570695
research-article2015
PENXXX10.1177/0148607115570695Journal of Parenteral and Enteral NutritionPetitcollin et al
Original Communication
Reproducible and Individualized Method to Predict Osmolality of Compounded Pediatric Parenteral Nutrition Solutions
Journal of Parenteral and Enteral Nutrition Volume XX Number X Month 201X 1–12 © 2015 American Society for Parenteral and Enteral Nutrition DOI: 10.1177/0148607115570695 jpen.sagepub.com hosted at online.sagepub.com
Antoine Petitcollin, PharmD1; Stéphanie Duval, PharmD2; Antoine Bouissou, MD3; and Hélène Bourgoin, PhD, PharmD1
Abstract Background: Osmolality is a well-known factor in complications associated with parenteral nutrition (PN). The osmolality of compounded pediatric PN solutions is often inappropriately approximated by theoretical osmolarity, which carries a major risk of underestimation, especially in highly concentrated solutions. Only a few studies have proposed equations to overcome this problem, and to date their accuracy in settings other than those of their development has not been assessed. We propose a reproducible method to develop a predictive model of osmolality adapted to local practice, and we compare its predictive performance to osmolarity calculation and other equations. Methods: From measures performed on dilutions of basic components of PN solutions, a predictive model establishing the relationship between the quantitative and qualitative composition of a PN solution and its osmolality was developed. This model was validated in routine practice on daily compounded pediatric PN solutions, and its predictive performance was compared with osmolarity calculation, 2 previously published predictive equations, and multilinear regression. Results: We measured the osmolality of 321 routinely produced PN solutions. The model predicted osmolality with a mean relative error of –0.28% (±2.75%). All the other ways to approximate osmolality were less precise and sometimes provided critically underestimated values (from –16.67% to –33.24%). Conclusions: Our model predicted osmolality accurately and may be used in routine practice in any setting once adapted to the local production practice. Approximations by osmolarity severely underestimate actual osmolality. Keeping osmolarity 4 decades,16 to our knowledge only a few equations can be found in the literature to determine the actual value of osmolality of a PN solution,13,18 and guidelines still use osmolarity, not osmolality, as a reference.13,14 The performance of these equations in predicting the osmolality of highly concentrated solutions >1000 mOsm/L is unclear, despite the fact that this value is often taken as a reference for the choice of the catheter access. Plus, the question remains of the ability of these equations to accurately predict osmolality in other experimental conditions, different than those used to develop them. Especially, the consequences of differences in production methods, notably the nature of the components used to prepare the PN solutions, have not been assessed. The objectives of this study were (1) to provide an experimental model to accurately predict the osmolality of a PN solution of known composition, including that in highly concentrated PN solutions >1000 mOsm/kg; (2) to propose a reproducible method for the development of such a model in accordance with local production methods; and (3) to compare the accuracy of this model with other means of approaching osmolality, in order to highlight the necessity of making a careful distinction between osmolality and osmolarity, and to assess the ability of previously published equations to work in experimental conditions that differ from those in which they were developed.
Materials and Methods The experiment included 3 phases: •• Development of an experimental model to closely predict the osmolality of a PN solution
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Table 1. Composition of the Solutions Included in Parenteral Nutrition. Solution
Manufacturer
Sodium chloride Potassium chloride Sodium lactate Magnesium sulfate Glucose Amino acids
AP-HP (Paris, France) AP-HP AP-HP AP-HP
Calcium gluconate– glucoheptonate Phosphorus
AP-HP
Macopharma (Mouvaux, France) Baxter SAS (Maurepas, France)
Aguettant (Lyon, France)
Composition
Concentration
NaCl 7.5% wt/vol KCl 10% wt/vol C3H5NaO3 11.2% wt/vol MgSO4, 7H2O 10% wt/vol Corresponding to total magnesium ion C6H12O6, H2O 50% wt/vol 20 various amino acids Corresponding to total nitrogen content Calcium gluconate monohydrate Calcium glucoheptonate Corresponding to total calcium ion Disodium glucose-1-phosphate tetrahydrate Corresponding to glucose Corresponding to phosphates Corresponding to total phosphorus
1.28 mEq/mL 1.34 mEq/mL 1.00 mEq/mL 10 mg/mL (0.82 mEq/mL) 500 mg/mL 100 mg/mL 15 mg/mL 70 mg/mL 32.8 mg/mL 8.8 mg/mL (0.42 mEq/mL) 125.4 mg/mL 0.33 mmol/mL 0.33 mmol/mL 10.23 mg/mL
AP-HP, Assistance Publique–Hôpitaux de Paris.
•• Validation of this model in routine practice •• Comparison of the predictive performances of this model with other approaches, including theoretical osmolarity calculation, multilinear regression, and approximation with simple equations found in the literature
Determination of the Experimental Predictive Model Test solutions and experimental devices. All values of osmolality were determined by measuring the freezing point depression using a Löser Messtechnik type 15 automatic micro-osmometer (Löser Messtechnik, Berlin, Germany). The measuring range was 0–2500 mOsm/kg. The osmometer was calibrated daily before each set of experiments using ultrahigh-quality (UHQ) water and commercial standard sodium chloride solutions (Instrumentation Laboratory Company, Bedford, MA). During the development phase, dilutions were performed with UHQ water. Since UHQ water was used to calibrate the osmometer and thus was known to have an osmolality value of 0 mOsm/kg, it did not interfere with osmolality measurement. Calculations and graphic correlations were performed using R 3.0.3 (R Core Team, Vienna, Austria) and Excel (Microsoft Office, Seattle, WA). PN solutions were prepared extemporaneously using a Baxter MM12 compounder (Baxter Inc., Deerfield, IL, USA) from the mixture of commercial solutions of basic nutrients, under supervision of experienced pharmacists. Relationship between osmolality and concentration in basic nutrient solutions. Experiments were conducted with the 8 main commercial solutions of basic nutrients used to prepare
the pediatric PN admixtures in our hospital (Table 1). We measured the osmolality of each commercial solution separately, pure and then at several levels of dilution. Five samples per level were prepared and analyzed. All dilutions were prepared independently from pure commercial solution. Data were plotted, and the relationship between measured osmolality and concentration was determined by linear or polynomial regression (least squares method), depending on the appearance of the plot and the value of the coefficient of determination R2. Linear regression was preferred if it did not result in a decrease of R2 of >0.05 compared with that obtained by polynomial regression and if the plot did not obviously display a polynomial trend curve. To characterize the difference between osmolality and osmolarity, the same work was performed after plotting measured osmolarity versus theoretical osmolarity of each component. Determination of total osmolality in multicomponent PN solutions. The theoretical osmolarity of a multicomponent solution is equal to the total number of osmoles contributed by the components divided by the total volume of the solution, which is equivalent to the sum of the separate theoretical osmolarities of all the components. Knowing that theoretical osmolarity follows this addition rule, we assumed that osmolality followed the same rule. Thus, in the experimental model, the total predicted osmolality was obtained by summing the predicted osmolalities of all the components.
Validation of the Experimental Model Data used for validation of the model were collected from samples of pediatric PN solutions prepared in routine practice
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during 1.5 months. PN solutions were prepared daily with the same commercial solutions of basic nutrients that were used in the first phase of our experiment, following the formula ordered by the clinicians. A 5-mL sample was taken from each PN solution, just after completion of the mixture and proper homogenization, for osmolality measurement. Measurements were performed on the day of production to avoid evaporation and concentration of the samples, which would have resulted in osmolality overestimation. No dilution was performed on PN samples used for the validation of the predictive model. The predictive performance of the model was graphically evaluated by plotting predicted versus measured osmolalities. Residuals expressed as relative error from the measured value were calculated, and their distribution was graphically assessed. Bias was estimated by the mean relative error. The precision of the predictions was estimated by calculating the root mean square error (RMSE). The conditions for validation of the model were as follows: normality of the residuals, mean relative error close to 0, no predicted value from the [–15%; 15%] interval, and no more than 5% of predicted values from the [–10%; 10%] interval. RMSE was calculated to compare the predictive performance with that of the other models.
