Aqueous suspensions

Abstract

To provide a technique for producing an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer.SOLUTION: In an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, by selecting a carboxyvinyl polymer having a viscosity retention ratio against salt of 18% or less measured under the conditions shown in the specification as the carboxyvinyl polymer, an increase in the particle size of suspension particles (brinzolamide and / or a salt thereof) in the aqueous suspension over time can be suppressed.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The present invention relates to an aqueous suspension comprising brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, which can inhibit the increase in particle size of suspended particles over time. [Background technology]

[0002] Brimonidine and its salts are known as adrenergic α2 receptor agonists, which have the effect of reducing intraocular pressure by inhibiting aqueous humor production and promoting the outflow of aqueous humor via the uveoscleral outflow pathway, and have traditionally been used to treat glaucoma and ocular hypertension.

[0003] Brinzolamide is also known as a carbonic anhydrase inhibitor, which has the effect of reducing intraocular pressure by suppressing the production of aqueous humor, and is used in the treatment of glaucoma.

[0004] In recent years, in order to enhance the therapeutic effects of glaucoma and ocular hypertension, preparations using brimonidine and / or a salt thereof in combination with brimonidine and / or a salt thereof and brinzolamide and / or a salt thereof have been proposed (e.g., Patent Documents 1 and 2).In addition, various formulations that aim to improve the stability and preservative effectiveness of preparations containing brimonidine and / or a salt thereof and brinzolamide and / or a salt thereof have also been reported (Patent Documents 2 to 5). [Prior art documents] [Patent documents]

[0005] [Patent Document 1] U.S. Patent No. 6,316,441 [Patent Document 2] U.S. Patent No. 6,247,430 [Patent Document 3] International Publication No. 2017 / 217450 [Patent Document 4] International Publication No. 2019 / 91596 [Patent Document 5] International Publication No. 2010 / 148190 Summary of the Invention [Problem to be solved by the invention]

[0006] The present invention provides a technology for producing an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer. [Means for solving the problem]

[0007] The present inventors have found that in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, by selecting a carboxyvinyl polymer having a salt viscosity retention rate of 18% or less as measured under the conditions described below, the increase over time in the particle size of suspended particles (brinzolamide and / or a salt thereof) in the aqueous suspension can be suppressed.

[0008] Furthermore, the present inventors have also found that in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, the redispersibility of suspended particles (brinzolamide and / or a salt thereof) in the aqueous suspension can be improved by selecting a carboxyvinyl polymer having a salt viscosity retention rate of 18% or less, as measured under the conditions described below.

[0009] The present invention was completed based on these findings and through further investigation.

[0010] That is, the present invention provides the following aqueous suspension as one embodiment. Item 1-1. Brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer are included, The aqueous suspension, wherein the carboxyvinyl polymer has a salt viscosity retention rate of 18% or less as measured under the following conditions: <Conditions for measuring viscosity retention against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 1 having a carboxyvinyl polymer concentration of 0.01 wt%. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 2 having a carboxyvinyl polymer concentration of 0.01 wt% and a sodium chloride concentration of 0.02 wt%. The viscosities of Aqueous Solutions 1 and 2 are then measured using an E-type viscometer. The viscosity measurement conditions are set to a rotor with a cone angle of 3° and a cone radius of 17.65 mm, a measurement temperature of 30°C, and a rotation speed of 20 rpm. The measured viscosity value is taken 90 seconds after the start of measurement. The viscosity retention rate against salt is calculated according to the following formula:

number

[0011] The present invention also provides, as one embodiment, a method for inhibiting an increase in suspended particles, as described below. Item 2-1. A method for suppressing an increase in particle size of suspended particles in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, comprising: A method for inhibiting an increase in suspended particles, comprising the step of blending brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a salt viscosity retention rate of 18% or less as measured under the following conditions to obtain an aqueous suspension. <Conditions for measuring viscosity retention against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 1 having a carboxyvinyl polymer concentration of 0.01 wt%. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 2 having a carboxyvinyl polymer concentration of 0.01 wt% and a sodium chloride concentration of 0.02 wt%. The viscosities of Aqueous Solutions 1 and 2 are then measured using an E-type viscometer. The viscosity measurement conditions are set to a rotor with a cone angle of 3° and a cone radius of 17.65 mm, a measurement temperature of 30°C, and a rotation speed of 20 rpm. The measured viscosity value is taken 90 seconds after the start of measurement. The viscosity retention rate against salt is calculated according to the following formula:

number

[0012] The present invention also provides, as one embodiment, a method for improving the redispersibility of suspended particles, as described below. Item 3-1. A method for improving the redispersibility of suspended particles in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, comprising: A method for improving the redispersibility of suspended particles, comprising the step of blending brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a salt viscosity retention rate of 18% or less as measured under the following conditions to obtain an aqueous suspension. <Conditions for measuring viscosity retention against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 1 having a carboxyvinyl polymer concentration of 0.01 wt%. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 2 having a carboxyvinyl polymer concentration of 0.01 wt% and a sodium chloride concentration of 0.02 wt%. The viscosities of Aqueous Solutions 1 and 2 are then measured using an E-type viscometer. The viscosity measurement conditions are set to a rotor with a cone angle of 3° and a cone radius of 17.65 mm, a measurement temperature of 30°C, and a rotation speed of 20 rpm. The measured viscosity value is taken 90 seconds after the start of measurement. The viscosity retention rate against salt is calculated according to the following formula:

number

[0013] According to one embodiment of the present invention, in an aqueous suspension comprising brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, the increase in particle size of suspended particles over time can be suppressed, and excellent formulation stability can be achieved.Furthermore, according to one embodiment of the present invention, in an aqueous suspension comprising brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, even if the suspended particles settle, they can be easily restored to their original dispersed state by simply shaking lightly, and excellent ease of use can be achieved. [Brief explanation of the drawings]

[0014] [Figure 1] 1 is a graph showing the salt viscosity retention rate of the carboxyvinyl polymers used in the aqueous suspensions of Examples 2 to 6 and Comparative Examples 1 to 5 on the horizontal axis and the rate of change in particle size after storage at 60° C. for 1 week on the vertical axis. DETAILED DESCRIPTION OF THE INVENTION

[0015] 1.Definition It should be understood that the terms used herein are used in the sense commonly used in the art unless otherwise specified. Therefore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this invention belongs. In the event of a conflict, the present specification (including definitions) shall prevail.

