Use of a non-parametric regression such as the loess regression for modelling the water activity of powders

Abstract

The present invention relates to the use of a non-parametric regression, for example a LOESS regression, for determining the water activity (Aw) of a compound in solid form, advantageously in the form of a powder, or of a mixture of at least two compounds in solid form, advantageously in the form of powders.

Description

[0001] USE OF NON-PARAMETRIC REGRESSION SUCH AS LOESS REGRESSION TO MODEL WATER ACTIVITY OF POWDERS

[0002] Technical field

[0003] The present invention relates to the field of powders, in particular in mixtures, and in particular to the possibility of determining optimal mixtures to obtain a determined and desired value of the water activity (Aw) of the mixture.

[0004] Prior art

[0005] Sorption isotherms allow water activity (Aw) to be estimated from the water content of a substance. Water activity is a well-known and important factor for the stability of material mixtures, particularly when the mixture includes an active compound such as a biotic whose activity must be preserved and stability ensured.

[0006] An example concerns the formulation of probiotics in dry feed mixes. The water activity (Aw) of the mix, as distinct from its water content, is a determining factor for microbial growth, toxin production, and the shelf life of probiotics. To protect probiotics, managing the Aw of feed mixes is necessary. Monitoring the Aw of complex mixes is the basis for probiotic formulation. Indeed, this Aw has a significant impact on the viability of ingredients over time and on the development of contaminating flora. In a mix, the moisture captured by the powder is unevenly distributed among the components despite the fact that the water activity is equal in all parts of this whole.Excess water and therefore high water activity will allow the growth of spoilage flora and, simultaneously, negatively impact the number of colony forming units (CFU) of probiotics.

[0007] In the specific case of probiotic formulation, to protect them from spoilage and prevent the growth of contamination, water activity must be kept as low as possible. Thus, mixtures that combine an excipient with a low water activity with a probiotic with a higher Aw have a protective effect on the probiotic by lowering its Aw. By mixing low Aw excipients with probiotics, the overall water activity of the mixture can be better controlled to reduce stability issues. Many mathematical models of sorption isotherms are available to understand how probiotics interact with excipients, so that the behavior of mixtures can be determined as accurately as possible.These mathematical models of moisture adsorption isotherms are described in the specialized literature, to estimate the evolution of water activity as a function of water content. Some have theoretical foundations (for example by taking into account the moisture monolayer as a model parameter), others are simply empirical. These models allow the generation of virtual mixtures of isotherms which are useful for identifying optimal formulations of ingredient mixtures. Their accuracy is however variable depending on the products and they can be more or less approximate. Some models work very well on some products but not at all for others. There are even products that cannot be represented correctly by sorption models because of overly complex inflection points.

[0008] Thus, there is a clear need to find a new tool for modeling sorption isotherms, applicable to any type of product in powder form, including mixtures.

[0009] Detailed description of the invention

[0010] The present invention is based on the demonstration that a local regression of the LOESS type makes it possible to model the water activity (Aw) of a compound in solid form, advantageously in powder form, but also of a mixture of at least two compounds in solid form, advantageously in powder form.

[0011] It is shown in Example I that this mathematical method is very efficient, far superior to the models used in the prior art, such as the Guggenheim-Anderson-deBoer model (GAB; Van den Berg, C. (1984), In BM McKenna (Ed.), Engineering and Foods, pp. 311-321, London Elsevier) with a correlation between the water content of the compound and the relative hygrometry for the points measured experimentally (for example at a temperature of 25 °C), and the curve obtained by modeling, equal to 1.

[0012] This method gave very good results and proved to be robust for all the ingredients tested, in particular for ingredients with complex isotherms (with inflection points) which are poorly taken into account by existing physical or empirical models. In the following description, the term moisture adsorption isotherm, hereinafter referred to as sorption isotherm, is understood to mean the equilibrium relationship between the water content and the relative humidity of the medium or relative hygrometry (P / PO), at a given temperature. In practice, this relationship can be represented by a curve with the water content on the ordinate and the P / PO quantity on the abscissa.

[0013] Water activity (Aw) represents the ratio of the water vapor pressure of a wet product (P) to the saturated vapor pressure (PO) at the same temperature, i.e. the relative humidity (P / PO).

[0014] The moisture content of a product (or MC for "Moisture Content") is the ratio of the mass of moisture to the mass of the dry product (or DM for "Dry Matter"). It quantifies the amount of water in a product.

[0015] The water content (X) of a product depends on the total mass of the wet product Mh and the mass of the dry product Ms according to the relationship: X = (Mh - Ms) / Ms.

