Journal of Pharmacy And Bioallied Sciences

: 2019  |  Volume : 11  |  Issue : 8  |  Page : 635--649

Kahar method: A novel calculation method of tonicity adjustment

Abd. K Umar1, Nasrul Wathoni1, Aliya N Hasanah2, Insan S Kurniawansyah1, Marline Abdassah1,  
1 Department of Pharmaceutics and Pharmaceutical Technology, Faculty of Pharmacy, Universitas Padjadjaran, Sumedang, Indonesia
2 Department of Pharmaceutical Analysis and Medicinal Chemistry, Faculty of Pharmacy, Universitas Padjadjaran, Sumedang, Indonesia

Correspondence Address:
Abd. K Umar
Department of Pharmaceutics and Pharmaceutical Technology, Faculty of Pharmacy, Universitas Padjadjaran, Sumedang, 45363.


Background: Hypertonic and hypotonic conditions in pharmaceutical preparations decrease the drug’s absorption and bioavailability. In addition, it can cause tissue damage. There are several calculation methods to regulate hypotonic preparations. However, there are no methods that can be used to regulate hypertonic preparations without causing dose-dividing problem. Objective: This study aimed to develop a new calculation using basic principle of freezing point depression method (cryoscopic) that can solve hypotonic and hypertonic problems, especially for hypertonic preparations through reducing the levels of additional ingredients. Methods: The calculation of Kahar method was successfully obtained by substitution and simplification in the basic principle equation of cryoscopic method, and then evaluated by resolving the problems in 42 sterile formula preparations and compared with White–Vincent method, cryoscopic method, equivalent NaCl method, and milliequivalent method through the analysis of its similarity and reliability. Results: The results of similarity analysis between Kahar method and other methods showed good similarity values with more than 0.880. Kahar method and cryoscopic method have the highest similarity of the calculation result with a similarity value of 1. The reliability analysis obtained very good result with Cronbach α = 0.990. Conclusions: These results suggest that Kahar method provides reliable equation with complete and efficient solution to hypotonic and hypertonic problems.

How to cite this article:
Umar AK, Wathoni N, Hasanah AN, Kurniawansyah IS, Abdassah M. Kahar method: A novel calculation method of tonicity adjustment.J Pharm Bioall Sci 2019;11:635-649

How to cite this URL:
Umar AK, Wathoni N, Hasanah AN, Kurniawansyah IS, Abdassah M. Kahar method: A novel calculation method of tonicity adjustment. J Pharm Bioall Sci [serial online] 2019 [cited 2022 Jun 25 ];11:635-649
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The parenteral drug formulation should be in isotonic drug condition to avoid cells and local tissues damaged in the body.[1],[2],[3],[4] The isotonic state is described as freezing point depression of blood at –0.52°C or 0.9% of NaCl in aqueous solution.[5],[6] The blood cells will swell or even rupture when the hypotonic solution (<0.9% of NaCl in liquid solution) is injected intravenously, whereas the cells can be shrunk in a hypertonic solution (>0.9% of NaCl in liquid solution).[2],[7],[8],[9] The previous study confirmed that the hypotonic and hypertonic nasal spray of salmon calcitonin significantly decreased the bioavailability of calcitonin compared to its isotonic preparation.[10] In addition, ophthalmic hypertonic preparations of hyaluronic acid increased the osmolarity of the tears, which may reduce drug absorption and drug contact time in the eye, whereas the hypotonic preparation reduced the post-lens tear volume and thus can induce stuck lens syndrome and corneal irritation.[11],[12],[13]

Nowadays, there are several methods that can be used for tonicity adjustments, such as cryoscopic method, NaCl equivalent method, White–Vincent method, Sprowls method, and milliequivalent method.[14] The cryoscopic method uses the freezing point depression to adjust the tonicity. This method is used to calculate how much salt is needed to obtain isotonic preparation from hypotonic preparation.[15] The NaCl equivalent method is defined as the number of grams of NaCl equivalent to 1g of certain material. The White–Vincent method uses the NaCl equivalent value of the material to obtain isotonic volume by multiplying the mass of the material and its NaCl equivalent value by 111.1 as a constant.[7] The Sprowls method, a modified method of the White–Vincent method, calculates the isotonic volume by using fixed mass of the material.[16],[17] The milliequivalent method is similar to the NaCl equivalent method in which the ingredient mixture must be equal to 0.9% of NaCl content in mEq/L.[18],[19]

The aforementioned method is generally used to solve hypotonic problems. However, several studies have shown that hypertonic solutions can cause moderate pain to cramps.[20] Weiss and Weiss[21] reported that 23.4% of their patients when administered with hypertonic solutions felt pain less than 5min after administration. Chou et al.[22] also reported that 16% of their 310 patients were unable to withstand pain after being given a hypertonic solution.