[0016] As used herein, the term "aqueous suspension" refers to a liquid preparation in which insoluble particles (suspended particles) are dispersed in water. Since brinzolamide and / or a salt thereof have extremely low solubility in water, in the aqueous suspension of the present invention, brinzolamide and / or a salt thereof become suspended particles.

[0017] As used herein, "brimonidine" refers to 5-bromo-N-(4,5-dihydro-1H-imidazol-2-yl)quinoxalin-6-amine, a compound known as an adrenergic α2 receptor agonist.

[0018] As used herein, "brinzolamide" refers to a compound known as a carbonic anhydrase inhibitor, (R)-4-(ethylamino)-3,4-dihydro-2-(3-methoxypropyl-2H-thieno[3,2,e]-1,2-thiazine-6-sulfonamide 1,1-dioxide.

[0019] As used herein, the term "carboxyvinyl polymer" refers to a water-soluble vinyl polymer having a carboxyl group, and refers to a polymer of acrylic acid and / or methacrylic acid.

[0020] In this specification, the "viscosity retention rate against salt" is an index of the viscosity stability of a carboxyvinyl polymer against salt, and is a value measured under the following conditions. It is known that the higher the degree of crosslinking of a carboxyvinyl polymer, the more likely its viscosity is to decrease in the presence of salt, and the viscosity retention rate against salt is a physical property value that is correlated with the degree of crosslinking of the carboxyvinyl polymer. <Conditions for measuring viscosity retention against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare an aqueous solution 1 having a carboxyvinyl polymer concentration of 0.01 wt %. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare an aqueous solution 2 having a carboxyvinyl polymer concentration of 0.01 wt % and a sodium chloride concentration of 0.02 wt %. Next, the viscosities of Aqueous Solutions 1 and 2 are measured using an E-type viscometer. The viscosity measurement conditions are set as follows: a rotor with a cone angle of 3° and a cone radius of 17.65 mm, a measurement temperature of 30°C, and a rotation speed of 20 rpm. The measured viscosity value is the value measured 90 seconds after the start of measurement. The retention rate of viscosity relative to salt is calculated according to the following formula.

number

[0021] In this specification, the "viscosity of an aqueous suspension at 30°C" refers to the viscosity value measured 90 seconds after the start of measurement using an E-type viscometer with a rotor having a cone angle of 3° and a cone radius of 17.65 mm, at a measurement temperature of 30°C and a rotation speed of 100 rpm.

[0022] In this specification, the "osmotic pressure of an aqueous suspension" is a value measured according to the method specified in "General Test Methods" of the 17th Edition of the Japanese Pharmacopoeia, section "30. Osmotic Pressure Measurement Method (Osmolality Measurement Method)."

[0023] As used herein, the term "osmotic pressure ratio of an aqueous suspension" refers to the ratio of the osmotic pressure of an aqueous suspension to the osmotic pressure of physiological saline (0.9 w / v % aqueous sodium chloride solution).

[0024] In this specification, the "average particle size of suspended particles" refers to the median particle size of particles of brinzolamide and / or a salt thereof, and is a value measured using a laser diffraction particle size distribution measuring device.

[0025] In this specification, expressions such as "an increase in particle size of suspended particles over time" refer to an increase in the particle size of particles of brinzolamide and / or a salt thereof dispersed in an aqueous suspension due to storage for a certain period of time. For example, when the rate of change in particle size after storage for one week at 60°C measured under the following conditions is 1.6 times or more, it can be said that an "increase in particle size of suspended particles over time" is observed. <Change in particle size after storage at 60°C for 1 week> An aqueous suspension containing brinzolamide and / or a salt thereof is prepared and stored for one week at 60°C. The average particle size of the suspended particles in the aqueous suspension is measured immediately after preparation and after one week of storage, and the rate of change (fold) in particle size after one week of storage at 60°C is calculated according to the following formula:

number

[0026] In this specification, the expression "suppressing the increase in particle size of suspended particles over time" refers to the suppression of an increase in the particle size of particles of brinzolamide and / or a salt thereof dispersed in an aqueous suspension after storage for a certain period of time. For example, this refers to the suppression of an increase in particle size of suspended particles after storage for a certain period of time compared to the aqueous suspension before storage. For example, if the rate of change in particle size after storage at 60°C for one week is 1.5 times or less, it can be said that "the increase in particle size of suspended particles over time is suppressed."

[0027] In this specification, expressions such as "method for inhibiting the increase in particle size of suspended particles" refer to a method carried out in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, for inhibiting the increase in particle size of suspended particles over time and maintaining the particle size of suspended particles.

[0028] As used herein, the term "redispersibility of suspended particles" refers to the property of returning suspended particles to a dispersed state by inverting an aqueous suspension in which sedimentation of suspended particles has occurred after storage for a certain period of time.

