bimatoprost is a moderately soluble compound intended for topical delivery to the skin to stimulate hair growth . hair growth includes , without limitation , stimulating the conversion of vellus hair to growth as terminal hair as well as increasing the rate of growth of terminal hair . embodiments disclosed herein provide formulations of bimatoprost and similar compounds with penetration enhancers . these penetration enhancers facilitate active component penetration and / or maintenance at their site of action in the skin . formulations disclosed herein can be self - preserved or contain an antimicrobial agent such as benzyl alcohol . in accordance with embodiments disclosed herein , active components are represented by the active components are provided in particular formulations that include penetration enhancers . some examples of representative compounds useful in the practice of embodiments disclosed herein include the compounds shown in table 1 : wherein y is 0 or 1 , x is 0 or 1 and x and y are not both 1 , y is selected from the group consisting of alkyl , halo , e . g . fluoro , chloro , etc ., nitro , amino , thiol , hydroxy , alkyloxy , alkylcarboxy , halo substituted alkyl wherein said alkyl radical comprises from one to six carbon atoms , etc . and n is 0 or an integer of from 1 to 3 and r 3 is ═ o , — oh or — o ( co ) r 6 wherein r 6 is as defined above or a pharmaceutically acceptable salt thereof . wherein hatched lines indicate a configuration , solid triangles are used to indicate β configuration . in another embodiment , y is 1 and x is 0 and r 1 , r 2 and r 3 are hydroxy . one exemplary active compound is cyclopentane n - ethyl heptanamide - 5 - cis - 2 -( 3α - hydroxy - 5 - phenyl - 1 - trans - pentenyl )- 3 , 5 - dihy - droxy , [ 1 α , 2 β , 3 α , 5 α ], also known as bimatoprost and sold under the name of lumigan ® by allergan , inc ., california , usa . this compound has the following structure : the synthesis of the above compounds has been disclosed in u . s . pat . no . 5 , 607 , 978 which is incorporated by reference in its entirety . the compound will generally range from about 1 × 10 − 7 to about 50 % w / w of the composition , in one embodiment from about 0 . 001 to about 50 % w / w of the composition and in another embodiment from about 0 . 1 to about 30 % w / w of the composition . in some embodiments , a preferred range of the active compound may be about 0 . 03 % w / w to about 5 %, more preferably about 0 . 3 % w / w to about 3 % w / w , and even more preferably , about 1 % w / w to about 3 % w / w . ranges and percentages within about 0 . 3 % w / w , 0 . 5 % w / w , 1 % w / w , 1 . 5 % w / w , 2 % w / w , 3 % w / w , 3 . 5 % w / w , 4 % w / w , 5 % w / w , 5 . 5 % w / w , 6 % w / w , 6 . 5 % w / w , 7 % w / w , 8 % w / w , 9 % w / w , 10 % w / w ; 10 - 50 % w / w ; about 20 - 50 % w / w ; about 30 - 40 % w / w and about 35 % are also included . the pharmaceutical formulations disclosed herein can include one or more penetration enhancers . the phrase “ penetration enhancers ” includes any agent that facilitates the transfer or delivery of active components to their site of action and / or maintains the active component at their site of action . non - limiting examples of classes of appropriate penetration enhancers include alcohols , glycols , fatty acids , ethers , esters , occlusive agents and surface active agents . representative and non - limiting examples of these classes are provided below . it will of course be understood that one or more penetration enhancers or classes thereof may be combined in the various embodiments disclosed herein . alcohols include , without limitation , aliphatic and aromatic alcohols , including ethanol , propanol , n - propanol , isopropanol , butyl alcohol , octanol , benzyl alcohol and acetyl alcohol , in one embodiment , as described in u . s . pat . no . 5 , 789 , 244 , the entire contents of which are incorporated by reference herein . fatty alcohols include , for example , saturated and unsaturated fatty alcohols , including for example those with c 8 - c 28 chain length , stearyl alcohol , oleyl alcohol , palmityl alcohol , and lauryl alcohol , and combinations thereof . in some embodiments , oleyl alcohol may be used in a range between about 0 . 5 % w / w to about 50 % w / w , preferably between about 1 % w / w and about 10 % w / w , and even more preferably between about 3 % w / w and about 6 % w / w . percentages of 1 % w / w , 1 . 5 % w / w , 2 % w / w , 3 % w / w , 3 . 5 % w / w , 4 % w / w , 5 % w / w , 5 . 