J Pharm Bioallied Sci. 2019 Dec; 11(Suppl 4): S635–S649. 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. 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. 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. 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. These results suggest that Kahar method provides reliable equation with complete and efficient
solution to hypotonic and hypertonic problems. Keywords:Content adjustment, hypertonic preparations, Kahar method, tonicity adjustment 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. 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] 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]. Ingredient data
Abstract
Background:
Objective:
Methods:
Results:
Conclusions:
Introduction
Materials and Methods
Determination of Kahar method equation
Determination of sample formulas
Table
1
Formula 1 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb
– C%)Previous preparation status Atropine sulfate USP
0.05
0.5
0.01
0.005
0.05
0.0005
Hypotonic
Sodium acetate
0.12
1.2
0.26
0.312
0.1408
0.0366
0.0208
Sodium chloride
0.65
6.5
0.576
3.744
0.7624
0.4392
0.1124
Sodium metabisulfite
0.1
1
0.38
0.38
0.1173
0.0446
0.0173
Total
4.441
0.5208
Formula 2 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Lidocaine HCl
1
10
0.12
1.2
1
0.12
Hypertonic
Sodium chloride
0.6
6
0.576
3.456
0.5945
0.3424
0.0055
Citric acid
0.02
0.2
0.09
0.018
0.0198
0.0018
0.0002
Sodium metabisulfite
0.15
1.5
0.38
0.57
0.1486
0.0565
0.0014
Epinephrine HCl
0.001
0.01
0.16
0.0016
0.0010
0.0002
0.0000
Total
5.2456
0.5208
Formula 3 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Menadione sodium bisulfite
0.5
5
0.11
0.55
0.5
0.055
Hypertonic
Sodium bisulfite
2
20
0.35
7
1.1793
0.4128
0.8207
Benzyl alcohol
1
10
0.09
0.9
0.5897
0.0531
0.4103
Total
8.45
0.5208
Formula 4 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Ephedrine HCl
5
50
0.16
8
5
0.8
Hypertonic
Total
8
0.8000
Formula 5 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Doxycycline hyclate
2.5
25
0.07
1.75
2.5
0.175
Hypertonic
Mannitol
7.5
75
0.09
6.75
1.3833
0.1245
6.1167
Ascorbic acid
12
120
0.1
12
2.2133
0.2213
9.7867
Total
20.5
0.5208
Formula 6 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Amikacin, USP
5
50
0.03
1.5
5
0.15
Hypotonic
Sodium citrate
0.57
5.7
0.17
0.969
2.0074
0.3413
1.4374
Sodium metabisulfite
0.12
1.2
0.07
0.084
0.4226
0.0296
0.3026
Total
2.553
0.5208
Formula 7 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Aminophylline, USP
5
50
0.03
1.5
5
0.15
Hypotonic
Total
1.5
0.1500
Formula 8 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Ascorbic acid
30
300
0.1
30
30
3
Hypertonic
Sodium bisulfite, USP
0.1
1
0.35
0.35
–1.4583
–0.5104
1.5583
Benzyl alcohol, NF
1.5
15
0.09
1.35
–21.8750
–1.9688
23.3750
Total
31.7
0.5208
Formula 9 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Benztropine mesylate
0.1
1
0.11
0.11
0.1
0.011
Hypotonic
Total
0.11
0.0110
Formula 10 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Bethanechol chloride
0.515
5.15
0.22
1.133
0.515
0.1133
Hypotonic
Total
1.133
0.1133
Formula 11 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Bretylium tosylate
0.4
4
0.08
0.32
0.4
0.032
Hypertonic
Dextrose anhydrous, USP
5
50
0.1
5
4.8883
0.4888
0.1117
Total
5.32
0.5208