[0029] In this specification, expressions such as "improved redispersibility of suspended particles" refer to an improvement in the ability to return suspended particles to a dispersed state by inverting an aqueous suspension that has undergone settling of suspended particles after storage for a certain period of time. For example, if the number of inversions required for redispersion measured under the following conditions is 5 or less, it can be said that "improved redispersibility of suspended particles" has been achieved. <Number of inversions required for redispersion> Five mL of an aqueous suspension containing brinzolamide and / or its salts is filled into a 5 mL glass ampoule and stored in an upright position at 40°C for six months to induce settling of the suspended particles and make them non-uniform. The glass ampoule is then repeatedly inverted, and the number of inversions required for redispersion is counted as the number of inversions required for redispersion. The glass ampoule is inverted 180° upside down, then inverted again 180° to return it to an upright position, counting as one inversion.

[0030] As used herein, expressions such as "method for improving the redispersibility of suspended particles" refer to a method carried out to improve the redispersibility of suspended particles in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer.

[0031] 2. Description of the Preferred Embodiment Although the following description of preferred embodiments is given, it should be understood that these embodiments are merely examples of the present invention and that the scope of the present invention is not limited to such preferred embodiments. It should also be understood that those skilled in the art can easily make modifications, changes, etc. within the scope of the present invention by referring to the following preferred examples. Those skilled in the art can combine any of these embodiments as appropriate.

[0032] 3. Aqueous suspension In ophthalmic solutions, thickeners such as carboxyvinyl polymers are used to improve retention of pharmacological ingredients on the ocular mucosal surface. Previously, aqueous suspensions containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer have been reported (e.g., Patent Documents 2 to 5). However, in suspension-type ophthalmic solutions, large suspended particles can cause problems such as discomfort and eye irritation upon administration, so quality that can maintain a stable particle size is required. The present inventors conducted various studies on the stability of aqueous suspensions containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer. As a result, they discovered a new problem: when a conventionally used carboxyvinyl polymer is used in the aqueous suspension, the particle size of the suspended particles (brinzolamide and / or a salt thereof) in the aqueous suspension increases over time.

[0033] Under these circumstances, the present inventors have conducted further studies and found that by selecting a carboxyvinyl polymer having a viscosity retention rate against salt of 18% or less and blending the carboxyvinyl polymer together with brimonidine and / or a salt thereof and brinzolamide and / or a salt thereof, it is possible to suppress the increase in particle size of suspended particles in an aqueous suspension over time.Furthermore, it has been found that an aqueous suspension blended with a carboxyvinyl polymer having a viscosity retention rate against salt of 18% or less, together with brimonidine and / or a salt thereof and brinzolamide and / or a salt thereof, can improve the redispersibility of suspended particles.

[0034] That is, in one embodiment, the present invention provides an aqueous suspension comprising brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a viscosity retention rate relative to salt of 18% or less. The aqueous suspension of the present invention will be described below.

[0035] [Brimonidine and / or its salts] The aqueous suspension of the present invention contains brimonidine and / or a salt thereof. Brimonidine salts are not particularly limited as long as they are pharmaceutically acceptable, and include organic acid salts and inorganic acid salts. Examples of organic acid salts include tartrate and acetate. Examples of inorganic acid salts include hydrochloride. Brimonidine or its salts may also be in the form of a solvate such as a hydrate. Among brimonidine and its salts, brimonidine tartrate is preferably used because it is commercially available as a pharmaceutical product and its safety has been established.

[0036] In the aqueous suspension of the present invention, either brimonidine or a salt thereof may be used alone, or these may be used in combination.

[0037] The concentration of brimonidine and / or a salt thereof in the aqueous suspension of the present invention is not particularly limited and may be appropriately determined depending on the severity of the symptoms of the patient to be treated, the amount administered per administration, etc., and may be, for example, 0.01 to 1 w / v%, preferably 0.05 to 0.3 w / v%, more preferably 0.1 to 0.2 w / v%. Unless otherwise specified, the concentration of brimonidine and / or a salt thereof herein is the concentration converted to brimonidine tartrate.

[0038] [Brinzolamide and / or its salts] The aqueous suspension of the present invention contains brinzolamide and / or a salt thereof. In the aqueous suspension of the present invention, brinzolamide and / or a salt thereof is present in a dispersed state as suspended particles. The salt of brinzolamide is not particularly limited as long as it is pharmaceutically acceptable, and specific examples thereof include hydrochloride and acetate. Among brinzolamide and its salts, brinzolamide is preferably used because it is marketed as a pharmaceutical product and its safety has been established.

[0039] The concentration of brinzolamide and / or a salt thereof in the aqueous suspension of the present invention is not particularly limited and may be appropriately determined depending on the severity of symptoms of the patient to be treated, the amount to be administered per dose, etc., and may be, for example, 0.1 to 3 w / v%, preferably 0.5 to 2 w / v%, and more preferably 1 w / v%. In this specification, the concentration of brinzolamide and / or a salt thereof is the concentration converted to brinzolamide unless otherwise specified.

[0040] [Carboxyvinyl polymer] The aqueous suspension of the present invention contains a carboxyvinyl polymer having a viscosity retention rate relative to salt of 18% or less. In one embodiment of the present invention, the use of a carboxyvinyl polymer having such a viscosity retention rate relative to salt can suppress an increase in particle size of suspended particles in the aqueous suspension over time. In another embodiment of the present invention, the use of a carboxyvinyl polymer satisfying the above-mentioned viscosity retention rate relative to salt can improve the redispersibility of suspended particles.

[0041] The carboxyvinyl polymer used in the present invention may have a viscosity retention rate relative to salt of 18% or less, but from the viewpoint of more effectively suppressing an increase in particle size over time of suspended particles in an aqueous suspension or more effectively improving the redispersibility of suspended particles in an aqueous suspension, it is preferably 16% or less, more preferably 14% or less, particularly preferably 12% or less, and even more preferably 10% or less. There is no particular restriction on the lower limit of the viscosity retention rate relative to salt of the carboxyvinyl polymer, and it is sufficient if it is 0% or more, but examples include 2% or more, 4% or more, or 6% or more.

