Quality assessment of total parenteral nutrition admixtures by the use of fractional factorial design

Background/Aim. Parenteral nutrition as a specific aspect of providing nutritients still remains a permanent topic of both theoretical and experimental research. Total parenteral nutrition (TPN) admixtures have complex contents making difficult to maintain their stability. The most critical parameter is the diameter of a lipid droplet, i.e. droplet size distribution. It is recommended that droplet size should not be more than 5 m and that the presence of greater droplets should not exceede the value of 0.05%. Lipid droplets size is affected particularly by electrolyte addition, especially polyvalent cations. There is a danger of the added electrolytes interaction with lipid droplets which leads to their aggregation and negative effects upon the admixtures stability. The aim of this study was to assess the effect of added electrolyte and lipid phase quantity on the admixture stability. Methods. Electrolytes were added to the studied admixture of a defined basic formulation contents in accordance with recommendations from the literature. Droplets size measurements were performed using the method of laser diffraction with a laser particles analyzer. Effects of independent variables were calculated and evaluated using commercial software. Na+, K+, Ca2+ and Mg2+ concentrations, as well as the quantity of fat phase were chosen as studied factors, i.e. independed variables. The system response, or dependent variable was the median of droplets size. Each of the factors was varied at two levels, higher (+1) and lower (-1), according to the 25-2 fractional factorial design. Results. The study suggested the presence of relative uniformity of the results of all the measurements regardless of the quantity of added electrolytes and lipid phase. It was shown that undoubtedly there is the influence of 2valent cations (calcium and magnesium) upon lipid droplets size, which is in a direct correlation with theoretical assumption. Conclusion. Within a 72-hour testing period there was no significant increase in droplet size, i.e. the studied admixtures remained stable considering droplet size median as the criterion of stability.

with a laser particles analyzer.Effects of independent variables were calculated and evaluated using commercial software.Na + , K + , Ca 2+ and Mg 2+ concentrations, as well as the quantity of fat phase were chosen as studied factors, i.e. independed variables.The system response, or dependent variable was the median of droplets size.Each of the factors was varied at two levels, higher (+1) and lower (-1), according to the 2 5-2 fractional factorial design.
Results.The study suggested the presence of relative uniformity of the results of all the measurements regardless of the quantity of added electrolytes and lipid phase.It was shown that undoubtedly there is the influence of 2valent cations (calcium and magnesium) upon lipid droplets size, which is in a direct correlation with theoretical assumption.Conclusion.Within a 72-hour testing period there was no significant increase in droplet size, i.e. the studied admixtures remained stable considering droplet size median as the criterion of stability.

Introduction
A major requirement to meet the safe and efficient use of total parenteral nutrition (TPN) admixtures concerns their stability, i.e. unchangeability over time.They are oil-inwater type emulsions (O/W) and containing more than 50 components (amino acids, carbohydrates, lipids, electrolytes, vitamins, oligoelements, insulin, heparin and water for injections).It is obviously difficult to obtain and maintain their quality, especially due to the fact that these components could interact, while these interactions are not visible.
The most critical parameter that could adversely affect the stability of TPN admixtures and endanger their suitability for the clinical use is the lipid droplet diameter.Numerous factors affect lipid droplet size, thus consequently, the stability of these emulsion systems.It is significant that lipid droplet size is particularly affected by electrolyte addition, especially by multivalent cations.However, while an admixture is required to contain electrolytes for the organism to maintain normal functioning, if high quantities of ions are added (which is the case in patients affected by metabolic disorder) it induces danger of their interaction with lipid droplets resulting in increasing of droplets size and their aggregation and imposing negative effect upon the stability of admixture 1 .
It has to be emphasized here that the droplets of fat are usually not of the regular spherical shape differing from each other almost always in size, so that polydispersity is present in each sample.It is, therefore, more reasonable to refer to "droplet size distribution" than to "droplet size", these two parameters, however, being most often regarding as identical 2,3 .It comes out that the most significant parameters to follow, except for the homogeneity, are the size stability, droplet size distribution, and even (uniform) distribution of individual droplets within the emulsion.
Attempts to introduce droplet (globule) size measurement technique into the emulsions quality analysis began in the 80s of the 20 century.It was then suggested the lipid droplet diameter to be 0.5-1 m that is approximately equal to the diameter of endogenous lipids (chyllomicrons), while the cut-off droplet size to be 5 m that was not a real requirement considering that there was no sophisticated measuring technique.It is not until 2004 that the United States Pharmacopeia (USP) introduced two criteria: globule size should not be more than 5 m, and the presence of globules larger than that size should not exceed 0.05% 2,4 .
Emulsions are known to belong to the group of colloidal systems.Yet, the droplet size in emulsions could not be determined by means of the methods usually used to determine the droplet size in colloids.The reason for that being the fact that the droplets in emulsions are deformable and tend to aggregate into large droplets.This affects light scattering and light refraction and other phenomena using to determine the size of droplets 5 .
It is well-known that there is no unique reliable method for measuring the size of emulsions droplets in a wide spectrum.Methods of measuring droplets, starting from classical to the most recent -modern ones, have been selectively used to cover a certain diapason of requirements and range of measuring 6,7 .Any methods are specific in their own way, have their disadvantages and limitations and cover a certain range of the droplets size that could be determined by them.Besides, neither of the methods could determine a full droplets size distribution (starting from a few nm to many m).The method of laser diffraction [8][9][10] is the most often used one.It is also the one used in this study.
The use of mathematical, statistical and other models make it possible to predict, that is to choose experimental settings.Although numerous, and titled as experimental design, the most often used are the methods of so-called factorial design.Factorial design is applied to determine the influence of certain factors on the system, giving the possibility to assess which of the factors exerts the most significant influence.Factorial design application provides a considerably high number of information on the studied system by a relatively low number of experiments 11,12 .
The aim of the study was to determine the impact of concentration and type of electrolytes, as well as a lipid phase on the size of lipid droplets by the use of experimental design as regard to the change of values ranging from the lowest to the highest ones, as required by the practice itself.The experimental design here helps understand the way the said factors influence the median value as the numerically and statistically significant characteristics of experimentally obtained values.