Formula 12 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Bupivacaine hydrochloride
0.75
7.5
0.09
0.675
0.75
0.0675
Hypertonic
Dextrose anhydrous, USP
8.25
82.5
0.1
8.25
4.5333
0.4533
3.7167
Total
8.925
0.5208
Formula 13 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Cefazolin
2
20
0.07
1.4
2
0.14
Hypotonic
Dextrose hydrous, USP
4
40
0.09
3.6
4.2315
0.3808
0.2315
Total
5
0.5208
Formula 14 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Cefotaxime
2
20
0.08
1.6
2
0.16
Hypotonic
Dextrose hydrous, USP
3.4
34
0.09
3.06
4.0093
0.3608
0.6093
Total
4.66
0.5208
Formula 15 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Ceftriaxone sodium
2
20
0.07
1.4
2
0.14
Hypotonic
Dextrose hydrous, USP
4
40
0.09
3.6
4.2315
0.3808
0.2315
Total
5
0.5208
Formula 16 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Cefuroxime sodium
1.5
15
0.07
1.05
1.5
0.105
Hypertonic
Dextrose hydrous, USP
2.8
28
0.09
2.52
0.2176
0.0196
2.5824
Sodium citrate hydrous
30
300
0.17
51
2.3309
0.3963
27.6691
Total
54.57
0.5208
Formula 17 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Chlorpromazine hydrochloride
1
10
0.07
0.7
1
0.07
Hypotonic
Ascorbic acid, USP
0.2
2
0.09
0.18
5.0093
0.4508
4.8093
Total
0.88
0.5208
Formula 18 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Clindamycin phosphate equivalent
30
300
0.04
12
30
1.2
Hypertonic
Dextrose anhydrous, USP
5
50
0.1
5
–6.7846
–0.6785
11.7846
Disodium edetate
0.004
0.04
0.13
0.0052
–0.0054
–0.0007
0.0094
Total
17.0052
0.5208
Formula 19 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Cromolyn sodium
0.4
4
0.08
0.32
0.4
0.032
Hypotonic
Benzalkonium chloride
0.01
0.1
0.09
0.009
0.3517
0.0317
0.3417
Disodium edetate
0.1
1
0.13
0.13
3.5168
0.4572
3.4168
Total
0.459
0.5208
Formula 20 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Promethazine hydrochloride
2.5
25
0.11
2.75
2.5
0.275
Hypotonic
Sodium bisulfite
0.025
0.25
0.35
0.0875
0.0592
0.0207
0.0342
Phenol, USP
0.5
5
0.19
0.95
1.1847
0.2251
0.6847
Total
3.7875
0.5208
Formula 21 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Doxapram hydrochloride
2
20
0.07
1.4
2
0.14
Hypotonic
Benzyl alcohol
0.9
9
0.09
0.81
4.2315
0.3808
3.3315
Total
2.21
0.5208
Formula 22 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Ephedrine sulfate, USP
5
50
0.13
6.5
5
0.65
Hypertonic
Total
6.5
0.6500
Formula 23 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Lincomycin hydrochloride
37.975
379.75
0.09
34.1775
37.975
3.41775
Hypertonic
Benzyl alcohol
0.945
9.45
0.09
0.8505
–32.1880
–2.8969
33.1330
Total
35.028
0.5208
Formula 24 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Magnesium sulfate, USP
50
500
0.09
45
50
4.5
Hypertonic
Phenol, USP
0.2
2
0.19
0.38
–20.9430
–3.9792
21.1430
Total
45.38
0.5208
Formula 25 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Menadione sodium bisulfite
5
50
0.11
5.5
5
0.55
Hypertonic
Sodium bisulfite
1
10
0.35
3.5
–0.0663
–0.0232
1.0663
Benzyl alcohol
1
10
0.09
0.9
–0.0663
–0.0060
1.0663
Total
9.9
0.5208
Formula 26 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Mepivacaine hydrochloride
0.1
1
0.11
0.11
0.1
0.011
Hypotonic
Sodium chloride
0.65
6.5
0.576
3.744
0.8274
0.476608
0.1774
Potassium chloride
0.03
0.3
0.43
0.129
0.0382
0.016422
0.0082
Calcium chloride
0.033
0.33
0.4
0.132
0.0420
0.016803
0.0090
Total
4.115