[0042] In the aqueous suspension of the present invention, one type of carboxyvinyl polymer may be used alone, or two or more types may be used in combination.

[0043] When one type of carboxyvinyl polymer is used alone, a carboxyvinyl polymer that satisfies the above-mentioned retention rate of viscosity against salt may be selected and used.

[0044] When two or more carboxyvinyl polymers are used in combination, the viscosity retention rate against salt of the combined carboxyvinyl polymers should be within the above range. For example, when two carboxyvinyl polymers, carboxyvinyl polymer A and carboxyvinyl polymer B, are used in combination at a weight ratio of 1:1, the viscosity retention rate against salt of a 1:1 mixture of carboxyvinyl polymer A and carboxyvinyl polymer B should be within the above range.

[0045] Commercially available carboxyvinyl polymers can be used. For example, Lubrizol Advanced Materials' "Carbopol 5984EP" and "Carbopol 980NF" have viscosity retention rates against salt of 12% and 8%, respectively, and can be used alone. Lubrizol Advanced Materials' "Carbopol 974PNF" has a viscosity retention rate against salt of 19%, but by combining Carbopol 974PNF and Carbopol 5984EP so that the amount of Carbopol 5984EP is 25 parts by weight or more per 100 parts by weight of the total, the viscosity retention rate against salt can be reduced to 18% or less.

[0046] The concentration of the carboxyvinyl polymer in the aqueous suspension of the present invention is not particularly limited and may be appropriately set depending on the viscosity to be imparted, the type of carboxyvinyl polymer to be used, etc., and may be, for example, 0.1 to 1 w / v%, preferably 0.1 to 0.5 w / v%, and more preferably 0.3 to 0.5 w / v%.

[0047] The viscosity of the carboxyvinyl polymer used in the present invention is not particularly limited, but examples thereof include those having a viscosity of 4,000 to 100,000 cP, preferably 10,000 to 60,000 cP, and more preferably 35,000 to 60,000 cP in a 0.5 wt % aqueous solution (25°C) adjusted to pH 7.5. The viscosity is measured using a Brookfield viscometer with a spindle #6 at a rotation speed of 20 rpm.

[0048] [Glycerin] In one embodiment, the aqueous suspension of the present invention may further comprise glycerin.

[0049] The concentration of glycerin in the aqueous suspension of the present invention is, for example, 0.1 to 2 w / v %, preferably 0.5 to 1.5 w / v %, and more preferably 0.5 to 0.7 w / v %.

[0050] [Metal chlorides] In one embodiment, the aqueous suspension of the present invention may further contain a metal chloride, which may act as an isotonicity agent or the like.

[0051] The metal chloride is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include alkali metal chlorides such as sodium chloride and potassium chloride; alkaline earth metal chlorides such as magnesium chloride and calcium chloride; zinc chloride, iron chloride, etc. These metal chlorides may be in the form of a hydrate. Of these metal chlorides, sodium chloride is preferred.

[0052] These metal chlorides may be used alone or in combination of two or more.

[0053] The concentration of the metal chloride in the aqueous suspension of the present invention may be appropriately set depending on the type of metal chloride used, and may be, for example, 0.01 to 1 w / v%, preferably 0.05 to 0.5 w / v%, and more preferably 0.1 to 0.3 w / v%. In the present specification, the concentration of the metal chloride is the concentration converted into the anhydrous form when the metal chloride is a hydrate.

[0054] [Surfactants] In one embodiment, the aqueous suspension of the present invention may further comprise a surfactant.

[0055] The surfactant is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include nonionic surfactants such as tyloxapol, polyoxyethylene hydrogenated castor oil, polyoxyethylene polyoxypropylene block copolymer, polyoxyethylene sorbitan fatty acid ester, octoxynol, etc.; amphoteric surfactants such as alkyldiaminoethylglycine, lauryldimethylaminoacetic acid betaine, etc.; anionic surfactants such as alkyl sulfates, N-acyltaurine salts, polyoxyethylene alkyl ether phosphates, polyoxyethylene alkyl ether sulfates, etc.; cationic surfactants such as alkylpyridinium salts, alkylamine salts, etc. Among these surfactants, nonionic surfactants are preferred, and tyloxapol is more preferred.

[0056] These surfactants may be used alone or in combination of two or more.

[0057] The concentration of the surfactant in the aqueous suspension of the present invention may be set appropriately depending on the type of surfactant used, etc., and may be, for example, 0.005 to 0.1 w / v%, preferably 0.1 to 0.05 w / v%, and more preferably 0.02 to 0.03 w / v%.

[0058] [Other additives] In one embodiment, the aqueous suspension of the present invention may further contain additives such as an isotonic agent (other than glycerin and metal chlorides), a viscosity agent (other than carboxyvinyl polymer), a chelating agent, a buffer, a preservative, a stabilizer, a pH adjuster, etc., as necessary.

[0059] The tonicity agent (other than glycerin and metal chlorides) is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include polyhydric alcohols such as propylene glycol, butylene glycol, and polyethylene glycol; metal salts such as sodium acetate, potassium acetate, sodium hydrogensulfite, sodium hydrogencarbonate, sodium carbonate, disodium hydrogenphosphate, and sodium dihydrogenphosphate; etc. These tonicity agents may be used alone or in combination of two or more.

