Also, the direct estimation process (through the use of analytical mathematical expressions) of the mechanical characteristics of the flesh is advantageous over methods (US2007/0104840 and EP0290540B1) that check these characteristics indirectly. In addition, the fact that mechanical characteristics associated with the elasticity and viscoelastic behavior of the flesh are evaluated is an advantage over other methods (Zwick hardness tester) which give direct results for a single mechanical characteristic (hardness).

Non-destructive dynamic loading on fish flesh causes the substrate on which the flesh is placed to react, in the form of a resistive force or displacement, or velocity or acceleration thereof recorded in an electronic computer file in real time. The form of this response is directly influenced by the mechanical characteristics of the fish flesh which are linked to its elasticity and viscoelasticity. The response data undergo automated (algorithmic) computer processing to calculate the mechanical characteristics of the fish flesh on the basis of an analytical mathematical relationship between them and the response. The latter are again compared in an automated way (algorithmic statistical decision-making process) with typical values for the species of fish being tested, at which point the level of mechanical flesh characteristics of the fish under test is evaluated. Therefore, both the inference of the mechanical characteristics of the flesh of the test fish and their comparison with the ideal values for the type of fish are not affected by the human factor, as in the case of the organoleptic tests mentioned above.

The non-destructive method of calculating - evaluating the mechanical characteristics of fish flesh is then analyzed and presented through a relevant example of its application using the following figures. In Figure 1 are described the possibilities of placing the fish flesh 1 on a fixed 2 or an endortic background 8 (connected with an elastic means 7 to the ground 3) for the non-destructive loading 4, as well as its profiles that can be used. Figure 2 describes the placement of the fish flesh 1 on a fixed background 2 and the corresponding equivalent Kelvin-Voigt model representing the fish flesh 1 placed on the background 2 by means of a damper 5 and a spring 6, illustrates displacement 14 and forces 15, 16 on it and is used in the exploitation of the experimental measurements following non-destructive loading 4. Figure 3 describes the placement of the fish flesh 1 on a ductile (movable) substrate 8 elastically connected 7 to the ground 3 and the equivalent Kelvin-Voigt model representing the fish flesh 1 connected to the background 8 through a damper 5 and a spring 6, illustrates displacements of flesh 17 and background 18 and is used in the exploitation of experimental measurements following non-destructive loading 4. In Figure 4 the forces 20, 21 developed in the fish flesh 1 and the displacements of background 18 and flesh 17 when it undergoes non-destructive loading 4, as well as the reaction 19 of soil 3 on the endotic background 8. Figure 5 shows a characteristic Force-Time diagram from a TPA texture analyzer where the double compression with maximum force H can be distinguished, at two times t1 and t2. Figure 6 shows sketch of a test setup used in taking experimental measurements by placing fish flesh 1 on an incompressible electronic dynamometer 11 fixed on the ground 3, non-destructively loading it with a step profile load created by dropping a weight 10 suspended at a given height 13 with a string 9, measuring the data (with the dynamometer) and their processing in a PC 12 to calculate the spring constants Kf and damper b/and their statistical comparison for the tested fish flesh.

Fish flesh presents specific mechanical characteristics which affect the way it reacts to any load imposed on it by an external factor. Indicatively, it is stated that consumers, when purchasing the product, feel or apply slight pressure on specific parts of the fish flesh to empirically assess its condition and draw conclusions about the freshness and overall quality of the product. A procedure of the same philosophy for drawing conclusions related to the mechanical characteristics of fish flesh is adopted by the present invention, with the obvious difference that the assessment is made in fully quantitative terms and both the values of the mechanical characteristics and the conclusions are drawn on the basis of strictly mathematical rules and automated algorithmic methods.