5 % w / w , 6 % w / w , 7 % w / w , 8 % w / w , 9 % w / w , and 10 % w / w are also contemplated . most preferably , oleyl alcohol may be present at about 5 % w / w . glycols include , without limitation , propylene glycol , polyethylene glycols ( including for example polyethylene glycols with a molecular weight from about 300 - 8000 daltons ), glycol derivatives , and other low molecular weight glycols such as glycerol and thioglycerol . fatty acids , esters and ethers include , without limitation , saturated , monounsaturated , and polyunsaturated c 8 - c 28 fatty acids and fatty esters , such as c 4 - c 20 saturated monocarboxylic and dicarboxylic acids , straight chain fatty acids , stearic acid , oleic acid , linoleic acid , palmitoleic acid , octanoic and decanoic acids , methyl laurate , ethyl oleate , polyethylene glycol monolaurate , propylene glycol monolaurate , propylene glycerol dilaurate , glycerol monolaurate , glyceryl monooleate , glyceryl monostearate , ethyl esters of linoleic acid , isopropyl n - decanoate , octyldodecyl myristate , diethylene glycol monoethyl ether , diethylene glycol monomethyl ether , crodamol mm , isopropyl myristate , and compounds wherein a c 2 - c 4 alkane diol or triol is substituted with one or two fatty ether substituents . occlusive agents include , without limitation , silicones ( including dow st - elastomer 10 , dow silky wax 10 ), mineral oils and greases , long chain acids , animal fats and greases , vegetable fats and greases , water insoluble polymers , paraffin , paraffin oil , liquid paraffin , petrolatum , liquid petrolatum , white petrolatum , yellow petrolatum , microcrystalline wax and ceresin . surface active agents include without limitation nonionic , anionic , and cationic agents , and combinations thereof , such as polysorbate 20 , 40 , 60 and 80 , tween ® ( 20 , 40 , 60 , 80 ) and optionally corresponding span series ( 20 , 40 , 60 , 80 ), poloxamer ® ( 231 , 182 , 184 ), sodium dodecyl sulfate ( sds ), macrogol 15 hydroxystearate , polyvinyl caprolactam - polyvinyl acetate - polyethylene glycol graft co - polymer . lecithin , lysolecithin , nonylphenoxypolyoxyethylene , lysophosphatidylcholine , polyethyleneglycol 400 , polyoxyethylene ethers , polyglycol ether surfactants , sodium laurate , sodium lauryl sulfate , cetyltrimethylammonium bromide , docusate sodium , and benzalkonium chloride . other penetration enhancers that may be useful include dimethylaminopropionic acid derivatives , such as 2 - dimethylaminopropionic acid dodecyl ester ( ddaip ); terpenes , including terpinolene , limonene , nerol , cineol ; sulfoxides such as dmso ; cyclic ethers ; amides and amines , such as didecyldimethylammonium bromide ( ddab ), sodium taurodeoxycholate , triethylamine ; octyl salicylate , and combinations thereof . additional penetration enhancers will be known to those of ordinary skill in the art of topical drug delivery , and / or are described in the pertinent texts and literature . embodiments disclosed herein can also include viscosity increasing agents . appropriate agents include , without limitation , methylcellulose , ethyl cellulose , hydroxyethyl cellulose , acrylamide / sodium acryloyldimethyltaurate copolymer , polyacrylic acid , polyvinyl alcohol , polyvinyl pyrrolidone , hyaluronic acid and chondroitin sulfate . certain embodiments disclosed herein can include preservatives including , without limitation , phenoxyethanol , benzyl alcohol , benzalkonium chloride , chlorhexidine , chlorobutanol , methyl -, propyl -, or butyl - parahydroxybenzoic acids , phenylmercuric salts including , without limitation , nitrate , chloride , acetate , and borate and betain . various other additives may be included in the compositions of the present invention in addition to those identified above . these include , but are not limited to , antioxidants , astringents , perfumes , emollients , pigments , dyes , humectants , propellants , and sunscreen agents , as well as other classes of materials whose presence may be cosmetically , medicinally or otherwise desirable . the compositions and formulations may also be taken in conjunction with minoxidil and propecia . compositions can also be formulated as “ slow - releasing ” formulations so that the activity of active components is sustained for a longer period of time between treatments . while particular embodiments disclosed herein can include each of the components discussed above , other particular embodiments can be required to be “ substantially free ” of one or more of these components in various combinations . “ substantially free ”, as used herein , means that the component is not added to a formulation and cannot be present in any amount greater than about 1 % w / w . while not limiting the scope of express exclusion of the preceding paragraph , particular embodiments disclosed herein can be substantially free of one