The adjustment of hypertonic to isotonic preparations can be carried out by diluting the solutions until the value of isotonic volume. However, these methods can influence the number of drug doses.[8] Of the five methods, only White–Vincent method and the Sprowls method can be used to calculate the isotonic volume. The other methods have limited application to calculate the amount of salt so they can not be used in adjusting the hypertonic preparations. Moreover, the addition of salt to adjust tonicity can disrupt the stability of the preparation by changing the potential zeta system, especially in the parenteral preparations of suspension and emulsion.[23] Therefore, for solving hypertonic problems, it is necessary to find a new method that can regulate the level of additives that are suitable to produce an isotonic preparation.

In this study, we developed the method of tonicity adjustment, which is not only able to calculate the amount of salt needed and its isotonic volume, but also able to calculate the level of the appropriate ingredients without changing the dose of the active substance. This method will help to solve hypertonic problems. In addition, with this method, we do not need to use an isotonic agent.

 Materials and Methods

Determination of Kahar method equation

To develop equation of Kahar method, we used a basic principle of freezing point depression method (cryoscopic) because the value of freezing point depression of the material is accurate, easier, and faster to observe.[24],[25],[26],[27],[28]

Determination of sample formulas

The sample used was a collection of sterile formulas from the Handbook of Pharmaceutical Manufacturing Formulations: Sterile Products.[29] The number of samples used were as many as 42 formulas that had data values of freezing point depression and the value of NaCl equivalent on each material in the formula. The number of samples used had fulfilled the requirements of the cooperation test with the minimum number of samples being 29.[30] The formulas can be seen in the [Table 1].{Table 1}

Application and comparison of Kahar method

Calculation comparison

To create an isotonic preparation, one formula of samples has been selected as an example to explain how Kahar method was applied for determining the amounts of appropriate volume (solution 1), salt needed (solution 2), and appropriate ingredient contents (solution 3). The following are several methods as comparative methods for solution 1 and solution 2 given by Kahar method.

Determining the amounts of appropriate volume (solution 1)

The White–Vincent equation adjusts tonicity by adjusting water volume,[3],[13] with the following equation:


where V is an isotonic volume in mL, W is ingredient weight, and E-NaCl is NaCl equivalent value of ingredient.[7]

Determining the appropriate amounts of salt (solution 2)

Cryoscopic method: Cryoscopic method is used to determine the amount of salt for adjusting isotonic condition.[15],[16],[17],[18],[19]


where W value is required salt content (g/100mL), α value is the sum of multiplication result between ingredient concentration and freezing point depression value [Σ (C% × ΔTf)], and b value is freezing point depression of NaCl at 1%.[15]

NaCl equivalent method: This method is used to obtain the required amount of salt by using the following equation:


The W value is the required salt concentration, E1% is NaCl equivalent value of the material, whereas C% is ingredient concentration.[15]

Milliequivalent Method: The basic principle of this method is similar to the NaCl equivalent method in which the ingredient mixture must be equal to 0.9% of NaCl content in mEq/L. To convert the concentration of the material to mEq/L, we can use the equivalent weight value (BE) by the following equation:


If the total concentration (mEq/L) of the material is denoted by a and the amount of NaCl concentration (mEq/L) that needs to be added is denoted by b, then we can use the following equation:


Determining the appropriate amounts of ingredient (solution 3)

The appropriate amount for each additional ingredient was determined by using Kahar method. The efficiency was measured by observing and comparing the number of steps and how many solutions were given in the calculation of tonicity adjustments to get the final results from Kahar, White–Vincent, cryoscopic, NaCl equivalence, and milliequivalence methods. Data were statistically analyzed by using the Statistical Package for the Social Sciences (SPSS) software, version 22 (IBM Corporation, New York). The validation parameters were observed by similarity and reliability.

 Results and Discussion

Determination of Kahar method equations

The development of Kahar method was based on the theory of freezing point depression because the value of freezing point depression was easy and fast to determine, and accurate.[1],[2],[3],[4] It was accurate because calculating the freezing point depression from a liquid solution with 1 molal base showed a value close to the theoretical value, and the more dilute the solution, the more similar the results between the experiment and the theoretical value.[24]

The method used in the preparation of Kahar method equation was substitution, where the basic principle equation of cryoscopic method was substituted with other equations to get the desired form of the equation. The concentration of the material in percent weight per volume (% wt/vol) or volume per volume (% vol/vol) shows the amount of substance (Qty) presented in 100mL of the total volume of the mixture. The amount of the substance can be in units of grams or milliliters, depending on the form of the substance. If the substance content is symbolized by the letter C, then


If the volume of the mixture is not equal to 100mL, the way to find the concentration of a material is as follows:


In isotonic preparation, the value of freezing point depression of total ingredients should equal to the value of NaCl freezing point depression, 0.52oC. Below is the basic equation used to develop kahar method based on freezing point depression method (cryoscopic).