[0016] As is known, sorption isotherms are determined experimentally using static or dynamic methods:

[0017] In the static or gravimetric method, the product to be analyzed is placed in an enclosure maintained at a fixed temperature and with constant relative humidity. The sample is allowed to reach equilibrium (with unchanged mass) for several days or even weeks.

[0018] In the dynamic method, the product is placed in an air current (e.g., a dryer) at constant temperature and relative humidity. Equilibrium (with unchanged mass) is generally reached after a few hours.

[0019] For the purposes of this application, water content (MC) is expressed in g per 100 g of dry matter (DM).

[0020] In this description, the terms substance, compound, component, material, ingredient or product will be used interchangeably. Thus, these terms, in particular the term compound, can designate a pure molecule as well as one already mixed with other molecules. In practice, it is a product available individually, for example commercially available. In the remainder of the description, powder(s) means a fractionated state of matter. It is a divided solid, present in the form of particles or granules, generally having a size (D) less than one tenth of a millimeter (100 μm). A powder is generally characterized by its particle size distribution curve which expresses the mass fraction of particles relating to each size class, i.e. the statistical distribution of the grain size.

[0021] A powder may or may not contain water.

[0022] A powder mixture is understood to mean at least two powders. Powder mixtures may be required for various reasons: each powder may have a specific activity of interest; for economic reasons, the powder with the activity of interest may be mixed with one or more other inactive but less expensive powders; certain powders may help to formulate or even stabilize the powder(s) with an activity of interest. In these last two cases, the inactive powders are chosen so as not to affect the activity of the powder of interest.

[0023] The present invention finds numerous applications, in particular in fields where material in powder form is commonly used, for example in the fields of cosmetics, food (for human or animal use), medicines (pharmaceutical and veterinary), paint, metals, chemistry (fertilizers, polymers, plastics, etc.) ...

[0024] Thus, certain compounds in the mixture exhibit an activity of interest in the field of application, for example a therapeutic activity in the medical field or a pigmenting activity in the field of paints.

[0025] Other compounds do not carry any activity as such but may be useful for formulating active ingredients (excipients and adjuvants) or for economic reasons. It is important that their presence does not affect and especially does not deteriorate the activity of the active compound, and in particular its water activity.

[0026] According to a first aspect, the present invention relates to the use of a non-parametric regression, for example a local regression of the LOESS type, to determine the water activity (Aw) of a compound in solid form, advantageously in powder form, or of a mixture of at least two compounds in solid form, advantageously in powder form. Thus and according to the invention, the modeling of sorption isotherms is based on the use of weighted local polynomial regression or LOESS (Locally Estimated Scatterplot Smoothing) regression, and more generally on the use of non-parametric regression approaches.Non-parametric regression methods are known to those skilled in the art and can, for example, be chosen from the following group: LOESS regression (LOcally Estimated Scatterplot Smoothing); regressogram (Bin smoother); moving average; weighted moving average (Nadaraya and Watson regression); Kernel regression, multivariate regression by adaptive spline (MARS for “Multivariate Adaptive Regression Spline”), advantageously LOESS regression.

[0027] LOESS regression was developed by W.S. Cleveland in the 1980s (“Robust Locally Weighted Regression and Smoothing Scatterplots”, Journal of the American Statistical Association, Vol. 74, No. 368, 1979, pp. 829-836). However, to the inventors’ knowledge, its use was never considered in connection with the present application, nor were other non-parametric regression models.

[0028] LOESS modeling fits a polynomial regression function to each point in the dataset, considering only the points in the neighborhood. LOESS regression is a completely empirical approach that considers all local regressions for all points. Two hyperparameters influence the smoothing characteristics of LOESS modeling: the proportion of neighborhood points used for local regression and the degree of the polynomials.

[0029] To optimize this application, the LOESS model can be parameterized such that only the two points in the vicinity of a given point are considered with a degree of 2 for the polynomial. This parameterization makes LOESS modeling very flexible in cases where the sorption isotherm is dense.

[0030] More specifically, the present invention relates to a method for establishing a sorption isotherm of a powder comprising the following steps:

[0031] - obtaining a set of points corresponding to the water content (MC) of the powder as a function of the relative hygrometry (P / PO);

[0032] - the application of a non-parametric regression, for example a LOESS regression, on these points to establish the sorption isotherm of the powder.

[0033] In the context of this application, the terms “establishment” (“to establish”), “obtaining” (“to obtain”) and “generation” (“to generate”) are used interchangeably. The points corresponding to the water content (MC) of the powder as a function of the relative humidity (P / PO) can be found in the literature or determined experimentally.

[0034] As is known, such points can be obtained by gravimetry or by dynamic vapor sorption (DVS) measurement. Suitably, the measurements are carried out at constant temperature, advantageously at room temperature, for example at 25°C.