Methods
The studied TPN admixtures were prepared in the hospital pharmacy using the techniques of aseptic procedures in a laminar chamber.The study was performed in various time intervals: immediately after the preparation -0 h, and after 12 h, both at the temperature of 25°C.Time of 12 h responds to the time of application TPN admixture to a patient.Next, the compounds were kept at the temperature spanning from 2°C to 8°C and analyzed after 72 hours.
Table 1 shows the basic formulation composition of a TPN compound, while Table 2 shows the independent variables, i.The quantity of electrolytes added to the admixtures for TPN was determined on the basis of daily requirements by patients with the increased need for electrolytes (for example polytraumatized patients) in compliance with the guidelines from the literature 13 .
The particle size was determined by a laser particle analyzer (Microtrac Fra 9200, Leeds & Northrup) which uses laser diffraction technique.Measurements were repeated three times for each sample.Visual analysis was used to observe flocculation and creaming of the emulsion after admixture 14 .
As mentioned above, the most significant parameters to control, besides homogenity, are the stability of the size and droplet size distribution, as well as the uniformity of individual droplet size distribution within an emulsion.Considering numeric characteristics of random variables (a diameter of lipid droplets) it is common to define a certain characteristic size which indicates a kind of medium or orientational value around which any experimentally obtained value for the random variable are grouped.The median random variable was used in this study.
The median is a value defined as specifically divide a numerical series in two equal parts.One part includes any elements of the value equal or less than the median, while the other includes these of the equal or greater than the median.In that sense, in a sequence of values set by the size ("arranged sequence"), the median values are found exactly in the middle, thus they are also called "50th percentile" 15,16 .
In setting the experimental conditions, as well as in analyzing the results obtained by the experiment, to calculate factorial effects the analysis of variance (ANOVA) method was used, performed using the computer program Design Expert 12,17 .The chosen factors, namely independent variables, were as follows: Na + , K + , Ca 2+ , and Mg 2+ concentrations, as well as the quantity of lipid phase.The system response, or dependent variable size was the median.The de-sign, referred as 2 3 , was chosen because according to the theory to obtain the response in the assessments like this one at least 8 experiments have to be performed.If each of the 5 factors would vary at 2 levels we could obtain a total factorial design type 2 5 , thus in 32 experiments we would often obtain insignificant effects of higher order of magnitude.
Each of the factors (X 1 -X 5 ) was varied at two levels, namely higher (+1) and lower (-1), that is the fractional factorial design 2 5-2 was applied.The responses were put into the mathematical model of the first-order polynomial including 5 variables and a constant member b 0 (further on referred to as constant) 12 .y = b 0 + b 1 X 1 + b 2 X 2 + b 3 X 3 + b 4 X 4 + b 5 X 5 y -response (in this case the median of the droplet size), b 0 -coefficient (Table 4).The constant b 0 is an average response for given in the any experiments, i.e. average effect of any factors; for the given experiment b 0 = 1 / 5 i = I 5 y i , b 1, b 2, b 3, b 4, b 5 -factorial effects, X 1 , X 2 , X 3 , X 4 , X 5 -independent variables.