Comparison of the Predictive Performance of the Experimental Model With That of Other Approaches We compared the predictive performances of several alternative approaches with those of our experimental model. The alternative approaches were theoretical osmolarity calculation (Equation 1), osmolarity approximation using an equation issued in PN guidelines13 (Equation 2), and 2 equations issued from multilinear regression (MLR) analysis. The first MLR equation (MLR I) was determined experimentally from the composition and the measured values of osmolality of PN solutions prepared in routine practice18 (Equation 3). We determined the second MLR equation (MLR II) from the composition and the measured values of osmolality of the same PN solutions we used to determine our experimental predictive model (Equation 4). The equations of the alternative models are given in Table 2. Multilinear regression (MLR II). We performed a linear multivariate analysis to determine a predictive equation for osmolality from the values measured in the PN samples and their composition. We used a stepwise approach and Akaike’s information criterion minimization to determine the best predictive equation. To ensure the best predictive performance of the multivariate model, the P value of the t test used to determine whether a variable must be retained in the multivariate model was fixed to .1. Thus, even “close to significant” (.05 < P < .1) variables were included into the final MLR model to obtain the best predictive performance, regardless of the principle of parsimony.
Comparison of the different approaches. For each approach, measured osmolality was plotted with the corresponding estimations, and residuals expressed as relative error to the measured value, mean relative error, and RMSE were calculated. All these parameters were compared with those of our experimental model. Residual distribution was inspected and compared between the different methods. Definition of maximum recommended values. From the results of our experiment, we determined the maximum acceptable values of osmolarity corresponding to several desired upper values of osmolality.
Results Determination of the Experimental Predictive Model Relationship between osmolality and concentration in basic nutrient solutions. The experiment resulted in the construction of 8 curves (1 per basic component) showing the relationship between concentration and measured osmolality. Experiments revealed that the osmolality of solutions of strong electrolytes (sodium chloride, potassium chloride, and magnesium sulfate) was a linear function of their concentration. In contrast, the osmolality of solutions of some organic components, particularly glucose and calcium glucoheptonate, did not show linear proportionality with their concentration, and polynomial trend curves were used to describe the relationship between them. Other organic components (amino acid solution and sodium lactate solution) and mixtures of organic components and electrolytes (phosphorus solution) had close to linear relationships between concentration and osmolality, and thus linear regression was performed. The equations of the curves were determined (Table 3). Relationship between osmolality and theoretical osmolarity in basic nutrient solutions. Glucose and amino acids, as the 2 major components of PN solutions, were the components that most increased the value of measured osmolality. After we plotted measured osmolality versus theoretical osmolarity (Figure 1), it appeared that there was a great difference between the 2 values. Considering glucose, the difference between theoretical osmolarity and measured osmolality increases faster than concentration. In the most concentrated solution of glucose we tested (275 g/L), corresponding to a theoretical osmolarity of 1528 mOsm/L, osmolality was measured at 2281 mOsm/kg (+49.28%). The osmolality of the amino acid solution was close to linearly correlated with theoretical osmolarity but was about 10% higher. Regarding strong electrolytes, data showed that theoretical osmolarity overestimated the real measured osmolality. Osmolality of sodium chloride and potassium chloride was, respectively, 0.93- and 0.88-fold the value of their theoretical
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Table 2. Predictive Equations Used as a Comparison. Number 1
Prediction
Equation
Theoretical osmolarity
2
Osmolarity approximation
3
Osmolality
4
Osmolality
Osm =
Osm =
∑(nk ik )
Term Definitions
Reference
mOsm/L
nk, quantity of component k (millimoles); ik, number of ions when component k is totally dissociated; V, volume (L) AA, amino acids (g/L); GLC, glucose (g/L); E, total electrolytes (mEq/L); V, volume (L) AA, amino acids (g); GLC, glucose (g); Na, sodium (mEq); V, volume (L)
16
V
AA × 10 + GLC × 5 + E V
mOsm/L
AA × 8 + GLC × 7 + Na × 2 + P × 0.2 Osm = − 50 V 9.78 + AA × 10.16 + GLC × 6.59 + NaCl × 1.68 + K × 2.79 + NaLact × Osm =
Unit
mOsm/kg
mOsm/kg
1.63 + P × 0.09 + Mg × 0.69 V
13
18
AA, GlC, NaCl, K, NaLact, P, Self-developed and Mg, number of osmoles of glucose, amino acids, sodium chloride, potassium chloride, sodium lactate, phosphorus solution, and magnesium sulfate, respectively
Table 3. Equations Describing the Correlations Between Concentration and Osmolality. Component Sodium chloride Potassium chloride Sodium lactate Magnesium sulfate Glucose Amino acids (AA) Calcium gluconate–glucoheptonate Phosphorus Total osmolality (mOsm/kg)
Equation
Term Definitions
Osm(NaCl) = 1.8689 × NaCl Osm(KCl) = 1.7631 × KCl Osm(NaLactate) = 2.0677 × NaLactate Osm(MgSO4) = 43.454 × Mg Osm(Glc) = 0.0124 × Glc2 + 5.275 × Glc Osm(AA) = 8.4557 × AA Osm(Ca) = –1.7709 × Ca2 + 48.092 × Ca Osm(P) = 75.326 × P Σ Osm (i)a
NaCl, Na (mEq/L) KCl, K (mEq/L) NaLactate, Na (mEq/L) MgSO4, Mg (mEq/L) Glc, Glucose (g/L) AA, total AA (g/L) Ca, total Ca (mg/L) P, total P (mg/L) —
a
Σ Osm (i) is the sum of the osmolalities of the components.
osmolarity. The osmolality of magnesium sulfate was 0.54fold the value of its theoretical osmolarity. Sodium lactate and the phosphorus mixture had close to linear relationships between theoretical osmolarity and measured osmolality, and the values of the 2 terms were very close regardless of the concentration. In the calcium gluconate–glucoheptonate solution, osmolarity increased faster than osmolality, and their values were very different. The most concentrated calcium gluconate–glucoheptonate solution we tested had a measured osmolality of 288 mOsm/kg for an osmolarity calculated at 669 mOsm/L. Determination of the final experimental model. The equations obtained from the regressions between measured osmolality and concentration were compiled into a spreadsheet for
routine prediction of the osmolality of PN solutions from the formula ordered by the clinician. The total predicted value of osmolality of a PN sample was obtained by summing predicted osmolalities of all the components. Note that the concentrations of sodium obtained by adding sodium lactate or sodium chloride to the PN solution may be the same, but corresponding osmolalities are different due to the nature of the salt (lactate or chloride). A solution of sodium lactate containing 1 mEq/mL of sodium has an osmolality of about 2068 mOsm/kg, whereas a solution of sodium chloride at 1 mEq/mL of sodium has an osmolality of about 1869 mOsm/ kg. That is why the concentrations of sodium provided by lactate or chloride are distinguished from each other in the experimental model for the calculation of predicted osmolality.
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2000
1500
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0
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Potassium chloride osmolarity (mOsm/L)
500
Glucose osmolarity (mOsm/L)
0
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Calcium gluconate osmolarity (mOsm/L)
100
Amino acid osmolarity (mOsm/L)
800
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Sodium chloride osmolarity (mOsm/L)
Phosphorus solution osmolarity (mOsm/L)
0
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0
0
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2000
Magnesium sulfate osmolarity (mOsm/L)
200
Sodium lactate osmolarity (mOsm/L)
Figure 1. Correlations between theoretical osmolarity and osmolality. All components had linear or close to linear correlations, except glucose, for which osmolality increased faster than osmolarity, and calcium gluconate-glucoheptonate, for which osmolality increased slower than osmolarity.