The first substitution is carried out by replacing the concentration value (Cn) of the material with the


This is carried out to enter the variable volume (V) into the equation, which will be used to obtain isotonic volume.

Because the ingredients are in the same mixture, all ingredients are concentrated in the same amount of volume. Therefore, the form of Equation 6 can be simplified into the following:


As Equation 7 was equal to the value of the freezing point depression of NaCl, the volume of the mixture (V) in Equation 7 was considered as the isotonic volume (Vi).


If the concentration of the material is known and the mass is unknown, then Equation 8 can be changed to the following equation:


Suppose the volume of the preparations is Vo and the content of the materials for isotonizing Vo is Cb. We can adjust the material content (Cb) by equating it with the content of the preceding material (Ci), which has been already isotonized by a number of solvents (Vi) as the following:


The substitution of the value of Vi in Equation 9 into Equation 10 gives the following equation:


The development of Kahar method equation has produced four core equations, which are able to calculate tonicity adjustment. The four core equations are Equations 8–11. Equations 8 and 9 can be used to calculate the isotonic volume of the solution. Equation 8 used the amount of material in gram or milliliter, whereas Equation 9 used the amount of material in concentration form (% b/vol or % vol/vol). These equations were compared with White–Vincent method to observe the similarity of calculation results of isotonic volume. In addition, Equations 10 and 11 were used to adjust the increasing or decreasing material contents based on the needs of its tonicity. Equation 10 was particularly useful if there were several ingredients whose content or dosage should not be altered as it affected the efficacy of the therapy. Therefore, Equation 10 adjusted the level of several materials and some others remain with the previous levels. Equation 11 was used to change all materials’ content. Surely, Equation 11 applied only to active substances, which had a wide range of therapies dosage.

Application and comparison of Kahar method

Calculation of comparison

To investigate the number of stages used in obtaining the final results of the calculations and to solve the problems in the tonicity adjustment, we compared the existing tonicity adjustment methods with Kahar method. [Table 2] showed that the formula 1 discussion as an example. Formula 1 was hypotonic that can be used as an example for an explanation and comparison of the calculation results of salt additions and volume setting, and it also described how tonicity adjustment was by regulating the levels of additional ingredients both in hypotonic and hypertonic preparations by using the same equation, namely Equation 10 or 11.{Table 2}

Completion of formula 1:

Kahar method

Solution 1: Volume adjustment.


From this calculation, the isotonic volume as much as 852.672mL of 1000mL can be obtained. However, this method will usually be difficult in the distribution of the administered dose. As dividing doses with a volume that is not round will produce a non-round dose too, of course, doses that have decimal number will be difficult to adjust, for example, those administered through syringe.

On the basis of the problem of dividing doses aforementioned, solution 2 and solution 3 are better used to solve the problem.

Solution 2: Salt addition

From solution 1, we already know the amount of volume that was isotonic. So the volume that was not isotonic yet = 1000 – 852.672mL = 147.328mL.


Solution 3: Adjustment of ingredients

Levels of active substances need not be changed so that the therapeutic dose was not disturbed. The adjusted ingredients were additional ingredients only. The first thing to do was to calculate the amount of solvent that has been isotonized by active substances by using Equation 8 or 9.


It can be observed that the volume of solvents, which was isotonized by active substances, was only 0.96 of 1000mL total volume. Volume that was not isotonic yet (Vo) = 1000 – 0.96mL = 999.04mL. The next step was to calculate the volume of the solvent (Vi) that had been isotonized by the additive by using Equation 8 or 9.


Before calculating Vi using Equation 9, we must recalculate the concentration of each additive materials in the remaining non-isotonic volume (999.04mL) using the weight used for 1L [Table 2] so that the value [∑C × ∆Tf] of the additive materials was 0.44403.


The isotonic volume (Vi) by additive materials was as much as 851.712mL. The final step was to adjust the content of each additional ingredients by using Equation 10.


The results of the aforementioned calculations indicated that the level of additional ingredients should be used in order for the preparation to reach isotonic state. To test the results of the adjustment of the aforementioned ingredients, it was necessary to compare with the NaCl equality. Here was the multiplication of the ingredients’ content with the value of the freezing point depression.

Atropine sulfate: 0.05 × 0.01 = 0.0005

Sodium acetate: 0.141 × 0.26 = 0.0367

Sodium chloride: 0.764 × 0.576 = 0.4401

Sodium metabisulfite: 0.1174 × 0.38 = 0.0446


White–Vincent method

This method was used to investigate the conformity of calculation result of volume adjustment (solution 1) from Kahar method.