[0035] According to an advantageous embodiment, each sorption isotherm is established from at least five or even ten points of measurement of the water content (MC) as a function of the relative hygrometry (P / Po).

[0036] According to another aspect, the present invention relates to a method for determining the water activity (Aw) of a powder sample comprising:

[0037] - establishing the sorption isotherm of the powder using the method described above;

[0038] - measurement of the water content of the sample;

[0039] - determination of the water activity of the sample using the water content of the measured sample and the established powder sorption isotherm model.

[0040] In the very particular case where the established sorption isotherm is represented using a curve, it is possible to graphically determine the water activity (Aw) of the powder sample by plotting the measured water content on the ordinate axis of the curve and reading the corresponding value on the abscissa axis, said value corresponding to the water activity of the sample.

[0041] As shown in the examples, these methods can also be implemented on mixtures of powders. In the following, the expressions “composition comprising at least two compounds” and “mixture of at least two compounds” are used interchangeably.

[0042] Thus, the invention also relates to a method for establishing the sorption isotherm of a solid composition comprising at least two compounds, advantageously in the form of a mixture of powders, comprising:

[0043] - obtaining the sorption isotherms of each of the compounds, the isotherm of at least one of the compounds, advantageously of all the compounds, being established using the method described above;

[0044] - establishing the sorption isotherm of the composition as a function of the weight proportion of each compound in the composition. In practice, the sorption isotherm of the composition is established using the sorption isotherm models of each of the compounds, weighted as a function of the weight proportion of each compound in the composition.

[0045] According to the invention, the isotherm of at least one of the compounds is established using the method described above, i.e. using a non-parametric regression. Advantageously, this is the compound(s) whose modeling using a parametric regression is not satisfactory. According to a particular embodiment, the isotherm of all the compounds of the composition or mixture is established using the method described above, i.e. using a non-parametric regression. However, and as demonstrated in the present application, it is possible to combine isotherms obtained by non-parametric and parametric regressions.

[0046] Indeed, it is known that it is possible to combine or cumulate two or more regressions, including parametric and non-parametric regressions. Thus, Peleg and Norman (Trends in Food Science & Technology July 1992 [Vol. 31]) described a strategy for estimating by microcomputer the sorption isotherms of complex formulations containing ingredients whose isotherms are known or unknown.

[0047] Again, the sorption isotherm of the composition thus established can be visualized in the form of a curve.

[0048] The weight or mass proportion is understood as the relative proportion of each of the compounds in the mixture, expressed in weight / weight (w / w).

[0049] Consequently and according to another aspect, the invention relates to a method for determining the water activity (Aw) of a mixture of powders comprising:

[0050] - establishing the sorption isotherm of the mixture using the method described above;

[0051] - the measurement of the water content of the mixture or the calculation of the water content of the mixture using the water contents of each of the compounds, weighted according to the weight proportion of each compound in the mixture;

[0052] - determination of the water activity of the mixture using the measured or calculated water content of the mixture and the established mixture sorption isotherm model.

[0053] In the very particular case where the established sorption isotherm is represented using a curve, it is possible to graphically determine the water activity (Aw) of the powder mixture by plotting the measured or calculated water content on the ordinate axis of the curve and reading the corresponding value on the abscissa axis, said value corresponding to the water activity of the mixture.

[0054] The water content (MC) of the mixture can be determined experimentally or by calculation as illustrated in the examples.

[0055] As already stated, a method according to the invention takes on its full meaning when at least one compound exhibits an activity of interest, which should be preserved while respecting its water activity. Thus, and as illustrated in the examples, for a probiotic, it is appropriate to maintain an Aw value of less than 0.3 or even less than 0.1, depending on the strain and its drying process. In the particular case where the active ingredient is hygroscopic chondroitin (for example chondroitin sulfate), it is recommended, to ensure its stability, to have a mixture exhibiting an Aw value of the order of 0.3. Its optimal values ​​or ranges of values ​​are given only as examples but are known to those skilled in the art.

[0056] According to a particular embodiment, the composition or mixture of powders comprises at least one active compound. An active compound may be a microorganism (yeast, bacteria or phage), living or dead, or an active molecule (vitamins, chondroitin, etc.). Thus, and by way of example, the active compound may belong to the following categories: zootechnical additives, prebiotics, proteins, enzymes, etc.

[0057] According to a particular embodiment, such a composition or mixture of powders is intended for the preparation of a food supplement or a medicine.

[0058] As illustrated in the examples, the method according to the invention makes it possible to determine the nature and / or the weight content of a compound other than the active compound, so as to obtain a mixture having a water activity compatible with that of the active compound.