0
Glucose osmolality (mOsm/kg)
Potassium chloride osmolality (mOsm/kg)
800 600 400 200 0 250 200 150 100 50 0
Amino acids solution osmolality (mOsm/kg) Calcium gluconate osmolality (mOsm/kg)
2500 2000 1500 1000 500 0 600 400 200 0
Sodium chloride osmolality (mOsm/kg) Phosphorus solution osmolality (mOsm/kg)
2000 1500 1000 500 0 100 200 300 400 500 600 0
Sodium lactate osmolality (mOsm/kg) Magnesium sulfate osmolality (mOsm/kg)
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Table 4. Typical Composition of the Parenteral Nutrition Solutions.a Substance Water, mL Glc, g Amino acids, g Na, mEq NaCl Na lactate K, mEq P, mg Ca, mg Mg, mg
Amount (unit per kg per 24 h) 82.1 [60.0; 120.0] 10.0 [7.5; 12.5] 2.0 [1.5; 3] 0.0 [0.0; 3.0] 3.0 [0.0; 4.0] 2.0 [2.0; 2.4] 25.0 [20.0; 30.0] 30.0 [30.0; 40.0] 10.0 [10.0; 10.0]
Concentration (unit per L) — 114.3 [96.7; 128.2] 25.0 [20.0; 33.3] 0.0 [0.0; 26.1] 28.7 [0.0; 28.4] 25.0 [17.4; 33.3] 0.30 [0.21; 0.40] 0.38 [0.28; 0.50] 0.10 [0.08; 0.15]
a
Data are shown as median [1st quartile; 3rd quartile].
Validation of the Predictive Model We measured the osmolality of 325 solutions from the daily production of pediatric PN. Typical compositions of test solutions are presented in Table 4. Four values were excluded from the statistical analysis because they were out of the measuring range (>2500 mOsm/kg). The maximum measured value was 2428 mOsm/kg and the minimum was 615 mOsm/kg. In decreasing order of importance, osmolality of PN solutions was due to glucose (representing about a third to a half of osmolality), amino acids (about a quarter), sodium chloride or sodium lactate, potassium chloride, phosphorus, calcium gluconate, and magnesium sulfate. These 3 last components contributed about 5%–7% of total osmolality. The results of predictive performance analysis are shown in Table 5. Using our model, only 1 predicted osmolality value out of 324 (0.31%) was >10% (11.29%) greater than the measured osmolality value, thus providing an overestimated value of osmolality, which is more safe than an underestimation. The study of relative errors showed that our model was able to predict osmolality with a good accuracy (±5%) in 93.14% of the PN solutions (299/321). The distribution of the relative error was approximately normal, with mean –0.28% and standard deviation of 2.75% (Figure 2).
Comparison of the Predictive Performance of the Experimental Model With That of Other Approaches Results of the multivariate analysis. Our linear multivariate analysis provided a model that included the number of osmoles provided by each of the components, except calcium. The equation of this multivariate model is referred to as Equation 4 and is given in Table 2. Comparison of the different approaches. The other techniques we assessed to estimate the osmolality of PN solutions all
appeared to be less accurate than our experimental model. In particular, the equation to approximate osmolarity (Equation 2) and the theoretical osmolarity calculation (Equation 1) tended to greatly underestimate the actual value of osmolality, with mean relative errors of –12.56% and –10.03%, respectively, and large standard deviations. The 2 linear multivariate models showed better results, with an average relative error of –6.03% for the model issued from the literature (Equation 3) and 0.45% for our own multivariate model (Equation 4). The predictive performances of the different models are presented in Table 5. However, it appeared clearly that the distribution of the residuals was bimodal in all the alternative approaches (Figure 3). Most of the residuals were distributed close to the mean relative error, but a nonnegligible part of them was also distributed around a value from –10% to –25% depending on the model. This bimodal distribution of the residuals was due to the inability of these models to predict accurately the osmolality of highly concentrated PN solutions, which they underestimated more or less severely. It was not the case with our experimental model, whose residuals were approximately normally distributed around the mean relative error, indicating a good accuracy in predicting osmolality, including in high-osmolality PN solutions. Definition of maximum recommended values. Maximum recommended values of osmolarity depending on several upper values of osmolality are presented in Table 6.
Discussion The role of osmolality in the development of adverse events during PN has been largely described concerning either PPN or CPN. According to certain authors, infusion-induced thrombophlebitis remains a limiting factor to efficient PN.19 Many studies showed that it was possible to minimize the occurrence of phlebitis using appropriate catheter type.14,20-25 Addition of heparin to the infusate26-28 and cyclic infusion29 were also reported to be effective methods to prevent phlebitis. Topical use of glyceryl trinitrate was reported to be effective,28 but later contradictory evidence indicated that this agent should not be applied on the insertion site of the catheter.26 The choice of the vein is still thought to be of utmost importance.25 However, several studies report that the physical and chemical characteristics of PN solutions, especially pH2,30 and osmolality, are critical factors to take into account to diminish the risks of complications. Hence, safe administration of PN results from the combination of improvements in catheter design, correct catheter placement, optimal conditions of administration, and knowledge of the characteristics of the PN solution, such as its osmolality. Our experiment showed that it is possible, with an appropriate model, to closely predict the measured value of osmolality of a PN solution in routine practice. Following our method, such an accurate predictive model could be established in other
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Table 5. Predictive Performances of the Different Models. Model Experimental model Theoretical osmolarity (Eq 1) Osmolarity approximation (Eq 2) MLR I (Eq 3) MLR II (Eq 4)
Mean Relative Error (95% CI), %
Median [1Q; 3Q],a %
Minimum,%
Maximum, %
SD, %
RMSE
–0.28 (–0.58 to 0.02) –10.03 (–10.66 to –9.4)
0.12 [–1.81; 1.45] –9.62 [–12.60; –7.07]
–9.37 –27.64
11.4 13.04
2.75 5.78
620,317 11,040,016
–12.56 (–13.36 to –11.76) –12.16 [–16.82; –7.45]
–33.24
9.04
7.29
16,525,857
–21.33 –16.67
5.509 22.57
4.99 5.21
5,863,438 2,105,915
–6.03 (–6.58 to –5.48) 0.45 (–0.12 to 1.02)
–4.52 [–8.79; –2.68] 1.23 [–1.36; 1.02]
MLR, multilinear regression; RMSE, root mean square error. a 1st quartile; 3rd quartile.
Distribution of the relative error 0.20 0.15
2000
0.10
1500
0.05
1000
0.00
500 0
Measured osmolality (mOsm/kg)
2500
Predictive performance of the experimental model
0
500
1000
1500
2000
2500
Predicted osmolality (mOsm/kg)
−30
−20
−10
0
10
20
30
Relative error (%)
Figure 2. Predictive performances of the experimental model. Mean relative error, –0.28%, standard deviation, 2.75%.
centers and adapted to the local practice. Indeed, we chose to consider 8 basic components that may be different in other care settings, and specific correlations between concentration and osmolality have to be established for every solution whose composition differs from those we tested. But there is evidence that such a correlation can be found for any solution, including complex mixtures such as a solution of multiple amino acids, as long as their relative composition does not change. Hence, once the correlation is established and the corresponding equation is determined by linear or polynomial regression, the osmolality of any solution contained in a PN solution can be easily calculated from its concentration. Then total osmolality of the PN solution is simply obtained by summing the osmolalities of all its components. It seems more convenient and
more accurate to perform such an analysis than linear multivariate regression, and there is no need for mathematical expertise. The study of the residuals showed that our experimental model provided accurate estimations, with a mean relative error close to 0 and ranging between –10% and +10%. The distribution of the residuals was approximately normal. These predictive performances, assessed using samples issued from routine production of pediatric PN solution, ensure safe use of the model in routine practice. It is particularly fitted to pharmacists who seek an accurate estimation of osmolality from the composition of a PN solution. Such a model can provide reference values to compare with measured values of osmolality for the quality control of pediatric PN solutions and can provide a
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−20
−10
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30
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Approximated osmolarity (mOsm/L)
2500
−20
−10
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30
Distribution of the relative error (Eq.2)
−30
0
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Predicted osmolality (mOsm/kg)
2500
−20
−10
0
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Distribution of the relative error (Eq.3)
−30
0
Multilinear regression I (Equation 3)
Relative error (%)
Relative error (%)
Relative error (%)
0.05
0.00
500
1000
1500
2000 Predicted osmolality (mOsm/kg)
2500
−20
0
10 Relative error (%)
−10
20
30
Distribution of the relative error (Eq.4)
−30
0
Multilinear regression II (Equation 4)
Figure 3. Predictive performances of the other models. Theoretical (Equation 1) and approximated (Equation 2) osmolarity underestimated actual osmolality (mean relative error around –10%). The more the parenteral nutrition solution was concentrated, the greater was the underestimation. Linear multivariate models (Equations 3 and 4) also underestimated osmolality, especially in highly concentrated PN solutions.