[0060] The thickening agent (other than carboxyvinyl polymer) is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include water-soluble polymers such as polyvinylpyrrolidone, polyethylene glycol, polyvinyl alcohol, xanthan gum, sodium chondroitin sulfate, and sodium hyaluronate; celluloses such as hydroxyethyl cellulose, methyl cellulose, hydroxypropyl cellulose, hydroxypropylmethyl cellulose, and sodium carboxymethyl cellulose; etc. These thickening agents may be used alone or in combination of two or more.

[0061] The chelating agent is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include edetic acid, citric acid, succinic acid, ascorbic acid, trihydroxymethylaminomethane, nitrilotriacetic acid, 1-hydroxyethane-1,1-diphosphonic acid, polyphosphoric acid, metaphosphoric acid, hexametaphosphoric acid, and salts thereof. The salt form is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include alkali metal salts such as sodium salts and potassium salts. These chelating agents may be used alone or in combination of two or more.

[0062] The buffer is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include borate buffer, phosphate buffer, Tris buffer, citrate buffer, tartrate buffer, acetate buffer, amino acid buffer, etc. These buffers may be used alone or in combination of two or more.

[0063] The preservative is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include sorbic acid or its salts, benzoic acid or its salts, methyl parahydroxybenzoate, ethyl parahydroxybenzoate, propyl parahydroxybenzoate, chlorobutanol, benzalkonium chloride, chlorhexidine hydrochloride, chlorhexidine gluconate, chlorhexidine acetate, dehydroacetic acid or its salts, benzethonium chloride, benzyl alcohol, zinc chloride, parachlormetaxylenol, chlorous acid or its salts, chlorcresol, phenethyl alcohol, polidronium chloride, thimerosal, dibutylhydroxytoluene, etc. Among these preservatives, benzalkonium chloride is more preferred. These preservatives may be used alone or in combination of two or more.

[0064] The concentration of the preservative in the aqueous suspension of the present invention may be appropriately set depending on the type of surfactant used, etc., and may be, for example, 0.0001 to 0.01 w / v%, preferably 0.001 to 0.005 w / v%.

[0065] The stabilizer is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include polyvinylpyrrolidone, sulfite, monoethanolamine, cyclodextrin, dextran, ascorbic acid, taurine, tocopherol, dibutylhydroxytoluene, etc. These stabilizers may be used alone or in combination of two or more.

[0066] The pH adjuster is not particularly limited as long as it is pharmaceutically acceptable, and examples thereof include acids such as hydrochloric acid, acetic acid, boric acid, aminoethylsulfonic acid, and epsilon-aminocaproic acid; alkalis such as sodium hydroxide, potassium hydroxide, borax, triethanolamine, monoethanolamine, sodium bicarbonate, and sodium carbonate. These pH adjusters may be used alone or in combination of two or more.

[0067] The concentrations of these additives may be appropriately determined depending on the types of additives used and the properties to be imparted to the aqueous suspension.

[0068] [Other pharmacological ingredients] In one embodiment, the aqueous suspension of the present invention may contain, as necessary, pharmacological ingredients other than brimonidine and / or a salt thereof and brinzolamide and / or a salt thereof. Examples of such pharmacological ingredients include carbonic anhydrase inhibitors such as dorzolamide; prostaglandins such as tafluprost, latanoprost, and isopropyl unoprostone; parasympathomimetics such as pilocarpine hydrochloride; anticholinesterase agents such as distigmine bromide; sympathomimetics such as dipivefrine hydrochloride; β-blockers such as betaxolol hydrochloride; β-blockers such as timolol maleate; α-β-blockers such as nipradilol and levobunolol hydrochloride; and α-blockers such as bunazosin hydrochloride. These pharmacological ingredients may be used alone or in combination. The concentrations of these pharmacological ingredients may be appropriately determined depending on the type of pharmacological ingredient used and the desired efficacy.

[0069] [viscosity] The viscosity of the aqueous suspension of the present invention at 30°C is not particularly limited, but may be, for example, 10 to 100 mPa·s, preferably 20 to 80 mPa·s, more preferably 30 to 70 mPa·s, and even more preferably 30 to 50 mPa·s.

[0070] [pH] The pH of the aqueous suspension of the present invention is not particularly limited as long as it is pharmaceutically acceptable, and may be, for example, 4 to 8. When the aqueous suspension of the present invention is an ophthalmic solution, the pH is preferably 5 to 8, more preferably 6 to 7, from the viewpoint of further reducing irritation to the eyes that can be applied to the ocular mucosa.

[0071] [Osmolality / Osmolality ratio] The osmotic pressure of the aqueous suspension of the present invention is not particularly limited as long as it is applicable to the intended use. When the aqueous suspension of the present invention is an ophthalmic solution, the osmotic pressure can be 250 to 350 mOsm / kg.

[0072] The osmotic pressure ratio of the aqueous suspension of the present invention is not particularly limited as long as it is applicable to the intended use. For example, when the aqueous suspension of the present invention is an ophthalmic solution, the osmotic pressure ratio is 0.85 to 1.15. From the viewpoint of alleviating eye irritation, the osmotic pressure ratio is preferably 0.9 to 1.1, more preferably 1.0.

[0073] [Particle size / rate of change of suspended particles] In the aqueous suspension of the present invention, particles of brinzolamide and / or a salt thereof are present in a dispersed and suspended state.

[0074] In the aqueous suspension of the present invention, the average particle size of the suspended particles immediately after preparation is, for example, 10 μm or less, preferably 2 to 10 μm, and more preferably 2 to 5 μm.

[0075] Furthermore, the aqueous suspension of the present invention can suppress an increase in particle size of suspended particles over time, and the rate of change in particle size after storage at 60°C for one week is 1.5 times or less. In a preferred embodiment, the rate of change in particle size after storage at 60°C for one week is preferably 1.0 to 1.3 times, more preferably 1.0 to 1.2 times, and even more preferably 1.0 to 1.1 times.