[0059] In practice, the compound other than the active compound may be an excipient or an adjuvant, for example maltodextrin or microcrystalline cellulose.

[0060] It is apparent that in view of the above description, a person skilled in the art is able to implement the invention as defined in the claims below.

[0061] EXAMPLES OF ACHIEVEMENT

[0062] The invention and the advantages resulting therefrom will become more clearly apparent from the following exemplary embodiments, supported by the appended figures. However, these are not intended to be limiting. FIGURE KEYS

[0063] Figure 1: This figure illustrates the correlation between the water content of the Vitamin K2 product (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), and the relative hygrometry (P / PO) for the points measured experimentally at a temperature of 25 °C, and the curve obtained by modeling using the GAB model.

[0064] Figure 2: This figure illustrates the correlation between the water content of the Vitamin K2 product (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), predicted by the GAB model and observed experimentally.

[0065] Figure 3: This figure illustrates the correlation between the water content of the Vitamin K2 product (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), and the relative humidity (P / P0) for the points measured experimentally at a temperature of 25 °C, and the curve obtained by modeling using LOESS regression. Figure 4: This figure illustrates the correlation between the water content of the Anhydrous Dextrose product (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), and the relative humidity (P / P0) for the points measured experimentally at a temperature of 25 °C, and the curve obtained by modeling using the GAB model.

[0066] Figure 5: This figure illustrates the correlation between the water content of the product Dextrose anhydrous (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), predicted by the GAB model and observed experimentally.

[0067] Figure 6: This figure illustrates the correlation between the moisture content (MC) of the product Dextrose anhydrous, expressed in g per 100 g of dry matter (DM), and the relative humidity (P / P0) for the points measured experimentally at a temperature of 25 °C, and the curve obtained by modeling using LOESS regression. Figure 7: This figure illustrates the correlation between the moisture content (MC), expressed in g per 100 g of dry matter (DM), of a vitamin K2 formulation also containing trehalose and an emulsifying starch (E1450 Sodium Starch Octenyl Succinate) and the relative humidity (P / P0) for the points measured experimentally at a temperature of 25 °C, and the curve obtained by modeling using LOESS regression.

[0068] Figure 8: This figure illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / P0) by modeling using LOESS regression:

[0069] - a probiotic Lactobacillus rhamno sus GG (solid line);

[0070] - 10% maltodextrin in water (large points);

[0071] - a formulation comprising, weight / weight (w / w), a 20 / 80 Lactobacillus rhamno sus GG / maltodextrin mixture at 10% water (dashed dotted line). Figure 9: This figure illustrates the correlation between the water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and the relative humidity (P / PO) by modeling using LOESS regression:

[0072] - a probiotic Lactobacillus rhamno sus GG (solid line);

[0073] - 5% maltodextrin in water (large points);

[0074] - a formulation comprising in weight / weight (w / w) a 20 / 80 Lactobacillus rhamno sus GG / 5% maltodextrin mixture in water (dotted line).

[0075] Figure 10: This figure illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / P0) by modeling using LOESS regression:

[0076] - a probiotic Lactobacillus rhamno sus GG (solid line);

[0077] - maltodextrin at 3.9% in water (large points);

[0078] - a formulation comprising in weight / weight (w / w) a 20 / 80 Lactobacillus rhamnosus GG / maltodextrin mixture at 3.9% in water (dotted line).

[0079] Figure 11: This figure illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / P0) by modeling using LOESS regression:

[0080] - chondroitin sulfate (light gray dots);

[0081] - 10% maltodextrin in water (dark gray dots);

[0082] - microcrystalline cellulose or CMC (continuous line);

[0083] - a formulation comprising in weight / weight (w / w) a 10 / 80 / 10 mixture of chondroitin / maltodextrin at 10% in water / CMC (dashed dotted line).

[0084] Figure 12: This figure illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / P0) by modeling using LOESS regression:

[0085] - chondroitin sulfate (light gray dots);

[0086] - 10% maltodextrin in water (dark gray dots);

[0087] - microcrystalline cellulose or CMC (continuous line);

[0088] - a formulation comprising in weight / weight (w / w) a 10 / 45 / 45 chondroitin / maltodextrin mixture at 10% in water / CMC (dashed dotted line).