In detail, the process (Figure 1) includes the exercise of dynamic loading 4 of periodic (for example sinusoidal or pulse) or impact (impulse) or step (step) type or a combination thereof on a given point of the fish flesh 1 placed in a fixed 2 or inductive 8 background. The imposition of dynamic loading 4 requires the use of an appropriate device at a time, proportional to the profile of the applied load. For example, in the case of impact loading, the load may be imposed by striking the flesh with a small ball or hammer dropped from a certain height and only momentarily contacting the flesh. Similarly, in the case of step loading, the load can be imposed by means of a small weight that is dropped from a certain height and strikes the flesh while remaining on it. As a general principle it can be argued that any device capable of producing the imposed load profile with repeatable accuracy is considered suitable for use within the scope of the invention.

During dynamic loading, the fish flesh receives an amount of energy which it must manage and deliver to its environment. For example, in the case of shock or step loading the impact energy will be absorbed by the flesh which will act as a damping body before letting some of that energy pass into the background. Reasonably, the part of energy that will pass to the background depends on the mechanical properties of the fish flesh characterized by elasticity, stiffness and related properties, and is proportional to the reaction force of the background if it is stationary or to its displacement, velocity or acceleration if it is inductive. Therefore, for constant background 2 (Figure 2), by measuring the reaction force over time (the sum of 15 and 16) we have an estimate of the energy passed into it relative to the energy initially attributed to fish flesh 1.

Accordingly, in a displaceable endotic background 8 (Figure 3), an estimate can be made of the energy transferred to it relative to the energy originally imparted to the fish flesh 1. This is achieved (Figure 4) by measuring either the reaction force 19 from the fixed ground 3 to this background 8, either the displacement 18 or background velocity or acceleration in time. The relationship between the energy imparted to the fish flesh (in the form of loading force 4) and the energy reaching the background (for example, in the form of soil reaction force 19, as described above) is therefore an indicator of how it is managed the energy the fish flesh. This ability to manage energy is directly linked to the mechanical characteristics of the flesh, as will be shown below.

For each cycle of dynamic loading of the flesh the response data (displacement or velocity or acceleration or force from the ground on) of the background is recorded in real time by an electronic device which may be a force recording system referred to as an electronic dynamometer 11 or any electromechanical construction that serves the above purpose. In this case we are referring to a recorded output signal which is a time series of response data. It is also possible to record the above response data as a function of the load imposed on the flesh in the form of force, in which case we refer to recorded input and output signals. In each case, the data is analyzed to calculate the critical mechanical damping and elasticity characteristics of the flesh based on a specific mathematical model of the system defined by the fish flesh and the background, and a fully defined algorithmic procedure, which is disclosed below for the layout cases with a stable or inductive background.

In the steady background case (Figure 1 left, Figure 2) fish flesh 1 is represented by the Kelvin-Voigt mechanical model which is extensively used in corresponding cases (Figure 2). This model considers that the fish flesh 1 of mass m is concentrated and suspended by means of a spring 6 with an elastic constant Kf and a damper 5 with a constant Bf. The spring 6 mathematically represents the elastic behavior of the fish flesh 1, i.e. its ability to return to its original form after being slightly deformed 14. The damper 5 mathematically represents the viscoelastic behavior of the fish flesh 1, i.e. the resistance of the flesh against its deformation (and therefore loading) at a specific speed.

During the application of external dynamic loading f(t) 4 the fish flesh 1 with mass m responds with spring forces 15 equal to Kf-x(t ) and damper 16 equal to Bfd/dt{x(t)}, where x(t ) and d/dt{x(t)} are the displacement 14 from the equilibrium position (i.e., the position of the initial displacement due to the weight of the fish flesh) and the velocity of the fish flesh, respectively. The foundation 2 in turn rests on the incompressible ground 3 which receives the spring and damper forces 15, 16 respectively, and responds with an equal and opposite reaction force Fg(t)= Kfx(t)+Bfd/dt{ x(t)}. Applying Newton's relevant law, it applies to the movement due to loading of fish flesh:

the

with d<2>dt<2>{x(t)} the acceleration of the mass m during the loading. The above differential equation can be investigated and solved using systems theory and automatic control (see for example Krikelis, 1990) as follows. Using Laplace transform on the above equation we get:

where X(s) and F(s) the displacement signals x(t) 14 and force ft) 4, respectively in the Laplace field. By applying the Laplace transform the differential equation (2) was transformed into an algebraic equation (3) in the Laplace field from which we can obtain the transfer function X(s)|F(s) as follows:

( ) f f

and since the background reaction is Fg(t)= Bfddt{x(t)} Kf-x(t ), working in the Laplace field we get:

Combining (4) and (5) we have?

with the ratio Fg(s) F(s ) being the transfer function between the background reaction force and the loading on the fish flesh. Working in (6) we get:

the

The relation (8) explains that the background force is equal to the loading force of the fish flesh minus the response of the secondary dynamic system

showing a static gain m/Kf at an input s<2>-F(s ) in the Laplace field. Considering the damping factor ζ and the natural frequency ω as follows, we have for G(s):

Based on (8), (9) and (10) it is therefore:

At this point we select the loading profile 4 that we impose on the fish flesh. If we consider the simplest step loading f(t)=A Newton of force for time t> 0, then in the Laplace field F(s)=A/s (from Tables of Transformations of Time Functions in the Laplace Field, Krikelis, 1990). It is noted that the term s F(s)=A, i.e. it corresponds to a shock loading function (see also the aforementioned Tables), or more simply to an instantaneous loading (hit) for t=0 and zero loading for any other time value. From (11) it is therefore understood that the term

corresponds to the shock input response of the standard quadratic system G(s). Therefore from (11) it finally follows that the reaction force of background 2 will be the loading force of the fish flesh minus the term s-H(s ) corresponding to the first derivative of the shock response H(s) of G(s). So, applying an inverse Laplace transform to (11) and using what was written above will hold:

dt

From relevant literature (Krikelis, 1990) we know that in (12) the shock response in the time domain h(t) of the secondary system G(s) shown in (10), is given by the formula:

so by combining (13) and (14) we will have:

or finally after the appropriate calculations:

with ζ and ωn determined in (10) and A the known loading force 4 of fish flesh 1. So, having recorded response data in the form of force time series Fg(t) for each loading cycle we can calculate the constants Kf and Bf which correspond to in the mechanical characteristics of spring 6 and damper 5 of fish flesh, respectively, in a direct way through the use of analytical mathematical expressions (10) and (15).

In practice, the calculation can be done by curve fitting methods in which for each value of time t during the loading cycle the corresponding value Fg(t) is considered the result of relation (15) for the appropriate z and ω values. Considering the set of time instants t, a curve of Fg(t) values is obtained over time, which the above-mentioned methods approximate by successive adjustment of ζ and ωn resulting from the use of a suitable algorithm. Such methods can either be programmed into a computer or exist as commands in specialized software such as MATLAB (registered trade name). Then the constants Kf and Bf corresponding to the mechanical characteristics of spring 6 and damper 5 of fish flesh 1, respectively, are easily calculated through (10).

At this point it should be emphasized that the use of dynamic loading of fish flesh 1 with a step function profile was done in order to arrive at the analytical relation (15) for the force Fg(t) and achieve the calculation of the constants Kf and Bf in the way that was described. Another dynamic loading profile (sine, shock, pulse) could be used and in combination with those reported in the system theory and automatic control literature (see for example Krikelis, 1990) derive relations analogous to (15) to use methods curve fitting to calculate the constants Kf and Bf

In the endotic background case (Figure 1 right, Figure 3, Figure 4) the fish flesh of mass 1 is again represented by the Kelvin-Voigt model but now the background 8 of mass mw is considered as a rigid flat disk which is suspended by a spring 7 of constant Kg in the incompressible soil 3. As in the case of the stable (non-yielding) background 2, the fish mass m 1 is considered concentrated and suspended by means of a spring 6 with an elastic constant Kf and a damper 5 with a constant Bf When applying external loading f(t) 4 in fish flesh 1, it responds with forces 20 (equal to Kf{x(t)-xw(t)j) and 21 (equal to Bfd|dt{x(t)-xw(t) }) shown in Figure 4 and due to the spring 6 of constant Kf and the damper 5 of constant Bf respectively. It is emphasized that both these forces are proportional to the relative motion {x(t)-xw(t}) between the fish of mass m 1 and the background 8 of mass mw, whose absolute displacements are x(t) 17 for the fish and xw(t) 18 for the foundation 8. The inductive foundation in turn transfers the load to the ground through the spring 7 with a constant Kg, so the latter also reacts with the force Fg(t)= Kg; xw(t ) 19. As in the case of fixed background 2, the relationship between the loading force f(t) 4 of the fish flesh and the ground reaction Fg(t) 19 is proportional to the relationship between the energy attributed to the fish flesh 1 and that of energy reaching the background and is therefore an indicator of how energy is managed by the fish flesh.Applying the relevant Newton's law, it applies to the motion of the fish flesh and the background:

with the variables x(t) and xw(t) measured from the equilibrium position, as in the case of the constant background. Using the Laplace transform and a slight rearrangement of terms yields:

and

For the reaction Fg(t)=Kg xw(t ) applies:

Fg(s) = Kg-Xw(s) (20) Combining (18), (19) and (20) gives the transfer function (relationship) in the Laplace field between the loading force of the fish flesh F(s) and the reaction Fg(s) :

The relation (21) represents a system of the fourth degree, therefore with four poles, while it also shows a zeroizer (where the poles are defined as the solutions of the polynomial of the denominator and the solutions of the polynomial of the numerator are defined as zeroes, if it exists, Krikelis, 1990). This system is too complex to study with free variables the spring constants Kf and damper Bf, respectively. It is noted that in such cases no analytical solutions are available as in the case of secondary systems of relation (12).

A realistic working assumption we can make is that the mass mw of background 8 is sufficiently smaller than that of fish flesh 1 which is equal to m that we consider it negligible. Then (21) simplifies as follows:

which is already third degree, so simpler. So it has three poles, one real and a pair of complex or three real (Krikelis, 1990). Following the analysis carried out on relation (7) will apply to (22):

or by doing elementary actions:

The relation (23) explains that the reaction Fg(s) is equal to the loading force of the fish flesh minus the response to F(s) of the tertiary dynamic system

In relation (24) we notice that if we put s=-Kf|Bf in the denominator we get a result m Kg Kf<2>Bf<2>>0, while if we put s=-(Kf+Kg)/Bf [i.e. we put the value of the nullifier of (24)] we obtain a result -Kg<2>< 0. So one of the three poles of (24), namely the real one, lies between the values -(Kf+ Kg)/ Bf and -KflBf. In fact the real pole of (24) will be equal to:

f

Substituting the value (25) of the pole in the denominator of (24) we end up after operations in the following relationship:

(26) can be solved in terms of n using symbolic computation software that provides an analytical solution of n as a function of the variables m, Bf, Kf, and Kg. Using the corresponding feature of MATLAB (registered trade name), three candidate values for η are obtained, of which two are complex (rejected since 0< n < 1) and one is real. The expression of the latter is given, indicatively, below:

The =

Now that there is an analytic expression for n, we can return by doing operations on (23):

or by factoring the denominator above in terms of the pole s=-(Kf+n-Kg)/Bf.

with the term ε being the remainder of the factorization with respect to the pole s=-( Kf+n-Kg)/ Bf and being equal to:

The fact that ε=0 is due to the fact that n has been used as given by (27), which in turn was derived from (26), which is essentially equivalent to the above relation for ε=0. If there is the prediction of having a sufficiently inductive background, i.e. Kf»Kg, then in (28) we have an approximate cancellation of the term [s+(Kf+Kg) Bf ] with the term [s+(Kf+n-Kg)/Bf] , This approach is only valid for Kf»Kg and is in fact very realistic for Kf>4 Kg. Then (28) becomes approximately equal to:

As in the case of constant background 2, if we consider a simple dynamic loading 4 such as step f(t)=A Newton force for time t>0, then in the Laplace field F(s)=A/s (from Tables of Transformations of Functions of Time in the Laplace Field, Krikelis, 1990). It is noted that the term s-F(s)=A, i.e. it corresponds to an impact loading function (see also the aforementioned Tables, Krikelis 1990), or more simply to an instantaneous loading (impact) for t=0 and zero loading for any other value of of time. So since (11) and (30) have exactly the same form (albeit with different coefficients ζ and ωn given by (10) and (31) respectively) the same analysis will apply to obtain in the time domain:

Therefore, having recorded response data in the form of force time series Fg(t) for each loading cycle we can directly calculate the constants Kf and Βf corresponding to the mechanical characteristics of spring 6 and damper 5 of fish flesh 1, respectively, using the analytical mathematical relations (27), (31) and (32). In practice, the calculation can be done as explained in the analysis of the constant background case by curve fitting methods based on relations (27), (31) and (32) with only free variables Bf and Kf since the remaining data m, Kg and A are measurable. As in the case of the fixed background, the use of dynamic loading of fish flesh with a step function profile was made to arrive at the analytical relation (32) for the force Fg(t) and achieve the calculation of the constants Kf and Bf in the manner described . The use of other dynamic loading profiles is not excluded, but the analytical relations for the force Fg(t) will necessarily be different from (32).

The terms Bf and Kf calculated through this approach can be translated in terms of traditional textural properties. For the needs of explaining the textural properties of the fish in terms of mechanical characteristics, the commonly accepted terms for explaining the textural properties are used here (in their most complete description by Civille G.V. & Szczesniak, A.S., 1973 and Szczesniak, 1998). For a simplified mechanical model representing the fish tissue, where we have a Kelvin-Voigt system with mass 1, spring 6 and damper 5, as for example in Figure 2, relations (10) apply.

Thus hardness (H) as a physical definition is the necessary force that must be exerted on the food to achieve a specific deformation. This means that the measured hardness depends on how the texture test is approached. The Zwick hardness meter, for example, evaluates the hardness of the fish after placing it on the surface of the fish being tested and then applying a specific force, at a constant zero speed. In this case, therefore, an almost static loading is used and what is measured as hardness is a force that is directly proportional only to the constant K/τ of the spring (measured hardness H= Kfx(t)).

On the contrary, the approach during the classic texture analysis (Figure 5), which is called the two bite test, where there is an imitation of the chewing process, is different. The piston exerts a dynamic load as it descends into the sample at a non-zero constant velocity (exercises a given initial force - trigger force) and compresses the tissue up to a certain height (or for a certain percentage of deformation). Then it rises (at the same constant speed) and stops at that point (height) where the initial force exerted in the first compression was. This is followed by a second compression at the same compression height (or strain rate).

If we want to interpret the quantities calculated from the texture analysis, in terms of mechanical characteristics, the hardness measurement includes both forces due to a constant Kf of the spring 6 and due to a constant damping Bf of the damper 5, precisely because of the non-zero movement speed of the piston . In this case the measured hardness H in Figure 5 is equal to H= Kfx(t)+Bfd/dt{x(t)}. In any case, the direct calculation of the constants Kf and Bf through the proposed method gives a clear idea of the hardness value, but also of the viscoelastic behavior of the tested fish flesh in general.

Regarding the measurement of elasticity (elasticity or springiness) which is expressed as the ratio of the time to reach the second compression t2 to that of the first tl in Figure 5, this is an expression of the ability of the fish to acquire its original shape after a given compression (of the degree of recovery of the original shape). Therefore, we can conclude that it is proportional to Kf since it fully expresses the elastic behavior of the fish flesh.

By carrying out several loading cycles using either a static or an inductive background, it is possible to calculate the spring constant Kf and damping values Bf for the flesh of the test fish. In the case where N loading cycles have been carried out for each of the tested fish flesh, N sets of {Kf , Bf} values have also been collected for each fish flesh. At a later stage, a statistical comparison can be made of these groups of { Kf, Bf } values of the different fish and conclusions can be drawn as to whether they differ from each other or with some groups of { Kf, Bf } values referred to reference (fish flesh) samples (p .eg flesh from fish in a state of absolute freshness or from fish with a specific diet history or origin).