[0076] In one embodiment of the aqueous suspension of the present invention, the redispersibility of suspended particles is also excellent, and even if suspended particles settle upon standing, they can be restored to a dispersed state by simply shaking gently. In one embodiment of the aqueous suspension of the present invention, the number of inversions required for the redispersion described above is 5 or less, preferably 4 or less, more preferably 3 or less, and even more preferably 2 or less.

[0077] [Form of formulation] The aqueous suspension of the present invention is prepared into a pharmaceutical composition for various uses, such as ophthalmology, dentistry, otolaryngology, dermatology, etc., and is used as a topical administration preparation. One embodiment of the aqueous suspension of the present invention is a composition for ophthalmology, dentistry, otolaryngology, or dermatology, and preferably an aqueous suspension for ophthalmology.

[0078] Specific examples of aqueous ophthalmic suspensions include eye drops, injections, etc. Among these, eye drops are preferred.

[0079] [Applications / Dosage / Directions] The aqueous suspension of the present invention exhibits an adrenergic α2 receptor agonist effect due to brimonidine and / or a salt thereof, and a carbonic anhydrase inhibitory effect due to brinzolamide and / or a salt thereof, and therefore, in one embodiment of the aqueous suspension of the present invention, it is provided as an eye drop solution and can be suitably used for treating glaucoma.

[0080] When the aqueous suspension of the present invention is used as an eye drop, several drops may be instilled into the eye once or multiple times a day. In one embodiment of the aqueous suspension of the present invention, one drop is instilled into the eye twice a day.

[0081] [Manufacturing method] The aqueous suspension of the present invention may be prepared according to a known method for preparing aqueous suspensions depending on the intended use, for example, by the method described in the General Provisions for Preparations of the Japanese Pharmacopoeia, 17th Edition. It is possible.

[0082] 4. Methods for suppressing the increase of suspended particles As one embodiment of the present invention, there is provided a method for suppressing an increase in particle size of suspended particles in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, the method comprising the step of blending brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a viscosity retention rate relative to salt of 18% or less to obtain an aqueous suspension.

[0083] According to the method of the present invention, in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, it is possible to suppress an increase in particle size of suspended particles over time and to provide an aqueous suspension having excellent formulation stability.

[0084] In the method of the present invention, the type and concentration of brimonidine and / or a salt thereof, the type and concentration of brinzolamide and / or a salt thereof, the type and concentration of carboxyvinyl polymer, the types of other additives and pharmacological ingredients incorporated into the aqueous suspension, the pH of the aqueous suspension, the osmotic pressure / osmotic ratio, the particle size / rate of change of suspended particles, the formulation, the use / dosage / administration, etc. are as described in the section "3. Aqueous suspension."

[0085] 5. Method for improving redispersibility of suspended particles As one embodiment of the present invention, there is provided a method for improving the redispersibility of suspended particles in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, the method comprising the step of blending brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a viscosity retention rate against salt of 18% or less as measured under the following conditions to obtain an aqueous suspension.

[0086] According to the method of the present invention, in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, even if the suspended particles settle, they can be easily restored to their original dispersed state by simply shaking the suspension lightly, making it possible to provide an aqueous suspension that is easy to use.

[0087] In the method of the present invention, the type and concentration of brimonidine and / or a salt thereof, the type and concentration of brinzolamide and / or a salt thereof, the type and concentration of carboxyvinyl polymer, the types of other additives and pharmacological ingredients incorporated into the aqueous suspension, the pH of the aqueous suspension, the osmotic pressure / osmotic ratio, the particle size / rate of change of suspended particles, the formulation, the use / dosage / administration, etc. are as described in the section "3. Aqueous suspension." [Example]

[0088] The present invention will be specifically explained below by way of examples, but the present invention is not limited to these examples.

[0089] 1. Carboxyvinyl Polymer Preparation The following carboxyvinyl polymers 1 to 11 were prepared. Carboxyvinyl polymer 1 Product name: Carbopol 5984EP, manufactured by Lubrizol Advanced Materials, Lot No. 0102235115 Carboxyvinyl polymer 2 Product name: Carbopol 980NF, manufactured by Lubrizol Advanced Materials, Lot No. 0102136170 Carboxyvinyl polymer 3 Product name: Carbopol 971PNF, manufactured by Lubrizol Advanced Materials, Lot No. 0102267016 Carboxyvinyl polymer 4 Product name: Carbopol 71GNF, manufactured by Lubrizol Advanced Materials, Lot No. 0000049293 Carboxyvinyl polymer 5 Product name: Carbopol 974PNF, manufactured by Lubrizol Advanced Materials, Lot No. 0102055429 Carboxyvinyl polymer 6 : A mixture of carboxyvinyl polymer 1 (50 parts by weight) and carboxyvinyl polymer 5 (50 parts by weight) Carboxyvinyl polymer 7: A mixture of carboxyvinyl polymer 1 (75 parts by weight) and carboxyvinyl polymer 5 (25 parts by weight) Carboxyvinyl polymer 8 : A mixture of carboxyvinyl polymer 1 (25 parts by weight) and carboxyvinyl polymer 5 (75 parts by weight) Carboxyvinyl polymer 9 : A mixture of carboxyvinyl polymer 1 (43.2 parts by weight) and carboxyvinyl polymer 5 (56.8 parts by weight) Carboxyvinyl polymer 10 : A mixture of carboxyvinyl polymer 1 (69.6 parts by weight) and carboxyvinyl polymer 5 (30.4 parts by weight) Carboxyvinyl polymer 11 : A mixture of carboxyvinyl polymer 1 (20.3 parts by weight) and carboxyvinyl polymer 5 (79.7 parts by weight)