[0089] Figure 13: This figure illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / P0) by modeling using LOESS regression:

[0090] - chondroitin sulfate (light gray dots);

[0091] - 10% maltodextrin in water (dark gray dots);

[0092] - microcrystalline cellulose or CMC (continuous line);

[0093] - a formulation comprising in weight / weight (w / w) a mixture of 10 / 36 / 54 chondroitin / maltodextrin at 10% water / CMC (dashed dotted line). Figure 14: This figure illustrates the correlation between the water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and the relative hygrometry (P / PO):

[0094] - vitamin K2, by modeling using LOESS regression (squares);

[0095] - a yeast fraction, by modeling using the GAB model (circles);

[0096] - dried potato starch, by modeling using the GAB model (triangle);

[0097] - a mixture comprising these 3 ingredients (5 / 25 / 70 weight / weight), by modeling using LOESS regression (light gray dashes);

[0098] - a mixture comprising these 3 ingredients (5 / 25 / 70 weight / weight), by modeling using Bin smoother regression (light gray dashes of variable thickness);

[0099] - a mixture comprising these 3 ingredients (5 / 25 / 70 weight / weight), by modeling using MARS regression (dark gray dashes).

[0100] 1 / Superiority of a LOESS-type local regression for modeling sorption isotherms:

[0101] 1 / Example with vitamin K2:

[0102] 1-1. Ingredient: Vitamin K2 MK-7 Matrix (maltodextrin powder 2000 ppm; Gnosis Bioresearch)

[0103] The sorption isotherm is determined experimentally using the static method. l-2.GAB model:

[0104] The correlation between the water content of the product (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), and the relative hygrometry (P / P0) is illustrated in Figure 1.

[0105] Figure 1 shows the experimentally measured points at a temperature of 25 °C, as well as the curve obtained by modeling using the GAB model.

[0106] The obtained correlation is equal to 0.988.

[0107] However, as illustrated in Figure 2, the correlation graph reveals a good general correlation but significant deviations for values ​​below 5% water content. Figure 2 shows the correlation between the product water content (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), predicted by the GAB model and observed experimentally.

[0108] 1-3. LOESS regression:

[0109] The data from Figure 1 were repeated but the curve was plotted between the experimental points using a LOESS-type local regression.

[0110] As shown in Figure 3, the correlation in this case is equal to 1, that is, perfect and much better than with the ATM model.

[0111] Figure 3 shows the experimentally measured points at a temperature of 25 °C, as well as the curve obtained by modeling using LOESS regression.

[0112] 2 / Example with anhydrous dextrose:

[0113] 2-1. Ingredient: Anhydrous dextrose (or anhydrous D-glucose)

[0114] The sorption isotherm is determined experimentally using the static method.

[0115] 2-2. ATM model:

[0116] The equivalent of Figure 1 is shown in Figure 4.

[0117] The obtained correlation is equal to 0.966.

[0118] The equivalent of Figure 2 is shown in Figure 5. This correlation plot shows a good overall correlation but significant deviations at the lowest and highest values.

[0119] 2-1. LOESS regression:

[0120] The data in Figure 4 were repeated but the curve was plotted between the experimental points using a LOESS-type local regression.

[0121] As shown in Figure 6, the correlation in this case is again equal to 1, i.e. perfect and much better than with the GAB model. 3 / Application to a mixture: Example with a mixture of vitamin K2, trehalose and emulsifying starch (E1450 Sodium starch octenyl succinate)

[0122] Figure 7 shows the observed sorption isotherm for a vitamin K2 formulation also containing trehalose and an emulsifying starch (E1450 Sodium Starch Octenyl Succinate), which is particularly complex with non-monotonic growth and a sharp inflection point. This product cannot be satisfactorily represented by any classical non-linear parametric model, whereas the curve generated by LOESS modeling fits the observed points very well.

[0123] CONCLUSION :

[0124] These examples reveal the superiority of a LOESS-type local regression for correlating the water content of a product (MC for "Moisture Content"), expressed in g per 100 g of dry matter (DM for "Dry Matter"), and its relative hygrometry (P / PO), and thus determining its water activity (Aw).

[0125] As seen previously, the LOESS model limits errors. Therefore, and on this basis, water activity (Aw) calculations are more accurate and closer to reality than with generic models, such as the GAB model, recommended in the prior art.

[0126] It is therefore no longer necessary to specify a deterministic function, a priori, to model sample data. The curve fit according to the invention is perfect, with excellent correlation coefficients between observed and predicted values. This is particularly interesting for predicting mixture results, when approximations on different constituents risk accumulating. On the other hand, the underlying method is relatively simple, which makes it easy to understand and interpret.

[0127] II / Use of a LOESS-type local regression to determine the nature of an excipient in a two-component system

[0128] The reliability of the LOESS model can, for example, be used to identify a suitable excipient, i.e. one that can be used in combination with an active ingredient without deleteriously modifying the water activity (Aw) of said active ingredient. Thus, in the particular case where the active ingredient is a probiotic, in this case the LifeinU™ strain Lactobacillus rhamnosus GG ((ATCC 53103); Gnosis), the stability of said probiotic is only ensured for an Aw value less than or equal to 0.1. In other words, in this case, the Aw of the mixture (probiotic + excipient) must be < 0.1.

