Kahar Method: A Novel Calculation Method of Tonicity Adjustment.

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. Copyright:

Introduction

The parenteral drug formulation should be in isotonic drug condition to avoid cells and local tissues damaged in the body.[1234] The isotonic state is described as freezing point depression of blood at –0.52°C or 0.9% of NaCl in aqueous solution.[56] 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).[2789] 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.[111213]

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.[1617] 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.[1819]

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.[2425262728]

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

Ingredient data

Formula 1
Ingredient name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆Tf	(Cb – C%)	Previous preparation status
Ephedrine HCl	5	50	0.16	8	5	0.8		Hypertonic
Total	8		0.8000
Formula 5
Ingredient name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆Tf	(Cb – C%)	Previous preparation status
Nikethamide	25	250	0.1	25	25	2.5		Hypertonic
Total	25		2.5000
Formula 29
Ingredient name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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 name	C%	Qty (g or mL)	∆Tf	Qty × ∆Tf	Cb	Cb × ∆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

C% = ingredient concentration, Qty = ingredient quantity (gram or mL), ∆Tf = freezing point depression, C = the concentration of ingredients that produce isotonic preparations (calculated using Kahar method), C – C% = to see how much changes in the ingredient concentration needed to produce isotonic preparations

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,[313] 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.[1516171819]

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.[1234] 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

or

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 (C) of the material with the previous equation, , so:

Equation 6

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:

Equation 7

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 (V).

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:

then

or Vi=1.92Vo[∑(C×ΔTf)]      Equation 9

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

then      Equation 10

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

Equation 11

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.

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

No.	Material name	C (%)	Qty (g or mL)	∆Tf (°C)	E (1%)	Qty × ∆Tf	Qty × E (1%)	C (%) × ∆Tf
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: V=192[∑(Qty×Δ Tf)]

V=192[(0.005)]=0.96mL

Equation 9: V=1.92Vo[∑(C×Δ Tf)]

=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 (V) = 1000 – 0.96 mL = 999.04 mL. The next step was to calculate the volume of the solvent (V) that had been isotonized by the additive by using Equation 8 or 9.

Equation 8: V=192[∑(Qty×Δ Tf)]

V=192[(4.436)]=851.712mL

Before calculating V 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: V=1.92Vo[∑(C×Δ Tf)]

=1.92(999.04mL)[(0.44403)]=851.712mL

The isotonic volume (V) 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

No.	Ingredient name	C (%)	E1%	C (%) × E1%
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

No.	Ingredient name	C (%)	BE	mEq/L
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%or

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

Problems	Kahar method	White–Vincent method	Cryoscopic method	NaCl equivalent method	mEq method
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

Method	Kahar	White–Vincent	Cryoscopic	NaCl equivalent	mEq
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

No.	Hypotonic formula	Salt needed (g)
		Kahar	White–Vincent	Cryoscopic	NaCl equivalent	mEq
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.[32333435] 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

Cronbach α	Cronbach α based on standardized items	No. of items
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

No.	Formula	Kahar	White–Vincent
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

	Correlation between vectors of values
	Kahar method	White–Vincent method
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

Cronbach α	Cronbach α based on standardized items	No. of items
0.999	1	2

Figure 1

Calculation of isotonic volume of Kahar method (red) and White–Vincent (blue) method

Figure 2

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.