[0090] 2. Measurement of viscosity retention rate against salt of carboxyvinyl polymer The viscosity retention rate against salt of carboxyvinyl polymers 1 to 11 was measured. The specific measurement method is as follows. A carboxyvinyl polymer was dissolved in purified water, and the pH was adjusted to 7.1 with 1 M aqueous sodium hydroxide solution to prepare aqueous solution 1 with a carboxyvinyl polymer concentration of 0.01 wt %. Separately, a carboxyvinyl polymer and sodium chloride were dissolved in purified water, and the pH was adjusted to 7.1 with 1 M aqueous sodium hydroxide solution to prepare aqueous solution 2 with a carboxyvinyl polymer concentration of 0.01 wt % and a sodium chloride concentration of 0.02 wt %.

[0091] Next, the viscosities of aqueous solutions 1 and 2 were measured using an E-type viscometer (TEV-25 viscometer, Toki Sangyo Co., Ltd.). The viscosity measurement conditions were set using a standard rotor (cone angle 3° and cone radius 17.65 mm), a measurement temperature of 30°C, and a rotation speed of 20 rpm, and the viscosity measured 90 seconds after the start of the measurement was used. The viscosity retention rate against salt was calculated according to the following formula.

number

[0092] Table 1 shows the measurement results of the retention rates of salt viscosity of Carboxyvinyl Polymers 1 to 11. [Table 1]

[0093] 3. Preparation of Aqueous Suspension Aqueous suspensions having the compositions shown in Tables 3 and 4 were prepared. Specifically, a carboxyvinyl polymer was first dispersed in a sodium chloride aqueous solution to prepare a carboxyvinyl polymer aqueous solution. Next, predetermined amounts of brimonidine tartrate, boric acid, tyloxapol, glycerin, benzalkonium chloride, and the carboxyvinyl polymer aqueous solution were added to purified water to obtain a solution. The pH of the solution was adjusted to 6.5 with sodium hydroxide, and then a predetermined amount of brinzolamide was added. The solution was stirred using a stirrer ("TK Robomix," Primix Corporation) under any of the stirring conditions A to C shown in Table 2 to obtain an aqueous suspension in which brinzolamide was dispersed in particulate form. The stirring conditions used in the preparation of each aqueous suspension are as shown in Tables 3 and 4. [Table 2]

[0094] 4. Measurement of viscosity of aqueous suspensions The viscosity of the aqueous suspension immediately after preparation at 30°C was measured using an E-type viscometer (TEV-25 viscometer, Toki Sangyo Co., Ltd.). The viscosity measurement conditions were set to a standard rotor (cone angle 3° and cone radius 17.65 mm), a measurement temperature of 30°C, and a rotation speed of 100 rpm, and the viscosity measured 90 seconds after the start of measurement was used.

[0095] 5. Measurement of the average particle size of the aqueous suspension and the rate of change in particle size after storage at 60°C for one week The aqueous suspension immediately after preparation was stored at 60°C for one week. The aqueous suspension immediately after preparation and after one week of storage were subjected to laser diffraction particle size distribution measurement to measure the average particle size (median size, D50) of the suspended particles. The measurement conditions were as follows: Equipment: Laser diffraction particle size distribution analyzer (SALD-2300, Shimadzu Corporation) -High concentration sample measurement unit used Refractive index: 1.75-0.02i

[0096] The rate of change (fold) in particle size after storage at 60°C for one week was calculated according to the following formula.

number

[0097] 6. Measurement results of the rate of change in particle size The results are shown in Tables 3 and 4. When a carboxyvinyl polymer having a viscosity retention rate relative to salt of 19% or more was blended with an aqueous suspension containing brimonidine tartrate and brinzolamide, the particle size change rate after storage at 60°C for 1 week was 1.6 times or more, indicating an increase in particle size of the suspended particles (Comparative Examples 1 to 5). In contrast, when a carboxyvinyl polymer having a viscosity retention rate relative to salt of 18% or less was blended with an aqueous suspension containing brimonidine tartrate and brinzolamide, the particle size change rate after storage at 60°C for 1 week was 1.2 times or less, indicating an increase in particle size of the suspended particles was suppressed (Examples 1 to 11). Furthermore, even when carboxyvinyl polymer 5 having a viscosity retention rate relative to salt of 19% was used, the increase in particle size of the suspended particles after storage was suppressed by combining carboxyvinyl polymers 1 and 5 in a ratio of 25 parts by weight or more of carboxyvinyl polymer 1 per 100 parts by weight of the total amount of carboxyvinyl polymer 1 and 5 (Examples 7 to 11). Furthermore, when a carboxyvinyl polymer with a salt viscosity retention rate of 18% or less was used, the increase in particle size of the suspended particles after storage was suppressed even when produced under high shear stirring conditions (Examples 3 and 5).

[0098] Figure 1 is a graph showing the viscosity retention rate against salt of the carboxyvinyl polymer used in aqueous suspensions (Examples 2 to 6, 9 to 11, and Comparative Examples 1 to 5) with a viscosity at 30°C in the range of 27 to 37 mPa s, plotted on the horizontal axis, and the rate of change in particle size after one week of storage at 60°C, plotted on the vertical axis. As can be seen more clearly from Figure 1, there is a correlation between the viscosity retention rate against salt of the carboxyvinyl polymer and the rate of change in particle size after one week of storage at 60°C. When the viscosity retention rate against salt of the carboxyvinyl polymer is in the range of 18% or less, the rate of change in particle size after one week of storage at 60°C is low. However, when the viscosity retention rate against salt of the carboxyvinyl polymer is in the range of 19% or more, the rate of change in particle size after one week of storage at 60°C increases dramatically as the viscosity retention rate against salt increases.