Measured osmolality (mOsm/kg)
2500
2000
1500
1000
500
0
0.20
0.15
Theoretical osmolarity (mOsm/L)
Distribution of the relative error (Eq.1)
−30
0
Measured osmolality (mOsm/kg) 0.05 0.00
0.10
2500 2000 1500 1000 500 0 0.20 0.15
Osmolarity approximation (Equation 2)
Measured osmolality (mOsm/kg) 0.05
0.10
2500 2000 1500 1000 500 0 0.20 0.15
Theoretical osmolarity (Equation 1)
Measured osmolality (mOsm/kg)
0.00
0.10
2500 2000 1500 1000 500 0 0.20 0.15 0.10 0.05 0.00
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Table 6. Maximum Recommended Values of Theoretical Osmolarity to Ensure Osmolality Value. Maximal Desired Osmolality, mOsm/kg 1500 1200 1000 900 800
Maximal Recommended Osmolarity, mOsm/L 1200 1000 800 750 660
safe estimation of osmolality in care settings. It can also be helpful to prescribers, because the calculation of total osmolality requires previous calculation of osmolalities of the different components, which means it is possible to modulate the composition of a PN solution to obtain a certain value of osmolality or to not exceed a maximum value. The accuracy of the model is also helpful in choosing the route and rate of administration in accordance with guidelines. Glucose was found to be the most important constituent of PN solutions to consider in predicting osmolality. The major role of glucose in the increase of osmolality of PN solutions is well described,13,14,18 but to our knowledge, the nonlinear relationship between its concentration and its osmolality has never been clearly reported and is not taken into account in equations that were previously proposed to estimate osmolality in routine practice.13,18 Amino acids should also be carefully considered because in our experiment, they contributed about a quarter of total osmolality, and their osmolality was 10% greater than their theoretical osmolarity. The other components we studied were necessary to obtain an accurate prediction of osmolality, but they were less implicated in the increase of osmolality. The correlation between concentration and osmolality was found to be very close to linearity in the basic commercial solutions of amino acids, sodium lactate, and phosphorus. This was unexpected, especially with the amino acid solution. Unlike the sodium lactate solution and the phosphorus solution, the amino acid solution contained no electrolytes apart from negligible amounts of chloride ion (0.019 mEq/mL or 0.6 mg/mL compared with 100 mg/mL of amino acids). We chose to use linear equations despite the fact that these solutions were logically supposed to permit nonlinear correlation as did the other organic components (glucose and calcium gluconate– glucoheptonate). Polynomial trend curves fitted slightly better and provided slightly higher R2 values, but at the concentrations in which these products were used in PN solutions, the difference between the values provided by polynomial or linear regression was negligible. Nevertheless, we performed a similar analysis of the accuracy of an experimental model including polynomial equations to predict osmolality of all nonelectrolyte components. The performance of this model was equivalent, so we chose the simplest one, which was presented here. Other minor components of PN solutions, such as vitamins and oligo-elements, were neglected in our experiment
despite their routine use in the preparation of PN solutions. We also chose to neglect additional components such as antibiotics. However, the results showed that these omissions did not affect the predictive performance of the model or affected it only minimally. Our experiment highlighted that the equations found in the literature may not be able to predict osmolality in experimental conditions other than those in which they were developed. We found that the predictive equation issued from the multivariate analysis performed by Pereira-da-Silva and colleagues,18 although having much better predictive performances than theoretical osmolarity calculation or approximation, presented an overall bias in predicting osmolality of our PN solutions, underestimating it. This bias was more pronounced in high-osmolality solutions. This may be due to several reasons. First, we showed that the relationship between concentration and osmolality is not linear in some major components, especially glucose. This was not taken into account in the equations issued from MLR, nor is it accounted for in theoretical osmolarity calculation (Equation 1) or osmolarity approximation (Equation 2). Plus, the results of an MLR analysis depend on the data used to perform it. Since Pereirada-Silva and colleagues used less concentrated PN solutions than we did, their MLR model logically could not correctly adjust to the characteristics of the highly concentrated solutions we used in our experiment; our MLR model had better predictive performance because it was more suited to our data. This may explain the differences of performance between the 2 MLR models even though the same method was used to determine them. These differences can also be partially explained by the fact that the nature of the components may differ, resulting in different values of osmolality. In our center, depending on the needs of the child, the clinician may prescribe sodium lactate or sodium chloride. We had to distinguish these 2 salts because they did not have similar characteristics. Notably, for the same concentration of sodium, the 2 solutions did not have the same osmolality. The same phenomenon could be found with other components of PN solutions depending on local practice, and this underscores the necessity not to use predictive equations developed in other experimental conditions. This is also true for our own predictive model, which should not be used unless the components used for PN solution compounding are the same as those we used in this experiment. Comparison of the predictive performance of our experimental model to preexisting means to estimate osmolality proved the superiority of our model. Depending on authors and guidelines, recommendations have suggested that the osmolarity of PPN solutions should not exceed 800–1000 mOsm/L.9,13-15 It is notable that maximum tolerated values are given as osmolarity, not osmolality values. Theoretical osmolarity and its approximations are clearly unable to provide reliable values, including in low-concentration solutions used for PPN, and should be definitely avoided unless there is no other choice.
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They provide imprecise estimations and are potentially dangerous because they always underestimate real osmolality, with an average value of about –10% that can reach almost –30% in the worst cases. This underestimation leads to a high risk to infuse PN solutions with osmolality exceeding maximum recommended values, thus increasing the risk of complications. The clinical significance of the differences between theoretical osmolarity and actual osmolality values needs to be evaluated. According to our results, an osmolality value 10%–20% higher than osmolarity is often observed in solutions used for peripheral administration. The clinical relevance of such a difference is not known, but it is reasonable to think that it may be at least partly responsible for the occurrence of complications, along with other factors we discussed previously. Only a few studies have assessed the role of the osmotic properties of PN solutions in the occurrence of complications. Most of them were conducted in the 1980s and 1990s and have methodological limitations.15 Regarding our results, the main limitation is that almost all of these studies consider osmolarity rather than osmolality. This confusion might have introduced a major bias in their results, because as we demonstrated, the values of osmolality depend on both quantitative and qualitative composition of PN admixtures. Thus, 2 solutions with different compositions can have the same osmolarity but different osmolalities, and thus osmolarity values are not reliable to assess the osmotic properties of a solution. This can partly explain the difficulty of determining a precise limit for safe administration. There were also a number of other methodological limitations in the studies from the 1980s and 1990s, such as small sample size, absence of blinding, and absence of control. The infusion rate, although being a known risk factor for thrombophlebitis, was frequently not controlled. There is also no consensus on what is considered an “acceptable” rate of thrombophlebitis or an acceptable duration of infusion before phlebitis occurrence. All these factors are probably responsible for the discordance of the results in these studies. Therefore, there is an urgent need to undertake studies with proper methods, notably with a reasonable estimation of osmolality, either by measuring PN solutions or by using accurate approximations such as those provided by our predictive model. The predictive performance of such a model should be properly validated before it is used in routine practice or clinical studies.