or more of bimatoprost , carbomer , naoh , tea , ethanol , glycerin , diethylene glycol , monoethyl ether , propylene glycol , polysorbate 20 , polysorbate 40 , polysorbate 60 , polysorbate 80 , ppg - 5 ceteth - 20 , oleic acid , isostearyl isostearate , isopropyl myristate , dipropylene glycol dimethyl ether , diethylene glycol , dipropylene glycol , triglycerides , caprylic / capric , benzyl alcohol , silicone and water . all components of formulations described herein will be included in amounts that are dermatologically - acceptable . as used herein , “ dermatologically - acceptable ” means that the compositions or components thereof are suitable for use in contact with human skin without undue toxicity , incompatibility , instability , allergic response , and the like . as used in herein as applied to active agents and excipients , the term “ about ” refers to variations in concentrations which are considered to be bioequivalent . embodiments disclosed herein find application in mammalian species , including both humans and animals . in humans , the compounds of embodiments disclosed herein can be applied without limitation , to the scalp , face , beard , head , pubic area , upper lip , eyebrows , and eyelids . the compositions of the present inventions may be used for treating various hair loss disorders including but not limited to alopecia areata , telogen effluvium , anagen effluvium , cicatricial alopecia and scarring alopecia ; hair shaft abnormalities such as trichorrexis nodosa , loose anagen syndrome , trichotillomania and traction alopecia ; infectious hair disorders such as tiniea capitis , sebohorreic dermatitis , and follicullitus of the scalp ; genetic disorders such as androgenetic alopecia and patients undergoing hair loss due to chemotherapy , hormonal imbalance ( e . g ., thyroid conditions such as hypothyroidism and hyperthyroidism , pregnancy , child birth , discontinuation of birth control pills and changes in menstrual cycle ), fungal infection of the scalp such as ringworm , medicines which cause hair loss such as anti - coagulants , medicine for gout , depression , high blood pressure and certain heart medications . the formulations of the present invention may be used to treat hair loss related to other disease such as diabetes , lupus , and poor nutrition , mental and physical stress such as due to surgery , illness and high fever . environmental factors and chemicals used in hair treatment ( dying , tinting and bleaching ). in animals raised for their pelts , e . g ., mink , the formulations can be applied over the entire surface of the body to improve the overall pelt for commercial reasons . the process can also be used for cosmetic reasons in animals , e . g ., applied to the skin of dogs and cats having bald patches due to mange or other diseases causing a degree of alopecia . the compositions and methods of the present invention may be applied to patients suffering from hair loss or in healthy patients simply wanting to increase hair growth in any part of the body . the compositions disclosed herein are formulated for topical administration . the term “ topical administration ” as used herein includes applying a formulation as described herein to the outer skin or hair . the application will generally occur at or near the area of desired hair growth . accordingly , appropriate formulation or composition types include , without limitation , solutions , gels , ointments , foams , films , liniments , creams , shampoos , lotions , pastes , jellies , sprays and aerosols . such formulation types can be applied in swaths , patches , applicators or through the use of impregnated dressings depending on the situation and part of the body to be treated . typically , the formulations described herein will be applied repeatedly for a sustained period of time to the part of the body to be treated . in particular embodiments , formulations disclosed herein can include one or more applications daily , one or more applications weekly , one or more applications monthly or one or more applications yearly for a period of treatment of at least one day , at least one week , at least one month , at least one year or until the treatment has achieved or achieved and maintained a desired result . formulations described herein will be administered in safe and effective amounts . as used herein , “ safe and effective amounts ” include an amount sufficient so that the composition provides the desired hair growth stimulation effect at a reasonable benefit / risk ratio attendant with any medical treatment . within the scope of sound medical judgment , the amount of active components used can vary with the particular condition being treated , the severity of the condition , the cause of the condition , the duration of the treatment , the specific active component employed , its concentration , the specific vehicle utilized , the general health of the patient , the tolerance of the patient to various effects of the administration , other drugs being administered to the patient , and like factors within the specific knowledge and expertise of the patient or attending physician . for daily administration , an appropriate dose can include , without limitation , about 0 . 