[0129] Maltodextrin is an excipient known for its compatibility with probiotics in formulations intended for ingestion.

[0130] A formulation comprising a 20 / 80 Lactobacillus rhamnosus GG / maltodextrin mixture on a weight / weight (w / w) basis is envisaged.

[0131] Knowing that there are several qualities of maltodextrin, i.e. with variable water contents, the LOESS model makes it possible to check whether maltodextrin is an acceptable excipient in this context and which maltodextrin to choose to respect a final Aw of the mixture of 0.1 maximum. Note that the maximum water content of maltodextrin is given with an accuracy of 0.1%.

[0132] Thus, the correlation between the water content of the mixture (MC for “Moisture Content”), expressed in g per 100 g of dry matter (DM for “Dry Matter”), and the relative hygrometry (P / P0) of the mixture was established using LOESS regression.

[0133] It is illustrated below for 3 qualities of maltodextrin: a) Maltodextrin with 10% water

[0134] Table 1: Characteristics of the products used Figure 8 illustrates the correlation between the water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and the relative hygrometry (P / PO) by modeling using LOESS regression.

[0135] The isotherm of the probiotic Lactobacillus rhamnosus GG (known or experimentally measured) is represented by a solid line.

[0136] The isotherm of maltodextrin at 10% water (known or experimentally measured) is represented by large dots.

[0137] The isotherm of the mixture, resulting from the modeling of each of the isotherms by the LOESS method and a weighting of the isotherm of each ingredient according to the weight proportion of these same ingredients, is represented by a broken dotted line.

[0138] According to the calculations in Table 1, the MC (Moisture Content) in g / 100g of the DM (Dry Matter) is equal to 8.7193. From this, we deduce, by reading the mixture curve, a final Aw of the mixture equal to 0.445, with a confidence interval between 0.433 and 0.457 (i.e. only 0.024 units).

[0139] This Aw value is much higher than the recommended value and makes it possible to exclude the use of this quality of maltodextrin in this quantity in the mixture. b) Maltodextrin with 5% water

[0140] The same approach was followed but using 5% maltodextrin in water, always in the same quantity.

[0141]

[0142] Table 2: Characteristics of the products implemented

[0143] Figure 9 illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / PO) by modeling using LOESS regression.

[0144] The isotherm of the probiotic Lactobacillus rhamnosus GG (known or experimentally measured) is represented by a solid line and remains unchanged.

[0145] The isotherm of maltodextrin at 5% water (known or experimentally measured) is represented by large dots.

[0146] The isotherm of the mixture, resulting from the modeling of each of the isotherms by the LOESS method and a weighting of the isotherm of each ingredient according to the weight proportion of these same ingredients, is represented by a broken dotted line.

[0147] According to the calculations in Table 2, the MC (Moisture Content) in g / 100g of the DM (Dry Matter) is equal to 4.1884. From this, we deduce, by reading the mixture curve, a final Aw of the mixture equal to 0.162, with a confidence interval between 0.150 and 0.173 (i.e. only 0.023 units).

[0148] To obtain the desired Aw value, there are therefore 2 options:

[0149] Increase the proportion of maltodextrin in the mixture;

[0150] Use a maltodextrin with a lower water content. c) Maltodextrin with 3.9% water The same approach was followed but using maltodextrin with 3.9% water, always in the same quantity:

[0151] Table 3: Characteristics of the products implemented

[0152] Figure 10 illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / PO) by modeling using LOESS regression.

[0153] The isotherm of the probiotic Lactobacillus rhamnosus GG (known or experimentally measured) is represented by a solid line and remains unchanged.

[0154] The isotherm of maltodextrin at 3.9% water (known or experimentally measured) is represented by large dots.

[0155] The isotherm of the mixture, resulting from the modeling of each of the isotherms by the LOESS method and a weighting of the isotherm of each ingredient according to the weight proportion of these same ingredients, is represented by a broken dotted line.

[0156] According to the calculations in Table 3, the MC (Moisture Content) in g / 100g of the DM (Dry Matter) is equal to 3.242. From this, we deduce, by reading the mixture curve, a final Aw of the mixture equal to 0.089, with a confidence interval between 0.072 and 0.106 (i.e. only 0.034 units). This value is compatible with the range of values ​​suitable for good stability of probiotics. This quality of maltodextrin therefore proves to be suitable. CONCLUSION:

[0157] These three examples reveal that the use of a LOESS-type local regression helps to choose a product in a mixture of two products, for example an excipient in a mixture consisting of an active ingredient and an excipient, so as to obtain an optimized water activity (Aw) with respect to said active ingredient.