0.5208
Formula 27 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Naloxone hydrochloride
0.002
0.02
0.08
0.0016
0.002
0.00016
Hypotonic
Sodium chloride
0.9
9
0.576
5.184
0.9039
0.5207
0.0039
Total
5.1856
0.5208
Formula 28 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Nikethamide
25
250
0.1
25
25
2.5
Hypertonic
Total
25
2.5000
Formula 29 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Pentobarbital Sodium
5
50
0.14
7
5
0.7
Hypertonic
Propylene glycol
0.04
0.4
0.25
0.1
–0.5231
–0.1308
0.5631
Alcohol, USP
0.01
0.1
0.37
0.037
–0.1308
–0.0484
0.1408
Total
7.137
0.5208
Formula 30 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Phenylbutazone sodium
20
200
0.1
20
20
2
Hypertonic
Benzyl alcohol, NF
1.5
15
0.09
1.35
–16.4352
–1.4792
17.9352
Total
21.35
0.5208
Formula 31 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Quinidine sulfate
87.713
877.13
0.1
87.713
87.713
8.7713
Hypertonic
Propylene glycol, USP (QS to 1L)
19
190
0.25
47.5
–33.0019
–8.2505
52.0019
Total
135.213
0.5208
Formula 32 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Ranitidine hydrochloride
0.5
5
0.1
0.5
0.5
0.05
Hypotonic
Sodium chloride
0.45
4.5
0.576
2.592
0.6944
0.4
0.2444
Citric acid
0.03
0.3
0.09
0.027
0.0463
0.0042
0.0163
Dibasic sodium phosphate
0.18
1.8
0.24
0.432
0.2778
0.0667
0.0978
Total
3.551
0.5208
Formula 33 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Sodium bicarbonate, USP
4
40
0.38
15.2
4
1.52
Hypertonic
Disodium edetate, USP
0.2214
2.214
0.13
0.28782
–7.6859
–0.9992
7.9073
Total
15.48782
0.5208
Formula 34 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Sodium chloride, USP
0.9
9
0.576
5.184
0.9
0.5184
Hypertonic
Benzyl alcohol, NF
2
20
0.09
1.8
0.0270
0.0024
1.9730
Total
6.984
0.5208
Formula 35 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Calcium chloride dihydrate
0.027
0.27
0.29
0.0783
0.027
0.00783
Hypotonic
Potassium chloride
0.04
0.4
0.43
0.172
0.0445
0.019137
0.0045
Sodium chloride
0.6
6
0.576
3.456
0.6676
0.3845
0.0676
Sodium lactate
0.317
3.17
0.31
0.9827
0.3527
0.1093
0.0357
Total
4.689
0.5208
Formula 36 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Sodium thiosulfate
27.5
275
0.18
49.5
27.5
4.95
Hypertonic
Total
49.5
4.9500
Formula 37 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Streptomycin sulfate
40
400
0.03
12
40
1.2
Hypertonic
Sodium citrate
1.2
12
0.17
2.04
–2.8152
–0.47858
4.0152
Phenol liquefied
0.25
2.5
0.19
0.475
–0.5865
–0.1114
0.8365
Sodium metabisulfite
0.1
1
0.38
0.38
–0.2346
–0.0891
0.3346
Total
14.895
0.5208
Formula 38 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Succinylcholine chloride, USP
5
50
0.11
5.5
5
0.55
Hypertonic
Total
5.5
0.5500
Formula 39 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Theophylline Sodium glycinate
0.04
0.4
0.18
0.072
0.04
0.0072
Hypertonic
Dextrose, USP
5
50
0.43
21.5
1.1945
0.5136
3.8055
Total
21.572
0.5208
Formula 40 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Thiotepa
1.5
15
0.09
1.35
1.5
0.135
Hypotonic
Sodium carbonate, anhydrate
0.2
2
0.4
0.8
0.9646
0.3858
0.7646
Total
2.15
0.5208
Formula 41 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Triflupromazine hydrochloride
1.08
10.8
0.05
0.54
1.08
0.054
Hypotonic
Benzyl alcohol, NF
1.5
15
0.09
1.35
2.0454
0.1841
0.5454
Sodium chloride
0.36
3.6
0.576
2.0736