The completion of formula 1 by using the White–Vincent method:


After an isotonic volume was known, the calculation of the amount of salt was required where the volume of the isotonic solvent = 1000 – 865.136mL = 134.864mL. Then the amount of salt needed was calculated as follows:


Cryoscopic method

This method was used to investigate the conformity of the calculated result of salt addition (solution 2) from Kahar method.

The following amount of salt addition was required in formula 1.


NaCl equivalent method

The NaCl equivalent method is defined as the number of grams of NaCl equivalent to 1g of a particular substance. [Table 3] simplifies to shorten the calculation.{Table 3}

From [Table 3], we obtained the value of Σ (E1% × C%) as much as 0.7787%, then, entered the value into the equation to get the required NaCl concentration to make the preparation isotonic.


Milliequivalent (mEq) method

To complete the calculation of salt addition in the sample formula in [Table 2], we required the value of molecular weight and ion valence of each material as mentioned in the equation. Equivalent weight of each material can be seen in [Table 4]. [Table 4] also shows the total value of mEq/L of all material and symbolized as “α”.{Table 4}

Next, we just enter the value α that had been obtained as 137.7 mEq/L into the equation.


After obtaining the concentration of NaCl (mEq/L) that was required to be added, we converted it to concentration (%wt/vol) as follows:


Comparison of efficiency for use of each method

Kahar method is easier and faster to use because it does not need to change the amount of material into its concentration form osr vice versa, Kahar method has Equation 8, which can directly use the amount of material in grams or milliliters into its calculation so that its calculation stages are shorter. It also provides more complete solutions in tonicity adjustment than other methods. [Table 5] shows the advantages of Kahar method in providing tonicity adjustment solutions.{Table 5}

In [Table 6], it can be seen that all four methods except the milliequivalent method have high similarity in the results. Calculation result between milliequivalent method and another methods was quite significantly different. However, the advantage of milliequivalent method was using the molecular weight of the material whose data was very easy to find, in contrast to the freezing point depression and equivalent value of NaCl, which was still limited to certain compounds that are known.{Table 6}

Statistical analysis of calculation results using Statistical Package for the Social Sciences software

Of the 42 tested formulas, 17 formulas required salt addition. The similarity test was performed by using Pearson principle, and reliability test by using Cronbach α principle. The Pearson principle shows how well the relationship between the two variables can be described in a linear function.[31] The Cronbach α principle is a function of the extent to which items in tests have high commonality with low data differences.[32] In addition, Cronbach α also shows how close the values are at the time of repeating the measurements.[33] The calculation result of salt addition can be seen in the [Table 7]. From the data, the value of similarity and reliability obtained was as follows:{Table 7}

On the basis of [Table 6], it can be observed that the correlation between Kahar method and other methods was above 0.7, where the acceptable value must be more than 0.7–1. The closer to 1, its correlation value, the more similar to the data.[32],[33],[34],[35] The most similar method with Kahar method was the cryoscopic method with a similarity value of 1.000. In addition, the White–Vincent method and the NaCl equivalent method also had high similarity value.

The milliequivalent method had the lowest similarity of 0.881 for Kahar method, 0.882 for cryoscopic method, and 0.888 for the White–Vincent method and the NaCl equivalent method. This value indicated that milliequivalent method was different from other methods because it was the most significant compared to other methods.

[Table 8] shows the reliability of Kahar method with Cronbach α value of 0.990, which means that the repetition of calculations from Kahar method would still produce the same result with other method calculations used as the comparison.{Table 8}

The cryoscopic method and the NaCl equivalent method are only limited to the tonicity adjustment through the salt addition, so it cannot be used to adjust the hypertonic preparation. Meanwhile, those who can count isotonic volume amount are only White–Vincent method and Sprowls method. Later, the comparison of isotonic volume calculation of 42 formulas is only performed between Kahar method and White–Vincent method, the result of which can be seen in [Table 9].{Table 9}

On the basis of [Table 10] and [Table 11], it can be observed that the value of correlation and Cronbach α value between Kahar method and White–Vincent method is 0.999, so it can be said that the results of both calculations are similar, and Kahar method will still produce the same result with White–Vincent method.[33] The greater the collation between values of a data, the greater the alpha value.[32] The graphs in [Figure 1] and [Figure 2] showed the similarity of the calculated data.{Table 10}, {Table 11}, {Figure 1}, {Figure 2}

On the basis of test results, it was found that Kahar method gave the same results as other methods, which was evidenced by the value of similarity and reliability close to 1.

The adjustment result of the ingredient content and preparation volume by using Kahar method also produced isotonic formula, and it was proven by comparing it to the freezing point depression value of NaCl.

Financial support and sponsorship

This work was supported by the Academic Leadership Grants (ALG) 2019, Universitas Padjadjaran (1373k/UN6.O/LT/2019), Indonesia.

Conflicts of interest

There are no conflicts of interest.


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