[0158] III / Use of a LOESS-type local regression to determine the relative proportion of compounds in a three-component system

[0159] The reliability of the LOESS model can, for example, be used to arbitrate the relative quantity of two excipients that can be used in combination with an active ingredient, without deleteriously modifying the water activity (Aw) of said active ingredient.

[0160] Thus, in the particular case where the active ingredient is chondroitin sulfate (Mythocondro®; Gnosis Bioresearch), it is recommended, to ensure its stability, to have a mixture with an Aw value of around 0.3.

[0161] This involves formulating chondroitin sulfate with a water content equal to 5% in a composition containing 10% by weight of said chondroitin.

[0162] The excipients used, which are low cost and whose addition aims to optimize the formula from an economic point of view, without sacrificing the stability of the active ingredient, are the following:

[0163] Excipient 1: maltodextrin (Glucidex 12D)

[0164] Excipient 2: micro-crystalline cellulose or CMC (MCC Vivapure 103).

[0165] It is therefore appropriate to determine their relative proportion, knowing that they must represent 90% by weight of the formulation. a) Majority maltodextrin

[0166] Table 4: Characteristics of the products implemented

[0167] Figure 11 illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / PO) by modeling using LOESS regression.

[0168] The chondroitin sulfate isotherm (known or experimentally measured) is represented by light gray points.

[0169] The isotherm of excipient 2, namely maltodextrin at 10% water (known or experimentally measured), is represented by dark gray points.

[0170] The isotherm of excipient 1, namely microcrystalline cellulose or CMC (known or experimentally measured), is represented by a continuous line.

[0171] The isotherm of the mixture, resulting from the modeling of each of the isotherms by the LOESS method and a weighting of each curve according to the weight proportion of each ingredient (10 / 80 / 10), is represented by a broken dotted line.

[0172] According to the calculations in Table 4, the MC (Moisture Content) in g / 100g of the DM (Dry Matter) is equal to 9.29. From this, we deduce, by reading the mixture curve, a final Aw of the mixture equal to 0.522, with a confidence interval between 0.509 and 0.534. We therefore obtain an inexpensive formula but with a water activity (Aw) that is too high to guarantee the stability of the active ingredient. b) Balanced mixture of maltodextrin and microcrystalline cellulose

[0173] The same approach was followed but balancing the quantities of maltodextrin and microcrystalline cellulose.

[0174] Table 5: Characteristics of the products implemented

[0175] Figure 12 illustrates the correlation between water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and relative humidity (P / PO) by modeling using LOESS regression.

[0176] The chondroitin sulfate isotherm (known or experimentally measured) is represented by light gray dots and remains unchanged.

[0177] The isotherm of excipient 1, namely maltodextrin at 10% water (known or experimentally measured), is represented by dark gray points and remains unchanged.

[0178] The isotherm of excipient 2, namely microcrystalline cellulose or CMC (known or experimentally measured), is represented by a continuous line and remains unchanged. The isotherm of the mixture, resulting from the modeling of each of the isotherms by the LOESS method and a weighting of each curve according to the weight proportion of each ingredient (10 / 45 / 45), is represented by a broken dotted line.

[0179] According to the calculations in Table 5, the MC (Moisture Content) in g / 100g of the DM (Dry Matter) is equal to 5.26. From this, we deduce, by reading the mixture curve, a final Aw of the mixture equal to 0.350, with a confidence interval between 0.342 and 0.357. We therefore obtain an improved formula but with a water activity (Aw) that is still too high to guarantee the stability of the active ingredient. c) Adjusted formula

[0180] The previous formula was adjusted to within 1% to obtain the target Aw with very low uncertainty.

[0181] Optimal formula:

[0182] Chondroitin sulfate: 10%

[0183] Maltodextrin: 36%

[0184] MCC: 54%

[0185] Table 6: Characteristics of the products implemented Figure 13 illustrates the correlation between the water content expressed in g per 100 g of dry matter (DM for “Dry Matter”) and the relative hygrometry (P / PO) by modeling using LOESS regression.

[0186] The chondroitin sulfate isotherm (known or experimentally measured) is represented by light gray dots and remains unchanged.

[0187] The isotherm of excipient 1, namely maltodextrin at 10% water (known or experimentally measured), is represented by dark gray points and remains unchanged.

[0188] The isotherm of excipient 2, namely microcrystalline cellulose or CMC (known or experimentally measured), is represented by a continuous line and remains unchanged.