0.4909
0.2828
0.1309
Total
3.9636
0.5208
Formula 42 Ingredient nameC%Qty (g or mL)∆TfQty × ∆TfCbCb × ∆Tf(Cb – C%)Previous preparation status Vancomycin HCl, USP
0.1
1
0.02
0.02
0.1
0.002
Hypotonic
Total
0.02
0.0020
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:
V = [ Σ(W × E − NaCl)] Equation 1
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]
W% =(0.52−α)/b Equation 2
where W value is required salt content (g/100 mL), α value is the sum of multiplication result between ingredient concentration and freezing point depression value [∑ (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:
W = 0.9%−∑(E1% × C%) Equation 3
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:
mEq / L = (C×10,000)/BE Equation 4
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:
b=308−a Equation 5
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 100 mL 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 100 mL, 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 Content of Material × Δ Tf of Material) = The content of NaCl × Δ Tf of NaCl(C1 × Δ Tf1)+(Cn × Δ Tfn)= 0.52
The first substitution is carried out by replacing the concentration value (Cn) of the material with the previous equation,
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).
Vi = 192[∑(Qtyn×Δ TFn)] Equation 8
If the concentration of the material is known and the mass is unknown, then Equation 8 can be changed to the following equation:
or Vi=1.92Vo[∑(Cn×ΔTfn)] Equation 9
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
Atropine sulfate formula
1 | Atropine sulfate USP | 0.05 | 0.5 | 0.01 | 0.13 | 0.005 | 0.065 | 0.0005 |
2 | Sodium acetate | 0.12 | 1.2 | 0.26 | 0.46 | 0.312 | 0.552 | 0.0312 |
3 | Sodium chloride | 0.65 | 6.5 | 0.576 | 1 | 3.744 | 6.5 | 0.3744 |
4 | Sodium metabisulfite | 0.1 | 1 | 0.38 | 0.67 | 0.38 | 0.67 | 0.038 |
5 | Water for injection USP | QS | QS to 1 L | - | - | - | - | - |
Total | 4.441 | 7.787 | 0.4441 |
Completion of formula 1:
Kahar method
Solution 1: Volume adjustment.
Equation 8: Vi=192[∑(Qty×Δ Tf)]
Vi=192[(4.441)]=852.672mL
Equation 9: Vi=1.92Vo[∑(C×Δ Tf)]
Vi=1.92(1000)[(0.4441)]=852.672 mL
From this calculation, the isotonic volume as much as 852.672 mL of 1000 mL 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 – 852.672 mL = 147.328 mL.
Salt needed =
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.
Equation 8: Vi=192[∑(Qty×Δ Tf)]
Vi=192[(0.005)]=0.96mL
Equation 9: Vi=1.92Vo[∑(C×Δ Tf)]
Vi=1.92(1000)[(0.0005)]=0.96 mL
It can be observed that the volume of solvents, which was isotonized by active substances, was only 0.96 of 1000 mL total volume. Volume that was not isotonic yet (Vo) = 1000 – 0.96 mL = 999.04 mL. 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.
Equation 8: Vi=192[∑(Qty×Δ Tf)]
Vi=192[(4.436)]=851.712mL
Before calculating Vi using Equation 9, we must recalculate the concentration of each additive materials in the remaining non-isotonic volume (999.04 mL) using the weight used for 1L [Table 2] so that the value [∑C × ∆Tf] of the additive materials was 0.44403.
Equation 9: Vi=1.92Vo[∑(C×Δ Tf)]
Vi=1.92(999.04mL)[(0.44403)]=851.712mL
The isotonic volume (Vi) by additive materials was as much as 851.712 mL. The final step was to adjust the content of each additional ingredients by using Equation 10.