1 ng to about 100 mg , about 1 ng to about 10 mg per day or in another embodiment about 10 ng to about 1 mg per day . non - limiting examples of some components with their appropriate concentration ranges and function are provided in tables 1a and b below . particular examples of non - limiting formulations or compositions are provided in table 2 . ethyl alcohol is weighed into a suitable media jar equipped for mixing , bimatoprost is then added to the ethyl alcohol and stirred at moderate speed until bimatoprost is dissolved . into separate mixing tank , glycerin , diethylene glycol monoethyl ether , and propylene glycol are added and mixed until the solvents are dispersed . ethyl alcohol / bimatoprost solution is then added into the non - aqueous solution and mixed until the components are homogenously mixed ( about 5 minutes of mixing ). to the above mixture the carbomer thickener previously dispersed in water is added and mixed until well dispersed , once dispersed a base is added to thicken the solution into a gel . representative formulations made according to the method above are shown in table 3 below . a study is initiated to systematically evaluate the appearance of hair on the scalp and eyebrows who are administered bimatoprost gel formulations as in table 3 . the study involves 10 subjects , 5 male , 5 female , average age 70 years , ( ranging from 50 - 94 years ). each subject is treated daily by the topical application of bimatoprost by the 0 . 3 % w / w bimatoprost formulation of table 3 . the study is limited to subjects who have administered bimatoprost for more than 3 months . the mean duration of exposure to the 0 . 3 % w / w bimatoprost gel formulation prior to assessing the parameter of hair or eyebrow growth between the control and study eye is 129 days ( range 90 - 254 days ). observations are made under high magnification at a slit lamp biomicroscope . documentation of differences between the control and treatment areas is accomplished using a camera specially adapted for use with a slit lamp biomicroscope . length of hair and eyebrows : increased length of hair in both groups is regularly observed . the difference in length varies from approximately 10 % to as much as 30 %. number of hairs and eyebrows : increased numbers of hairs are observed on the scalp and eyebrows of each patient . the difference in number of hair and eyebrows varies from approximately 5 % to as much as 30 %. whether statistically significant or not , bimatoprost with a penetration enhancer will provide better and / or faster results than bimatoprost without a penetration enhancer . the foregoing observations will establish that 0 . 03 % w / w bimatoprost composition penetrates skin and grows hair . a topical 0 . 2 % w / w bimatoprost cream is prepared as follows : tegacid and spermaceti are melted together at a temperature of 70 - 80 ° c . methylparaben is dissolved in about 500 gm of water and propylene glycol , polysorbate 80 , bimatoprost and a penetration enhancer are added in turn , maintaining a temperature of 75 - 80 ° c . the methylparaben mixture is added slowly to the tegacid and spermaceti melt , with constant stirring . the addition is continued for at least 30 minutes with additional stirring until the temperature has dropped to 40 - 45 ° c . finally , sufficient water is added to bring the final weight to 1000 gm and the preparation stirred to maintain homogeneity until cooled and congealed . a 0 . 1 % w / w bimatoprost topical cream is prepared as follows : tegacid and spermaceti are melted together at a temperature of 70 - 80 ° c . methylparaben is dissolved in water and propylene glycol , polysorbate 80 , bimatoprost and a penetration enhancer are added in turn , maintaining a temperature of 75 - 80 ° c . the methylparaben mixture is added slowly to the tegacid and spermaceti melt , with constant stirring . the addition is continued for at least 30 minutes with additional stirring until the temperature has dropped to 40 - 45 ° c . finally , sufficient water is added to bring the final weight to 1000 gm and the preparation stirred to maintain homogeneity until cooled and congealed . white petrolatum and wool fat are melted , strained and liquid