Conclusion Since parenteral feeding cannot be avoided in many cases, it has to be as safe as possible. Factors to be improved include osmolality, because it is an important cause of complications when infusion solution is delivered. This study confirmed that theoretical osmolarity and other approximations of osmolarity severely underestimate osmolality in many cases and should not be used as references to estimate it. Other equations, especially those obtained by linear multivariate analysis, are not
reliable if they are not used in strict accordance with the practice of their authors in terms of preparing PN solutions. Equations issued from the literature may not be suitable in all settings, due to differences in qualitative and quantitative composition of PN solutions depending on local production practice or patients’ needs. These equations also do not take into account the nonlinear relationship between concentration and osmolality in major, critical components such as glucose, and they are expected to be inaccurate. The experimental model we proposed here is simple and efficient, including in highly concentrated PN solutions. In addition to its predictive performance, the interest of our model lies in the method we followed to develop it, which is easily reproducible in any care setting, allowing one to individualize the model to local practices. Such a model can be used by clinicians as a helpful tool for secured PN prescription and access choice or by pharmacists to obtain a reliable reference value for the quality control of PN solutions. The clinical significance of underestimating osmolality still needs to be investigated, but it is reasonable to think that controlling the osmotic strength of PN solutions is a major issue to be considered in optimizing PN safety. Based on our results, theoretical osmolarity up to 1000 mOsm/L allows one to obtain actual osmolality
research-article2015
PENXXX10.1177/0148607115570695Journal of Parenteral and Enteral NutritionPetitcollin et al
Original Communication
Reproducible and Individualized Method to Predict Osmolality of Compounded Pediatric Parenteral Nutrition Solutions
Journal of Parenteral and Enteral Nutrition Volume XX Number X Month 201X 1–12 © 2015 American Society for Parenteral and Enteral Nutrition DOI: 10.1177/0148607115570695 jpen.sagepub.com hosted at online.sagepub.com
Antoine Petitcollin, PharmD1; Stéphanie Duval, PharmD2; Antoine Bouissou, MD3; and Hélène Bourgoin, PhD, PharmD1
Abstract Background: Osmolality is a well-known factor in complications associated with parenteral nutrition (PN). The osmolality of compounded pediatric PN solutions is often inappropriately approximated by theoretical osmolarity, which carries a major risk of underestimation, especially in highly concentrated solutions. Only a few studies have proposed equations to overcome this problem, and to date their accuracy in settings other than those of their development has not been assessed. We propose a reproducible method to develop a predictive model of osmolality adapted to local practice, and we compare its predictive performance to osmolarity calculation and other equations. Methods: From measures performed on dilutions of basic components of PN solutions, a predictive model establishing the relationship between the quantitative and qualitative composition of a PN solution and its osmolality was developed. This model was validated in routine practice on daily compounded pediatric PN solutions, and its predictive performance was compared with osmolarity calculation, 2 previously published predictive equations, and multilinear regression. Results: We measured the osmolality of 321 routinely produced PN solutions. The model predicted osmolality with a mean relative error of –0.28% (±2.75%). All the other ways to approximate osmolality were less precise and sometimes provided critically underestimated values (from –16.67% to –33.24%). Conclusions: Our model predicted osmolality accurately and may be used in routine practice in any setting once adapted to the local production practice. Approximations by osmolarity severely underestimate actual osmolality. Keeping osmolarity 4 decades,16 to our knowledge only a few equations can be found in the literature to determine the actual value of osmolality of a PN solution,13,18 and guidelines still use osmolarity, not osmolality, as a reference.13,14 The performance of these equations in predicting the osmolality of highly concentrated solutions >1000 mOsm/L is unclear, despite the fact that this value is often taken as a reference for the choice of the catheter access. Plus, the question remains of the ability of these equations to accurately predict osmolality in other experimental conditions, different than those used to develop them. Especially, the consequences of differences in production methods, notably the nature of the components used to prepare the PN solutions, have not been assessed. The objectives of this study were (1) to provide an experimental model to accurately predict the osmolality of a PN solution of known composition, including that in highly concentrated PN solutions >1000 mOsm/kg; (2) to propose a reproducible method for the development of such a model in accordance with local production methods; and (3) to compare the accuracy of this model with other means of approaching osmolality, in order to highlight the necessity of making a careful distinction between osmolality and osmolarity, and to assess the ability of previously published equations to work in experimental conditions that differ from those in which they were developed.
Materials and Methods The experiment included 3 phases: •• Development of an experimental model to closely predict the osmolality of a PN solution
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Table 1. Composition of the Solutions Included in Parenteral Nutrition. Solution
Manufacturer
Sodium chloride Potassium chloride Sodium lactate Magnesium sulfate Glucose Amino acids
AP-HP (Paris, France) AP-HP AP-HP AP-HP
Calcium gluconate– glucoheptonate Phosphorus
AP-HP
Macopharma (Mouvaux, France) Baxter SAS (Maurepas, France)
Aguettant (Lyon, France)
Composition
Concentration
NaCl 7.5% wt/vol KCl 10% wt/vol C3H5NaO3 11.2% wt/vol MgSO4, 7H2O 10% wt/vol Corresponding to total magnesium ion C6H12O6, H2O 50% wt/vol 20 various amino acids Corresponding to total nitrogen content Calcium gluconate monohydrate Calcium glucoheptonate Corresponding to total calcium ion Disodium glucose-1-phosphate tetrahydrate Corresponding to glucose Corresponding to phosphates Corresponding to total phosphorus
1.28 mEq/mL 1.34 mEq/mL 1.00 mEq/mL 10 mg/mL (0.82 mEq/mL) 500 mg/mL 100 mg/mL 15 mg/mL 70 mg/mL 32.8 mg/mL 8.8 mg/mL (0.42 mEq/mL) 125.4 mg/mL 0.33 mmol/mL 0.33 mmol/mL 10.23 mg/mL
AP-HP, Assistance Publique–Hôpitaux de Paris.
•• Validation of this model in routine practice •• Comparison of the predictive performances of this model with other approaches, including theoretical osmolarity calculation, multilinear regression, and approximation with simple equations found in the literature
Determination of the Experimental Predictive Model Test solutions and experimental devices. All values of osmolality were determined by measuring the freezing point depression using a Löser Messtechnik type 15 automatic micro-osmometer (Löser Messtechnik, Berlin, Germany). The measuring range was 0–2500 mOsm/kg. The osmometer was calibrated daily before each set of experiments using ultrahigh-quality (UHQ) water and commercial standard sodium chloride solutions (Instrumentation Laboratory Company, Bedford, MA). During the development phase, dilutions were performed with UHQ water. Since UHQ water was used to calibrate the osmometer and thus was known to have an osmolality value of 0 mOsm/kg, it did not interfere with osmolality measurement. Calculations and graphic correlations were performed using R 3.0.3 (R Core Team, Vienna, Austria) and Excel (Microsoft Office, Seattle, WA). PN solutions were prepared extemporaneously using a Baxter MM12 compounder (Baxter Inc., Deerfield, IL, USA) from the mixture of commercial solutions of basic nutrients, under supervision of experienced pharmacists. Relationship between osmolality and concentration in basic nutrient solutions. Experiments were conducted with the 8 main commercial solutions of basic nutrients used to prepare
the pediatric PN admixtures in our hospital (Table 1). We measured the osmolality of each commercial solution separately, pure and then at several levels of dilution. Five samples per level were prepared and analyzed. All dilutions were prepared independently from pure commercial solution. Data were plotted, and the relationship between measured osmolality and concentration was determined by linear or polynomial regression (least squares method), depending on the appearance of the plot and the value of the coefficient of determination R2. Linear regression was preferred if it did not result in a decrease of R2 of >0.05 compared with that obtained by polynomial regression and if the plot did not obviously display a polynomial trend curve. To characterize the difference between osmolality and osmolarity, the same work was performed after plotting measured osmolarity versus theoretical osmolarity of each component. Determination of total osmolality in multicomponent PN solutions. The theoretical osmolarity of a multicomponent solution is equal to the total number of osmoles contributed by the components divided by the total volume of the solution, which is equivalent to the sum of the separate theoretical osmolarities of all the components. Knowing that theoretical osmolarity follows this addition rule, we assumed that osmolality followed the same rule. Thus, in the experimental model, the total predicted osmolality was obtained by summing the predicted osmolalities of all the components.
Validation of the Experimental Model Data used for validation of the model were collected from samples of pediatric PN solutions prepared in routine practice
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during 1.5 months. PN solutions were prepared daily with the same commercial solutions of basic nutrients that were used in the first phase of our experiment, following the formula ordered by the clinicians. A 5-mL sample was taken from each PN solution, just after completion of the mixture and proper homogenization, for osmolality measurement. Measurements were performed on the day of production to avoid evaporation and concentration of the samples, which would have resulted in osmolality overestimation. No dilution was performed on PN samples used for the validation of the predictive model. The predictive performance of the model was graphically evaluated by plotting predicted versus measured osmolalities. Residuals expressed as relative error from the measured value were calculated, and their distribution was graphically assessed. Bias was estimated by the mean relative error. The precision of the predictions was estimated by calculating the root mean square error (RMSE). The conditions for validation of the model were as follows: normality of the residuals, mean relative error close to 0, no predicted value from the [–15%; 15%] interval, and no more than 5% of predicted values from the [–10%; 10%] interval. RMSE was calculated to compare the predictive performance with that of the other models.