Sodium Accetate;
Sodium Chloride;
Sodium Metabisulfite;
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
∑(The content of material × ΔTf of material = 0.0005+0.0367+0.4401+0.0446=0.5219
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:
V=[∑(W×ENaCl)]×111.1
V=[(0.5×0.13)+(1.2×0.46)+(6.5×1)+(1×0.67)]×111.1
V=[0.065+0.552+6.5+0.67]×111.1
V=[7.787]×111.1=865.136mL
After an isotonic volume was known, the calculation of the amount of salt was required where the volume of the isotonic solvent = 1000 – 865.136 mL = 134.864 mL. Then the amount of salt needed was calculated as follows:
Salt needed=
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
The NaCl equivalent value and the concentration of each material of atropine sulfate formula
1 | Atropine sulfate | 0.05 | 0.13 | 0.0065 |
2 | Sodium acetate | 0.12 | 0.46 | 0.0552 |
3 | Sodium chloride | 0.65 | 1 | 0.65 |
4 | Sodium metabisulfite | 0.1 | 0.67 | 0.067 |
Total | 0.7787 |
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.
W = 0.9% - ∑(E1%×C%)
W = 0.9% - 0.7787% = 0.1213%
W = 0.1213gram/100mL=1.213 gram/L
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
Equivalent weight and concentration (mEq/L) of each material of atropine sulfate formula
1 | Atropine sulfate | 0.05 | 347.42 | 1.44 |
2 | Sodium acetate | 0.12 | 82 | 14.63 |
3 | Sodium chloride | 0.65 | 58.5 | 111.11 |
4 | Sodium metabisulfite | 0.1 | 95.05 | 10.52 |
Total | 137.7 |
Next, we just enter the value α that had been obtained as 137.7 mEq/L into the equation.
b =308-a
b =308-137.7 = 170.3 mEq/L
After obtaining the concentration of NaCl (mEq/L) that was required to be added, we converted it to concentration (%wt/vol) as follows:
Salt needed=
Salt needed=0.497%
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
Advantages of Kahar method in providing tonicity adjustment solutions compared to other methods
Salt addition | √ | √ | √ | √ | √ |
Volume adjustment | √ | √ | - | - | - |
Ingredient adjustment | √ | - | - | - | - |
Gram or milliliter | √ | √ | - | - | - |
Concentration (% b/b or % b/v) | √ | - | √ | √ | √ |
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
Similarity matrix calculation of salt addition using the Statistical Package for the Social Sciences software
Kahar | 1.000 | 0.999 | 1.000 | 0.999 | 0.881 |
White–Vincent | 0.999 | 1.000 | 0.999 | 1.000 | 0.888 |
Cryoscopic | 1.000 | 0.999 | 1.000 | 0.999 | 0.882 |
NaCl equivalent | 0.999 | 1.000 | 0.999 | 1.000 | 0.888 |
mEq | 0.881 | 0.888 | 0.882 | 0.888 | 1.000 |
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
Comparison of the result of salt addition calculation
1 | Formula 1 | 1.326 | 1.214 | 1.318 | 1.213 | 4.976 |
2 | Formula 6 | 4.588 | 4.589 | 4.595 | 4.589 | 4.200 |
3 | Formula 9 | 8.810 | 8.790 | 8.837 | 8.790 | 8.928 |
4 | Formula 10 | 7.042 | 6.992 | 7.061 | 6.992 | 8.637 |
5 | Formula 13 | 0.360 | 0.001 | 0.347 | 0.000 | 0.530 |
6 | Formula 14 | 0.948 | 0.561 | 0.938 | 0.560 | 1.420 |
7 | Formula 15 | 0.360 | 0.001 | 0.347 | 0.000 | 1.149 |
8 | Formula 17 | 7.479 | 7.380 | 7.500 | 7.380 | 7.846 |
9 | Formula 19 | 8.207 | 8.194 | 8.231 | 8.194 | 8.009 |