Statistical comparison of different groups of values to infer the difference or similarity of fish can be done (indicatively, but not exclusively) by the following methods. After statistical control of the normality of the distributions of Kf and Bf measurements in case of normality with ANOVA analysis of variance, while in case of non-normality with its non-parametric counterpart, the Kruskal-Wallis method. In this way the differences between the meat samples for Kf and Bf values separately can be compared. Alternatively, for example, using Discriminant Analysis, where each sample of fish flesh is represented by the set of measurement groups { Kf, Bf } and making use of group centroids and confidence ellipses ), in diagrams of canonical discriminant functions (canonical discriminant functions) the total differences between the flesh samples can be attributed.

Indicative example of the application of the method with results: For the application of the method of direct estimation of the mechanical characteristics of the fish flesh we consider the installation shown in Figure 6. The fish flesh 1 of mass mf is placed on the electronic dynamometer disc 11 which can record the reaction force in time. This data is then forwarded to computer 12 for processing. For the dynamic loading, a small weight 10 is used which is suspended by a thread 9 at a given point 13 in relation to the position of the fish and the dynamometer. By cutting the thread, the mass weight mb falls from a specific small height 13 equal to 2 cm onto a specific point of the flesh implementing an almost stepwise dynamic loading 4 of the fish flesh. The reaction data is recorded through the electronic dynamometer 11 and processed in the PC 12, using relations (10) and (15) to determine the constants Kf and Bf of elements 6 and 5, respectively, of Figure 2, by the procedure curve fit described in the corresponding paragraph. It is noted that the sum mf+mb is used as mass m in relations (10) and (15).

4 fish flesh with the masses shown in Table 1 were used, two caught one day before the test and preserved on ice and another two caught well in advance, about 6 days before the test and also preserved on ice. The spoilage mechanisms operating during this time lead to the appearance of different mechanical characteristics compared to day-old fish flesh. 28 test cycles are performed per fish flesh and then {Kf Bf} data per fish flesh. The results (descriptive statistics for each tested fish flesh sample) are shown in Table 2.

Table 1: Coding, characteristics and masses of tested fish flesh samples

Table 2: Descriptive statistics of the four fish flesh samples

Table 3: Result of distribution normality check (by SPSS statistical program) for A/<'>and Bf To Sign <0.05 (checked with both Kolmogorov-Smimov and Saphiro-Wilk tests) indicates non-normal distributions.

Tests of Normality

<a>- Lilliefors Significance Correction

Table 4: Kruskal-Wallis statistical difference test results

Test Statistics<a,b>

a- Kruskal Wallis Test

b. Grouping Variable: fish

The results (the sets of measurements {Kf Bf) for each fish) are checked for their distributions Due to the non-normal distributions of the data (Table 3), they are statistically processed with the non-parametric Kruskal-Wallis method to detect differences in mechanical characteristics. The Kruskal-Wallis method showed that there is a statistically significant difference (Asymp. Sig. p<0.05, Table 4) only in the case of Bf, and not in that of Kf.

Then the Post-hoc results with the LSD (least significant difference) method, for grouping the samples according to their Bf showed differences between the samples as shown in Table 5. Analyzing the results we see that the averages of both Kf and and Bf of the 6<th>day samples (6mb and 6mc) are smaller than these two reference samples (1mc and 1md), which can be easily attributed to the solution of the dead stiffness that appears around the 6<th>day ( and therefore by definition loss of hardness and elasticity). However, it is observed that statistical differences appear only for Bf This is due to the high standard deviations between the measurements for each sample (Table 2), probably due to the need for greater precision in the repeatability of the measurements than Table 5: Multiple comparisons (post-hoc) between fish flesh samples and finding differences and significance.

Experimental setup. It is expected that with improvement of experimental conditions the differences will become statistically significant for all sizes.

It is observed that the Bf of samples 1mc and 1md are not differentiated (grouped together), which is expected since both are reference samples. However, we see differentiation of one (6mc) from both benchmarks (1mc and 1md), but the other (6mb) only with respect to one benchmark (lmd). Similar signs of variation can be expected due to the different behavior of each sample that has been preserved for some time. Interindividual variations are the norm in biological samples, which are subject to the influence of many confounders with a high degree of uncertainty.