Comparison of the Predictive Performance of the Experimental Model With That of Other Approaches We compared the predictive performances of several alternative approaches with those of our experimental model. The alternative approaches were theoretical osmolarity calculation (Equation 1), osmolarity approximation using an equation issued in PN guidelines13 (Equation 2), and 2 equations issued from multilinear regression (MLR) analysis. The first MLR equation (MLR I) was determined experimentally from the composition and the measured values of osmolality of PN solutions prepared in routine practice18 (Equation 3). We determined the second MLR equation (MLR II) from the composition and the measured values of osmolality of the same PN solutions we used to determine our experimental predictive model (Equation 4). The equations of the alternative models are given in Table 2. Multilinear regression (MLR II). We performed a linear multivariate analysis to determine a predictive equation for osmolality from the values measured in the PN samples and their composition. We used a stepwise approach and Akaike’s information criterion minimization to determine the best predictive equation. To ensure the best predictive performance of the multivariate model, the P value of the t test used to determine whether a variable must be retained in the multivariate model was fixed to .1. Thus, even “close to significant” (.05 < P < .1) variables were included into the final MLR model to obtain the best predictive performance, regardless of the principle of parsimony.
Comparison of the different approaches. For each approach, measured osmolality was plotted with the corresponding estimations, and residuals expressed as relative error to the measured value, mean relative error, and RMSE were calculated. All these parameters were compared with those of our experimental model. Residual distribution was inspected and compared between the different methods. Definition of maximum recommended values. From the results of our experiment, we determined the maximum acceptable values of osmolarity corresponding to several desired upper values of osmolality.
Results Determination of the Experimental Predictive Model Relationship between osmolality and concentration in basic nutrient solutions. The experiment resulted in the construction of 8 curves (1 per basic component) showing the relationship between concentration and measured osmolality. Experiments revealed that the osmolality of solutions of strong electrolytes (sodium chloride, potassium chloride, and magnesium sulfate) was a linear function of their concentration. In contrast, the osmolality of solutions of some organic components, particularly glucose and calcium glucoheptonate, did not show linear proportionality with their concentration, and polynomial trend curves were used to describe the relationship between them. Other organic components (amino acid solution and sodium lactate solution) and mixtures of organic components and electrolytes (phosphorus solution) had close to linear relationships between concentration and osmolality, and thus linear regression was performed. The equations of the curves were determined (Table 3). Relationship between osmolality and theoretical osmolarity in basic nutrient solutions. Glucose and amino acids, as the 2 major components of PN solutions, were the components that most increased the value of measured osmolality. After we plotted measured osmolality versus theoretical osmolarity (Figure 1), it appeared that there was a great difference between the 2 values. Considering glucose, the difference between theoretical osmolarity and measured osmolality increases faster than concentration. In the most concentrated solution of glucose we tested (275 g/L), corresponding to a theoretical osmolarity of 1528 mOsm/L, osmolality was measured at 2281 mOsm/kg (+49.28%). The osmolality of the amino acid solution was close to linearly correlated with theoretical osmolarity but was about 10% higher. Regarding strong electrolytes, data showed that theoretical osmolarity overestimated the real measured osmolality. Osmolality of sodium chloride and potassium chloride was, respectively, 0.93- and 0.88-fold the value of their theoretical
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Table 2. Predictive Equations Used as a Comparison. Number 1
Prediction
Equation
Theoretical osmolarity
2
Osmolarity approximation
3
Osmolality
4
Osmolality
Osm =
Osm =
∑(nk ik )
Term Definitions
Reference
mOsm/L
nk, quantity of component k (millimoles); ik, number of ions when component k is totally dissociated; V, volume (L) AA, amino acids (g/L); GLC, glucose (g/L); E, total electrolytes (mEq/L); V, volume (L) AA, amino acids (g); GLC, glucose (g); Na, sodium (mEq); V, volume (L)
16
V
AA × 10 + GLC × 5 + E V
mOsm/L
AA × 8 + GLC × 7 + Na × 2 + P × 0.2 Osm = − 50 V 9.78 + AA × 10.16 + GLC × 6.59 + NaCl × 1.68 + K × 2.79 + NaLact × Osm =
Unit
mOsm/kg
mOsm/kg
1.63 + P × 0.09 + Mg × 0.69 V
13
18
AA, GlC, NaCl, K, NaLact, P, Self-developed and Mg, number of osmoles of glucose, amino acids, sodium chloride, potassium chloride, sodium lactate, phosphorus solution, and magnesium sulfate, respectively
Table 3. Equations Describing the Correlations Between Concentration and Osmolality. Component Sodium chloride Potassium chloride Sodium lactate Magnesium sulfate Glucose Amino acids (AA) Calcium gluconate–glucoheptonate Phosphorus Total osmolality (mOsm/kg)
Equation
Term Definitions
Osm(NaCl) = 1.8689 × NaCl Osm(KCl) = 1.7631 × KCl Osm(NaLactate) = 2.0677 × NaLactate Osm(MgSO4) = 43.454 × Mg Osm(Glc) = 0.0124 × Glc2 + 5.275 × Glc Osm(AA) = 8.4557 × AA Osm(Ca) = –1.7709 × Ca2 + 48.092 × Ca Osm(P) = 75.326 × P Σ Osm (i)a
NaCl, Na (mEq/L) KCl, K (mEq/L) NaLactate, Na (mEq/L) MgSO4, Mg (mEq/L) Glc, Glucose (g/L) AA, total AA (g/L) Ca, total Ca (mg/L) P, total P (mg/L) —
a
Σ Osm (i) is the sum of the osmolalities of the components.
osmolarity. The osmolality of magnesium sulfate was 0.54fold the value of its theoretical osmolarity. Sodium lactate and the phosphorus mixture had close to linear relationships between theoretical osmolarity and measured osmolality, and the values of the 2 terms were very close regardless of the concentration. In the calcium gluconate–glucoheptonate solution, osmolarity increased faster than osmolality, and their values were very different. The most concentrated calcium gluconate–glucoheptonate solution we tested had a measured osmolality of 288 mOsm/kg for an osmolarity calculated at 669 mOsm/L. Determination of the final experimental model. The equations obtained from the regressions between measured osmolality and concentration were compiled into a spreadsheet for
routine prediction of the osmolality of PN solutions from the formula ordered by the clinician. The total predicted value of osmolality of a PN sample was obtained by summing predicted osmolalities of all the components. Note that the concentrations of sodium obtained by adding sodium lactate or sodium chloride to the PN solution may be the same, but corresponding osmolalities are different due to the nature of the salt (lactate or chloride). A solution of sodium lactate containing 1 mEq/mL of sodium has an osmolality of about 2068 mOsm/kg, whereas a solution of sodium chloride at 1 mEq/mL of sodium has an osmolality of about 1869 mOsm/ kg. That is why the concentrations of sodium provided by lactate or chloride are distinguished from each other in the experimental model for the calculation of predicted osmolality.
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2000
1500
1000
500
0
2000
1500
1000
500
0
0
500
1000
1000
1500
2000
2500
1500
Potassium chloride osmolarity (mOsm/L)
500
Glucose osmolarity (mOsm/L)
0
0
200
400
600
200
300
400
500
600
Calcium gluconate osmolarity (mOsm/L)
100
Amino acid osmolarity (mOsm/L)
800
500
1000
1500
2000
200
400
600
800
2500
Sodium chloride osmolarity (mOsm/L)
Phosphorus solution osmolarity (mOsm/L)
0
0
0
0
500
1000
1500
400
600
800
1000
2000
Magnesium sulfate osmolarity (mOsm/L)
200
Sodium lactate osmolarity (mOsm/L)
Figure 1. Correlations between theoretical osmolarity and osmolality. All components had linear or close to linear correlations, except glucose, for which osmolality increased faster than osmolarity, and calcium gluconate-glucoheptonate, for which osmolality increased slower than osmolarity.