10 | Formula 20 | 2.455 | 2.598 | 2.452 | 2.598 | 2.824 |
11 | Formula 21 | 5.181 | 5.070 | 5.191 | 5.070 | 5.160 |
12 | Formula 26 | 1.820 | 1.732 | 1.884 | 1.731 | 5.359 |
13 | Formula 32 | 2.864 | 2.791 | 2.863 | 2.790 | 5.458 |
14 | Formula 35 | 0.897 | 0.816 | 0.887 | 0.815 | 4.912 |
15 | Formula 40 | 5.285 | 5.200 | 5.295 | 5.200 | 5.581 |
16 | Formula 41 | 2.151 | 1.879 | 2.147 | 1.878 | 2.337 |
17 | Formula 42 | 8.965 | 8.950 | 8.993 | 8.950 | 8.980 |
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
Reliability statistics calculation of salt addition using the Statistical Package for the Social Sciences software
0.990 | 0.990 | 5 |
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
Comparison of the result of isotonic volume calculation
1 | Formula 42 | 3.84 | 5.555 |
2 | Formula 9 | 21.12 | 23.331 |
3 | Formula 19 | 88.128 | 89.5466 |
4 | Formula 17 | 168.96 | 179.982 |
5 | Formula 10 | 217.536 | 223.14435 |
6 | Formula 7 | 288 | 277.75 |
7 | Formula 40 | 412.8 | 422.18 |
8 | Formula 21 | 424.32 | 436.623 |
9 | Formula 6 | 490.176 | 490.0621 |
10 | Formula 32 | 681.792 | 689.931 |
11 | Formula 20 | 727.2 | 711.31775 |
12 | Formula 41 | 761.0112 | 791.2542 |
13 | Formula 26 | 801.1392 | 807.5859 |
14 | Formula 1 | 852.672 | 865.1357 |
15 | Formula 14 | 894.72 | 937.684 |
16 | Formula 35 | 900.288 | 909.37572 |
17 | Formula 13 | 960 | 999.9 |
18 | Formula 15 | 960 | 999.9 |
19 | Formula 27 | 995.6352 | 1,000.21108 |
20 | Formula 2 | 1,007.1552 | 1,026.99729 |
21 | Formula 11 | 1,021.44 | 1,062.116 |
22 | Formula 38 | 1,056 | 1,111 |
23 | Formula 22 | 1,248 | 1,277.65 |
24 | Formula 34 | 1,340.928 | 1,377.64 |
25 | Formula 29 | 1,370.304 | 1,415.0807 |
26 | Formula 4 | 1,536 | 1,666.5 |
27 | Formula 3 | 1,622.4 | 1,655.39 |
28 | Formula 12 | 1,713.6 | 1,791.4875 |
29 | Formula 25 | 1,900.8 | 1,977.58 |
30 | Formula 37 | 2,932.8 | 3,770.1785 |
31 | Formula 33 | 2,973.66144 | 2,945.174342 |
32 | Formula 18 | 3,264.9984 | 3,667.32212 |
33 | Formula 5 | 3,936 | 4,149.585 |
34 | Formula 30 | 4,099.2 | 4,282.905 |
35 | Formula 39 | 4,141.824 | 4,235.5764 |
36 | Formula 28 | 4,800 | 4,999.5 |
37 | Formula 8 | 6,086.4 | 6,350.476 |
38 | Formula 23 | 6,725.376 | 6,928.91815 |
39 | Formula 24 | 8,712.96 | 9,521.27 |
40 | Formula 36 | 9,504 | 9,471.275 |
41 | Formula 16 | 10,477.44 | 11,046.673 |
42 | Formula 31 | 25,960.896 | 26,617.71574 |
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 Figures 1 and 2 showed the similarity of the calculated data.
Table 10
Matrix similarity of isotonic volume calculation using the Statistical Package for the Social Sciences software
Kahar method | 1 | 0.999 |
White–Vincent method | 0.999 | 1 |
Table 11
Reliability of statistics calculation of isotonic volume using the Statistical Package for the Social Sciences software
0.999 | 1 | 2 |
Calculation of isotonic volume of Kahar method (red) and White–Vincent (blue) method
The linearity of Kahar method and White–Vincent method by using the Statistical Package for the Social Sciences software
Conclusion
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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