[0099] [Table 3]

[0100] [Table 4]

[0101] 7. Measuring the redispersibility of suspended particles Using the aqueous suspensions of Examples 2, 4 and Comparative Example 3 shown in Table 3, Hanging The redispersibility of suspended particles was evaluated. Specifically, 5 mL of each aqueous suspension immediately after preparation was filled into a 5 mL glass ampoule and stored in an upright position at 40°C for 6 months. After storage, the suspended particles had settled and were in an uneven state. After storage, the container containing the aqueous suspension was inverted, and the number of inversions required for redispersion was counted until the suspended particles were uniformly dispersed throughout the liquid (number of inversions required for redispersion). The number of inversions was counted as one operation of inverting the container 180° upside down, then inverting it again 180° to return it to an upright position. The redispersibility of suspended particles was measured using n=3 The average number of turns required for redispersion was calculated.

[0102] 8. Measurement results of redispersibility of suspended particles The results are shown in Table 5. When a carboxyvinyl polymer having a viscosity retention rate against salt of 19% or more was blended with an aqueous suspension containing brimonidine tartrate and brinzolamide, the number of inversions required for redispersion after 6 months of storage at 40°C was about 7.3, indicating poor redispersibility (Comparative Example 3). In contrast, when a carboxyvinyl polymer having a viscosity retention rate against salt of 18% or less was blended with an aqueous suspension containing brimonidine tartrate and brinzolamide, the number of inversions required for redispersion after 6 months of storage at 40°C was 2 or less, indicating excellent redispersibility (Examples 2 and 4).

[0103] [Table 5]

Claims

1. comprising brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer; The aqueous suspension, wherein the carboxyvinyl polymer has a salt viscosity retention rate of 18% or less as measured under the following conditions: <Conditions for measuring retention rate of viscosity against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 1 having a carboxyvinyl polymer concentration of 0.01 wt%. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 2 having a carboxyvinyl polymer concentration of 0.01 wt% and a sodium chloride concentration of 0.02 wt%. Next, the viscosities of Aqueous Solutions 1 and 2 are measured using an E-type viscometer. The viscosity measurement conditions are set to a measurement temperature of 30°C and a rotation speed of 20 rpm using a rotor with a cone angle of 3° and a cone radius of 17.65 mm. The viscosity measured 90 seconds after the start of measurement is used as the measured value. The viscosity retention rate against salt is calculated according to the following calculation formula: [Equation 1]

2. 2. The aqueous suspension of claim 1, further comprising glycerin.

3. 3. The aqueous suspension according to claim 1, wherein the brimonidine and / or salt thereof is brimonidine tartrate.

4. 4. The aqueous suspension according to claim 1, wherein the brinzolamide and / or a salt thereof is brinzolamide.

5. 5. The aqueous suspension according to claim 1, wherein the concentration of the carboxyvinyl polymer is 0.1 to 1 w / v %.

6. 6. The aqueous suspension according to any one of claims 1 to 5, wherein the viscosity of the aqueous suspension at 30°C measured with an E-type viscometer (using a rotor with a cone angle of 3° and a cone radius of 17.65 mm, at a rotation speed of 100 rpm during measurement, and measurement is performed 90 seconds after the start of measurement) is 10 to 100 mPa s.

7. The aqueous suspension according to any one of claims 1 to 6, which is an eye drop.

8. 8. The aqueous suspension according to claim 1, which is used for treating glaucoma.

9. A method for suppressing particle size increase of suspended particles in an aqueous suspension containing brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, comprising: A method for inhibiting an increase in suspended particles, comprising the step of blending brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a salt viscosity retention rate of 18% or less as measured under the following conditions to obtain an aqueous suspension. <Conditions for measuring retention rate of viscosity against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 1 having a carboxyvinyl polymer concentration of 0.01 wt%. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 2 having a carboxyvinyl polymer concentration of 0.01 wt% and a sodium chloride concentration of 0.02 wt%. Next, the viscosities of Aqueous Solutions 1 and 2 are measured using an E-type viscometer. The viscosity measurement conditions are set to a measurement temperature of 30°C and a rotation speed of 20 rpm using a rotor with a cone angle of 3° and a cone radius of 17.65 mm. The viscosity measured 90 seconds after the start of measurement is used as the measured value. The viscosity retention rate against salt is calculated according to the following calculation formula: [Equation 2]

10. A method for improving the redispersibility of suspended particles in an aqueous suspension comprising brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer, comprising: A method for improving the redispersibility of suspended particles, comprising the step of blending brimonidine and / or a salt thereof, brinzolamide and / or a salt thereof, and a carboxyvinyl polymer having a salt viscosity retention rate of 18% or less as measured under the following conditions to obtain an aqueous suspension. <Conditions for measuring retention rate of viscosity against salt> A carboxyvinyl polymer is dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 1 having a carboxyvinyl polymer concentration of 0.01 wt%. Separately, a carboxyvinyl polymer and sodium chloride are dissolved in purified water, and the pH is adjusted to 7.1 to prepare Aqueous Solution 2 having a carboxyvinyl polymer concentration of 0.01 wt% and a sodium chloride concentration of 0.02 wt%. Next, the viscosities of Aqueous Solutions 1 and 2 are measured using an E-type viscometer. The viscosity measurement conditions are set to a measurement temperature of 30°C and a rotation speed of 20 rpm using a rotor with a cone angle of 3° and a cone radius of 17.65 mm. The viscosity measured 90 seconds after the start of measurement is used as the measured value. The viscosity retention rate against salt is calculated according to the following calculation formula: [Equation 3]

Images