0
Glucose osmolality (mOsm/kg)
Potassium chloride osmolality (mOsm/kg)
800 600 400 200 0 250 200 150 100 50 0
Amino acids solution osmolality (mOsm/kg) Calcium gluconate osmolality (mOsm/kg)
2500 2000 1500 1000 500 0 600 400 200 0
Sodium chloride osmolality (mOsm/kg) Phosphorus solution osmolality (mOsm/kg)
2000 1500 1000 500 0 100 200 300 400 500 600 0
Sodium lactate osmolality (mOsm/kg) Magnesium sulfate osmolality (mOsm/kg)
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Table 4. Typical Composition of the Parenteral Nutrition Solutions.a Substance Water, mL Glc, g Amino acids, g Na, mEq NaCl Na lactate K, mEq P, mg Ca, mg Mg, mg
Amount (unit per kg per 24 h) 82.1 [60.0; 120.0] 10.0 [7.5; 12.5] 2.0 [1.5; 3] 0.0 [0.0; 3.0] 3.0 [0.0; 4.0] 2.0 [2.0; 2.4] 25.0 [20.0; 30.0] 30.0 [30.0; 40.0] 10.0 [10.0; 10.0]
Concentration (unit per L) — 114.3 [96.7; 128.2] 25.0 [20.0; 33.3] 0.0 [0.0; 26.1] 28.7 [0.0; 28.4] 25.0 [17.4; 33.3] 0.30 [0.21; 0.40] 0.38 [0.28; 0.50] 0.10 [0.08; 0.15]
a
Data are shown as median [1st quartile; 3rd quartile].
Validation of the Predictive Model We measured the osmolality of 325 solutions from the daily production of pediatric PN. Typical compositions of test solutions are presented in Table 4. Four values were excluded from the statistical analysis because they were out of the measuring range (>2500 mOsm/kg). The maximum measured value was 2428 mOsm/kg and the minimum was 615 mOsm/kg. In decreasing order of importance, osmolality of PN solutions was due to glucose (representing about a third to a half of osmolality), amino acids (about a quarter), sodium chloride or sodium lactate, potassium chloride, phosphorus, calcium gluconate, and magnesium sulfate. These 3 last components contributed about 5%–7% of total osmolality. The results of predictive performance analysis are shown in Table 5. Using our model, only 1 predicted osmolality value out of 324 (0.31%) was >10% (11.29%) greater than the measured osmolality value, thus providing an overestimated value of osmolality, which is more safe than an underestimation. The study of relative errors showed that our model was able to predict osmolality with a good accuracy (±5%) in 93.14% of the PN solutions (299/321). The distribution of the relative error was approximately normal, with mean –0.28% and standard deviation of 2.75% (Figure 2).
Comparison of the Predictive Performance of the Experimental Model With That of Other Approaches Results of the multivariate analysis. Our linear multivariate analysis provided a model that included the number of osmoles provided by each of the components, except calcium. The equation of this multivariate model is referred to as Equation 4 and is given in Table 2. Comparison of the different approaches. The other techniques we assessed to estimate the osmolality of PN solutions all
appeared to be less accurate than our experimental model. In particular, the equation to approximate osmolarity (Equation 2) and the theoretical osmolarity calculation (Equation 1) tended to greatly underestimate the actual value of osmolality, with mean relative errors of –12.56% and –10.03%, respectively, and large standard deviations. The 2 linear multivariate models showed better results, with an average relative error of –6.03% for the model issued from the literature (Equation 3) and 0.45% for our own multivariate model (Equation 4). The predictive performances of the different models are presented in Table 5. However, it appeared clearly that the distribution of the residuals was bimodal in all the alternative approaches (Figure 3). Most of the residuals were distributed close to the mean relative error, but a nonnegligible part of them was also distributed around a value from –10% to –25% depending on the model. This bimodal distribution of the residuals was due to the inability of these models to predict accurately the osmolality of highly concentrated PN solutions, which they underestimated more or less severely. It was not the case with our experimental model, whose residuals were approximately normally distributed around the mean relative error, indicating a good accuracy in predicting osmolality, including in high-osmolality PN solutions. Definition of maximum recommended values. Maximum recommended values of osmolarity depending on several upper values of osmolality are presented in Table 6.
Discussion The role of osmolality in the development of adverse events during PN has been largely described concerning either PPN or CPN. According to certain authors, infusion-induced thrombophlebitis remains a limiting factor to efficient PN.19 Many studies showed that it was possible to minimize the occurrence of phlebitis using appropriate catheter type.14,20-25 Addition of heparin to the infusate26-28 and cyclic infusion29 were also reported to be effective methods to prevent phlebitis. Topical use of glyceryl trinitrate was reported to be effective,28 but later contradictory evidence indicated that this agent should not be applied on the insertion site of the catheter.26 The choice of the vein is still thought to be of utmost importance.25 However, several studies report that the physical and chemical characteristics of PN solutions, especially pH2,30 and osmolality, are critical factors to take into account to diminish the risks of complications. Hence, safe administration of PN results from the combination of improvements in catheter design, correct catheter placement, optimal conditions of administration, and knowledge of the characteristics of the PN solution, such as its osmolality. Our experiment showed that it is possible, with an appropriate model, to closely predict the measured value of osmolality of a PN solution in routine practice. Following our method, such an accurate predictive model could be established in other
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Table 5. Predictive Performances of the Different Models. Model Experimental model Theoretical osmolarity (Eq 1) Osmolarity approximation (Eq 2) MLR I (Eq 3) MLR II (Eq 4)
Mean Relative Error (95% CI), %
Median [1Q; 3Q],a %
Minimum,%
Maximum, %
SD, %
RMSE
–0.28 (–0.58 to 0.02) –10.03 (–10.66 to –9.4)
0.12 [–1.81; 1.45] –9.62 [–12.60; –7.07]
–9.37 –27.64
11.4 13.04
2.75 5.78
620,317 11,040,016
–12.56 (–13.36 to –11.76) –12.16 [–16.82; –7.45]
–33.24
9.04
7.29
16,525,857
–21.33 –16.67
5.509 22.57
4.99 5.21
5,863,438 2,105,915
–6.03 (–6.58 to –5.48) 0.45 (–0.12 to 1.02)
–4.52 [–8.79; –2.68] 1.23 [–1.36; 1.02]
MLR, multilinear regression; RMSE, root mean square error. a 1st quartile; 3rd quartile.
Distribution of the relative error 0.20 0.15
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Figure 2. Predictive performances of the experimental model. Mean relative error, –0.28%, standard deviation, 2.75%.
centers and adapted to the local practice. Indeed, we chose to consider 8 basic components that may be different in other care settings, and specific correlations between concentration and osmolality have to be established for every solution whose composition differs from those we tested. But there is evidence that such a correlation can be found for any solution, including complex mixtures such as a solution of multiple amino acids, as long as their relative composition does not change. Hence, once the correlation is established and the corresponding equation is determined by linear or polynomial regression, the osmolality of any solution contained in a PN solution can be easily calculated from its concentration. Then total osmolality of the PN solution is simply obtained by summing the osmolalities of all its components. It seems more convenient and
more accurate to perform such an analysis than linear multivariate regression, and there is no need for mathematical expertise. The study of the residuals showed that our experimental model provided accurate estimations, with a mean relative error close to 0 and ranging between –10% and +10%. The distribution of the residuals was approximately normal. These predictive performances, assessed using samples issued from routine production of pediatric PN solution, ensure safe use of the model in routine practice. It is particularly fitted to pharmacists who seek an accurate estimation of osmolality from the composition of a PN solution. Such a model can provide reference values to compare with measured values of osmolality for the quality control of pediatric PN solutions and can provide a
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Multilinear regression I (Equation 3)
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Figure 3. Predictive performances of the other models. Theoretical (Equation 1) and approximated (Equation 2) osmolarity underestimated actual osmolality (mean relative error around –10%). The more the parenteral nutrition solution was concentrated, the greater was the underestimation. Linear multivariate models (Equations 3 and 4) also underestimated osmolality, especially in highly concentrated PN solutions.