Results
There was no visual change in color, clarity, creaming or precipitates in the studied TPN during the study period.
To simplify factorial effects analysis, the parameters to verify are marked as coded (Table 3) presents experimental matrix of 2 5-2 fractional factorial design; values of independent variables are presented in coded values.Table 3 also shows the values of median obtained by data processing of droplet sizes measured by a Microtrac Fra 9200.
The results indicate a relative uniform data for all the measurements regardless the quantity of electrolytes and the quantity of lipid phase in the studied compounds for TPN.There were no significant differences in droplets size distribution.Also, in all the measurements done the median values were not more than 0.6 m.This fact implies that the com- pounds within the whole period of testing, i.e. in a 72-hour period, were stable as regard to the droplet size median as the stability criterion.

Factorial effects analysis
Factorial analysis was done in order to assess which of the chosen factors significantly affect the median.
As displayed in the Table 4, it is obvious that the values of the regression coefficient during the time period in which the mixtures were analyzed had been the greatest when it is the question of the impact of calcium.These results are in direct correlation with theoretical postulations of the influence of polyvalent cations upon the droplets size increase 18 .However, immediately after the production of TPN mixture (0 h), the value of the regression coefficient shows that the impact of potassium is very similar to the value showing the influence of calcium.
Factorial effects can be presented graphically as Pareto chart (Figure 1).

Discussion
Since the beginning of using TPN admixtures, i.e. within the last 30 years, numerous studies on their stability 9, 19-21 have been performed.The majority of authors have suggested that the stability of each admixture has to be verified and that the obtained results cannot be generally accepted as well.Special attention has to be paid to limitations regarding the electrolyte addition, especially polyvalent cations.

Fig. 1 -Pareto chart (median of droplets size)
Regardless the mentioned facts no clear guidelines have been defined for the maximal quantity of electrolytes that could be added.Due to the need to daily prepare TPN admixtures customized to the requirements of each patient it is necessary to study this problem in details.
Electrolytes addition to a TPN admixture, as mentioned above, disturbs its stability, that is to say it causes physicochemical changes.There are two kinds of interactions between electrolytes and fat globule surface: non-  specific and specific adsorption.Non-specific adsorption occurs when added monovalent cations Na + and K + are adsorbed at the surface of fat droplets.At high electrolyte concentrations, and above the critical flocculation concentration (CFC), electrostatic repulsive forces decrease their value thus, becoming equal to the Van der Waals attractive forces, and at a certain moment, the flocculaton process of an emulsion starts.Another adsorption kind, that, besides electrostatic interactions, involves the chemical interaction of ions and the surface of droplets is a so-called specific adsorption.It is the chemical process of adsorption occurring between polyvalent cations (Ca 2+ and Mg 2+ ) and lipid droplets which forms a bridge with the anionic emulgator component of the two lipid droplets.It, thus, leads to the increase of the droplet size and the occurrence of various types of instability such as aggregation, coalescence, flocculation, phase separation, and emulsion phase inversion as well.In the terminal stage of destabilisation of the emulsion, a droplets size could range from 5 m to 50 m which is not allowed in parenteral emulsions.It has been shown that a higher concentration and valency of cations cause the destabilisation of the emulsion to a higher extent 21 .
In planning the experiment, we started from the fact that the number of factors that could affect the stability of an emulsion for parenteral nutrition is high, thus it was necessary to choose adequate factors for the study.This choice was based on the previous experiences with this issue assessed both theoretically and practically.We also considered all the known results obtained in the earlier studies 12,22 .In designing the research, as well as in the results processing, we considered the correlation between theoretical assumptions and the obtained results applicability in pharmacy and the clinical practice.
Since the levels of independent variables are marked by coded values, absolute values of regression coefficients directly give information about their influence upon the studied system.The higher absolute value of the regression coefficient, the higher the influence of the corresponding independent variable.If the regression coefficient has the sign of "+", or "-", the increase in the level of independent variable conditions increase, or decrease in the dependent variable, that is the studied system response.

Conclusion
The results of this study suggest that the assessed TPN admixture could be used within a 72-hour period (duration of the analysis).No significant increase in a droplet size was observed.Considering the droplet size median as the criterion of stability, the studied admixtures remained stable.Thus, this study also clarified how the changes in values of individual factors influence the system to respond.It could be concluded that the metod of the fractional factorial design is suitable for planning a trial and assessing the obtained results.

R E F E R E N C E S
e. component values of various quantities (concen-Mirkovi D, et al.Vojnosanit Pregl 2013; 70(4): 374-379.tration of the added electrolytes and the quantity of the lipid component).

Table 1 The composition of a total parenteral nutrition (TPN) admixture
* Fresenius Kabi;