[0189] The isotherm of the mixture, resulting from the modeling of each of the isotherms by the LOESS method and a weighting of each curve according to the weight proportion of each ingredient (10 / 36 / 54), is represented by a broken dotted line.

[0190] According to the calculations in Table 6, the MC (Moisture Content) in g / 100g of the DM (Dry Matter) is equal to 4.28. From this, we deduce, by reading the mixture curve, a final Aw of the mixture equal to 0.299, with a confidence interval between 0.293 and 0.305. We therefore obtain a formula which guarantees the stability of the active ingredient, while having a maximum quantity of excipient 1 (maltodextrin at 10% water).

[0191] CONCLUSION :

[0192] These three examples reveal that the use of a LOESS-type local regression helps to choose the proportions of products in a mixture of three products, for example two excipients in a mixture consisting of an active ingredient and two excipients, so as to obtain an optimized water activity (Aw) with respect to said active ingredient and an optimized cost.

[0193] IV / Combination of a non-parametric regression (LOESS, Bin smoother or MARS type) and a parametric regression (GAB) in a three-component system

[0194] A mixture comprising 3 ingredients, namely vitamin K2 (Tastetech) at 5%, a yeast fraction (LYNSIDE® Wall Basic) at 25% and dried potato starch (Potato starch extra dry) at 70%, was studied under the following conditions:

[0195] The behavior of the yeast fraction and dried potato starch was modeled using the GAB model; The behavior of vitamin K2 was modeled using LOESS, Bin-smoother, and MARS regression, respectively, because parametric models such as GAB cannot adequately model the observed drop in water content around 65% P / PO;

[0196] The behavior of the mixture is built on predictions from models applied to the ingredients of the mixture.

[0197] Figure 14 shows that the 3 curves relating to the mixture are superimposable.

[0198] CONCLUSION :

[0199] Figure 14 shows that in a three-component system, it is possible to use non-parametric regression only for the ingredient that is not satisfactorily modeled using parametric regression, in this case vitamin K2 (see Example 1-1). Furthermore, it demonstrates that other non-parametric regressions such as Bin smoother and MARS can be implemented instead of LOESS regression.

Claims

Claims 1. Method for establishing a sorption isotherm of a powder comprising: - obtaining a set of points corresponding to the water content (MC) of the powder as a function of the relative hygrometry (P / PO); - the application of a non-parametric regression on these points to establish the sorption isotherm of the powder.

2. Method for determining the water activity (Aw) of a powder sample comprising: - establishing the sorption isotherm of the powder using the method according to claim 1; - measurement of the water content of the sample; - determination of the water activity of the sample using the water content of the measured sample and the established powder sorption isotherm model.

3. Method for establishing the sorption isotherm of a solid composition comprising at least two compounds, advantageously in the form of a mixture of powders, comprising: - obtaining the sorption isotherms of each of the compounds, the isotherm of at least one of the compounds being established using the method according to claim 1; - the establishment of the sorption isotherm of the composition as a function of the weight proportion of each compound in the composition.

4. The method of claim 3, wherein the isotherm of all compounds is established using the method of claim 1.

5. Method for determining the water activity (Aw) of a mixture of powders comprising: - establishing the sorption isotherm of the mixture using the method according to claim 3 or 4; - the measurement of the water content of the mixture or the calculation of the water content of the mixture using the water contents of each of the compounds, weighted according to the weight proportion of each compound in the mixture; - determination of the water activity of the mixture as a function of the water content of the sample and the sorption isotherm model of the mixture using the measured or calculated water content of the mixture and the established sorption isotherm model of the mixture.

6. Method according to one of claims 1 to 5, in which the non-parametric regression is chosen from the following group: LOESS regression (LOcally Estimated Scatterplot Smoothing); regressogram (Bin smoother); moving average; weighted moving average (Nadaraya and Watson regression); Kernel regression, multivariate regression by adaptive spline (MARS for “Multivariate Adaptive Regression Spline”).

7. The method of claim 6, wherein the non-parametric regression is a LOESS regression.

8. Method according to claim 6 or 7, in which the LOESS regression is parameterized so that: - only the two points in the vicinity of a given point are taken into consideration; and / or - the polynomial is of degree 2.

9. Method according to one of claims 1 to 8, in which the sorption isotherm is based on at least ten measurement points of the water content (MC) as a function of the relative hygrometry (P / Po).

10. Method according to one of claims 3 to 8, in which the composition or mixture is intended for the preparation of a food supplement or a medicament.

11. Use of the method according to claim 10 for determining the nature and / or the weight content of a compound other than the active compound, so as to obtain a mixture having a water activity compatible with that of the active compound.

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