Measured osmolality (mOsm/kg)
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Journal of Parenteral and Enteral Nutrition XX(X)
Table 6. Maximum Recommended Values of Theoretical Osmolarity to Ensure Osmolality Value. Maximal Desired Osmolality, mOsm/kg 1500 1200 1000 900 800
Maximal Recommended Osmolarity, mOsm/L 1200 1000 800 750 660
safe estimation of osmolality in care settings. It can also be helpful to prescribers, because the calculation of total osmolality requires previous calculation of osmolalities of the different components, which means it is possible to modulate the composition of a PN solution to obtain a certain value of osmolality or to not exceed a maximum value. The accuracy of the model is also helpful in choosing the route and rate of administration in accordance with guidelines. Glucose was found to be the most important constituent of PN solutions to consider in predicting osmolality. The major role of glucose in the increase of osmolality of PN solutions is well described,13,14,18 but to our knowledge, the nonlinear relationship between its concentration and its osmolality has never been clearly reported and is not taken into account in equations that were previously proposed to estimate osmolality in routine practice.13,18 Amino acids should also be carefully considered because in our experiment, they contributed about a quarter of total osmolality, and their osmolality was 10% greater than their theoretical osmolarity. The other components we studied were necessary to obtain an accurate prediction of osmolality, but they were less implicated in the increase of osmolality. The correlation between concentration and osmolality was found to be very close to linearity in the basic commercial solutions of amino acids, sodium lactate, and phosphorus. This was unexpected, especially with the amino acid solution. Unlike the sodium lactate solution and the phosphorus solution, the amino acid solution contained no electrolytes apart from negligible amounts of chloride ion (0.019 mEq/mL or 0.6 mg/mL compared with 100 mg/mL of amino acids). We chose to use linear equations despite the fact that these solutions were logically supposed to permit nonlinear correlation as did the other organic components (glucose and calcium gluconate– glucoheptonate). Polynomial trend curves fitted slightly better and provided slightly higher R2 values, but at the concentrations in which these products were used in PN solutions, the difference between the values provided by polynomial or linear regression was negligible. Nevertheless, we performed a similar analysis of the accuracy of an experimental model including polynomial equations to predict osmolality of all nonelectrolyte components. The performance of this model was equivalent, so we chose the simplest one, which was presented here. Other minor components of PN solutions, such as vitamins and oligo-elements, were neglected in our experiment
despite their routine use in the preparation of PN solutions. We also chose to neglect additional components such as antibiotics. However, the results showed that these omissions did not affect the predictive performance of the model or affected it only minimally. Our experiment highlighted that the equations found in the literature may not be able to predict osmolality in experimental conditions other than those in which they were developed. We found that the predictive equation issued from the multivariate analysis performed by Pereira-da-Silva and colleagues,18 although having much better predictive performances than theoretical osmolarity calculation or approximation, presented an overall bias in predicting osmolality of our PN solutions, underestimating it. This bias was more pronounced in high-osmolality solutions. This may be due to several reasons. First, we showed that the relationship between concentration and osmolality is not linear in some major components, especially glucose. This was not taken into account in the equations issued from MLR, nor is it accounted for in theoretical osmolarity calculation (Equation 1) or osmolarity approximation (Equation 2). Plus, the results of an MLR analysis depend on the data used to perform it. Since Pereirada-Silva and colleagues used less concentrated PN solutions than we did, their MLR model logically could not correctly adjust to the characteristics of the highly concentrated solutions we used in our experiment; our MLR model had better predictive performance because it was more suited to our data. This may explain the differences of performance between the 2 MLR models even though the same method was used to determine them. These differences can also be partially explained by the fact that the nature of the components may differ, resulting in different values of osmolality. In our center, depending on the needs of the child, the clinician may prescribe sodium lactate or sodium chloride. We had to distinguish these 2 salts because they did not have similar characteristics. Notably, for the same concentration of sodium, the 2 solutions did not have the same osmolality. The same phenomenon could be found with other components of PN solutions depending on local practice, and this underscores the necessity not to use predictive equations developed in other experimental conditions. This is also true for our own predictive model, which should not be used unless the components used for PN solution compounding are the same as those we used in this experiment. Comparison of the predictive performance of our experimental model to preexisting means to estimate osmolality proved the superiority of our model. Depending on authors and guidelines, recommendations have suggested that the osmolarity of PPN solutions should not exceed 800–1000 mOsm/L.9,13-15 It is notable that maximum tolerated values are given as osmolarity, not osmolality values. Theoretical osmolarity and its approximations are clearly unable to provide reliable values, including in low-concentration solutions used for PPN, and should be definitely avoided unless there is no other choice.
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Petitcollin et al
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They provide imprecise estimations and are potentially dangerous because they always underestimate real osmolality, with an average value of about –10% that can reach almost –30% in the worst cases. This underestimation leads to a high risk to infuse PN solutions with osmolality exceeding maximum recommended values, thus increasing the risk of complications. The clinical significance of the differences between theoretical osmolarity and actual osmolality values needs to be evaluated. According to our results, an osmolality value 10%–20% higher than osmolarity is often observed in solutions used for peripheral administration. The clinical relevance of such a difference is not known, but it is reasonable to think that it may be at least partly responsible for the occurrence of complications, along with other factors we discussed previously. Only a few studies have assessed the role of the osmotic properties of PN solutions in the occurrence of complications. Most of them were conducted in the 1980s and 1990s and have methodological limitations.15 Regarding our results, the main limitation is that almost all of these studies consider osmolarity rather than osmolality. This confusion might have introduced a major bias in their results, because as we demonstrated, the values of osmolality depend on both quantitative and qualitative composition of PN admixtures. Thus, 2 solutions with different compositions can have the same osmolarity but different osmolalities, and thus osmolarity values are not reliable to assess the osmotic properties of a solution. This can partly explain the difficulty of determining a precise limit for safe administration. There were also a number of other methodological limitations in the studies from the 1980s and 1990s, such as small sample size, absence of blinding, and absence of control. The infusion rate, although being a known risk factor for thrombophlebitis, was frequently not controlled. There is also no consensus on what is considered an “acceptable” rate of thrombophlebitis or an acceptable duration of infusion before phlebitis occurrence. All these factors are probably responsible for the discordance of the results in these studies. Therefore, there is an urgent need to undertake studies with proper methods, notably with a reasonable estimation of osmolality, either by measuring PN solutions or by using accurate approximations such as those provided by our predictive model. The predictive performance of such a model should be properly validated before it is used in routine practice or clinical studies.
Conclusion Since parenteral feeding cannot be avoided in many cases, it has to be as safe as possible. Factors to be improved include osmolality, because it is an important cause of complications when infusion solution is delivered. This study confirmed that theoretical osmolarity and other approximations of osmolarity severely underestimate osmolality in many cases and should not be used as references to estimate it. Other equations, especially those obtained by linear multivariate analysis, are not
reliable if they are not used in strict accordance with the practice of their authors in terms of preparing PN solutions. Equations issued from the literature may not be suitable in all settings, due to differences in qualitative and quantitative composition of PN solutions depending on local production practice or patients’ needs. These equations also do not take into account the nonlinear relationship between concentration and osmolality in major, critical components such as glucose, and they are expected to be inaccurate. The experimental model we proposed here is simple and efficient, including in highly concentrated PN solutions. In addition to its predictive performance, the interest of our model lies in the method we followed to develop it, which is easily reproducible in any care setting, allowing one to individualize the model to local practices. Such a model can be used by clinicians as a helpful tool for secured PN prescription and access choice or by pharmacists to obtain a reliable reference value for the quality control of PN solutions. The clinical significance of underestimating osmolality still needs to be investigated, but it is reasonable to think that controlling the osmotic strength of PN solutions is a major issue to be considered in optimizing PN safety. Based on our results, theoretical osmolarity up to 1000 mOsm/L allows one to obtain actual osmolality
![[Should pediatric parenteral nutrition be individualized?].](/assets/img/hold.png)