Claims (8)

A X I O S E I S 1. A method based on experimental measurements of non-destructive testing that achieves the direct calculation - assessment using analytical mathematical expressions of the mechanical characteristics of fish flesh (describing textural properties such as elasticity-elasticity, hardness-hardness) intended for consumption, applicable throughout the during their storage, which includes the following phases: a) Experimental procedure that includes non-destructive exercise of dynamic loading (4) of periodic (indicative but not exclusive, sine-sinusoidal or pulse-pulse) or impact (impulse) or step (step) type or a combination thereof, on a given point of the fish flesh (1) placed on a fixed (2) or inductive (8) base, which is called a "substrate". b) Experimental procedure involving the real-time collection and recording in an electronic file or table of the experimental data as a result of loading (4) of fish flesh (1), which are characterized as "data of one loading cycle". c) Processing of the recorded experimental data as they result from each loading cycle of the fish flesh for the calculation of critical damping (5) and elasticity (6) characteristics of the fish, in a direct way on the basis of a mathematical model of the process and resulting analytical mathematical expressions that link the above features to the experimental data. d) Comparison of damping (5) and elasticity (6) characteristics calculated with corresponding "reference" values (which are available or have been calculated at an earlier time) and correspond to a given "reference level" of mechanical characteristics (elasticity-elasticity, hardness- hardness) for the specific type of fish, to achieve an evaluation of the mechanical characteristics of the flesh of the tested fish in relation to "reference values" of the specific type of fish, or any other reference fish. 2.  Method according to claim 1, characterized by the fact that the term "fish flesh" may describe a whole fish or a part thereof containing muscle tissue, indicatively (but not exclusively) a piece, a slice, a fillet. 3.  Method according to claims 1 and 2, characterized in that the loading (4) applied to the fish flesh is dynamic and of periodic or impact or step type or a combination thereof and is done in a way either direct (by direct loading of fish flesh) or indirectly (through a component that comes into contact with fish flesh). 4.  A method according to claims 1, 2 and 3, characterized in that the loading of the fish flesh is carried out in such a way as to ensure the repeatability of the test with satisfactory accuracy, so that it is possible to carry out more than one cycle of equal- of comparable loadings in the same or another fish. 5. Method according to claims 1, 2, 3 and 4, characterized in that the experimental data reported per cycle of dynamic loading relate to background response values following loading of the fish flesh which have the form of either reaction forces (15), ( 16) of the background when it is fixed (2), or force from the ground (19) on the background, displacement or velocity or acceleration of a point of the background or a component connected to it, exclusively when it is inductive (8). 6.  A method according to claims 1, 2, 3, 4, and 5, characterized in that the per dynamic loading cycle response data, in a form defined in claim 5, is recorded either as time response values, or as response values at function with the charge values so that they are available in the form of an electronic file or a table of measurements or an engraved diagram. 7. Method according to claims 1, 2, 3, 4, 5 and 6, characterized in that the data recorded according to claim 6 per dynamic load cycle are used either in their raw form or after they have been processed (indicatively but not exclusively with methods of signal analysis -- signal processing/filtering, descriptive statistics — descriptive statistics or others) to calculate the viscoelastic damping (5) and elasticity (6) characteristics of fish flesh using a representative model of the process (with indicative example the Kelvin-Voigt model) and resulting analytical mathematical expression that connects the above characteristics with the recorded data. Method according to claims 1, 2, 3, 4, 5, 6 and 7, characterized in that the viscoelastic damping (5) and elasticity (6) characteristics of all dynamic loading cycles calculated according to claim 7 and corresponding to in the tested fish flesh are compared to "reference" values for the fish species either using statistical decision-making methods or simple rules of thumb, indicatively but not exclusively by comparing the "worst" (in the sense of the least favorable of all cycles loading) value of the viscoelastic damping (5) and elasticity (6) characteristics of the test fish with the corresponding "reference" values, in order to achieve an evaluation of the level of the mechanical characteristics of the flesh of the test fish in relation to the "reference level" of the specific fish type, or any other reference fish.