petrolatum is added thereto . bimatoprost , a penetration enhancer , zinc oxide , and calamine are added to the remaining liquid petrolatum and the mixture milled until the powders are finely divided and uniformly dispersed . the mixture is stirred into the white petrolatum , melted and cooled with stirring until the ointment congeals . in other variants , the zinc oxide and / or calamine can be omitted such that the formulation is substantially free of the zinc oxide or calamine . an ointment containing 5 % w / w bimatoprost and a penetration enhancer is prepared by adding the active compound to light liquid petrolatum . white petrolatum is melted together with wool fat , strained , and the temperature adjusted to 45 - 50 ° c . the liquid petrolatum slurry is added and the ointment stirred until congealed . the ointment can be packaged in 30 gm tubes . an aqueous spray formulation containing 0 . 03 %, w / w bimatoprost and a penetration enhancer are prepared as follows . bimatoprost and a penetration enhancer are dissolved in water and the resulting solution is sterilized by filtration . the solution is aseptically filled into sterile containers with a spray nozzle for application on top of the head . the formulation is presented in table 4a below . an alternative formulation is also listed in table 4b . a sample of bimatoprost and a penetration enhancer is dissolved in the vehicle of n - methylpyrrolidone and propylene glycol to make a 0 . 5 % w / w bimatoprost lotion for application to the scalp or other parts of the body for growing hair . an aerosol containing approximately 0 . 1 % w / w bimatoprost and a penetration enhancer is prepared by dissolving the bimatoprost and a penetration enhancer in absolute alcohol . the resulting solution is filtered to remove particles and lint . this solution is chilled to about − 30 ° c . a chilled mixture of dichlorodifluoromethane and dichlorotetrafluoroethane is then added to the solution . thirteen ml plastic - coated amber bottles can be cold filled with 11 . 5 gm each of the resulting solution and capped . the aerosol may be sprayed onto the scalp or other parts of the body to grow hair . a 0 . 1 % w / w bimatoprost topical foam formulation is prepared as follows : methylparaben is dissolved in about 500 gm of water and propylene glycol , polysorbate 80 , bimatoprost and a penetration enhancer are added in turn , maintaining a temperature of 75 - 80 ° c . the methylparaben mixture is added slowly to tegacid and spermaceti , with constant stirring . the addition is continued for at least 30 minutes with additional stirring until the temperature has dropped to 40 - 45 ° c . finally , sufficient water is added to bring the final weight to 1000 gm and the preparation stirred to maintain homogeneity until cooled and congealed . alternative foam formulations prepared in a similar manner as taught in example 10 are described below in tables 5a - b . a powder of the compound bimatoprost and a penetration enhancer is prepared by mixing in dry form with talcum powder at a weight / weight ratio of 1 : 1 : 10 . following the procedures of the preceding examples , compositions are similarly prepared substituting an equimolar amount of a compound of table 1a for the bimatoprost disclosed in the preceding examples . unless otherwise indicated , all numbers expressing quantities of ingredients , properties such as molecular weight , reaction conditions , etc . used in the specification and claims are to be understood as being modified in all instances by the term “ about .” “ about ” refers to variations in concentrations of excipients and types of excipients which are considered to be bioequivalent according to the fda and other regulatory authorities . a 44 year old caucasian male undergoing hair loss due to alopecia areata applies once daily before sleeping the 0 . 1 % w / w bimatoprost composition of table 3 for a period of 6 months . after 3 months of application , the subject will notice new hair growth where there previously had been none and darkening of the follicles of old hair . observations of new hair growth are made under high magnification at the slit lamp biomicroscope and by computer assisted image analysis . documentation of differences between the control and treatment areas is accomplished using a camera specially adapted for use with the slit lamp biomicroscope . a 37 year old hispanic male suffering from male pattern baldness due to androgenetic alopecia applies the 0 . 2 % w / w bimatoprost composition of table 3 twice daily in areas where hair is noticeably thinning . after 63 days of application , increased growth of hair will be noticed as will be new hair growth as measured by high magnification at the slit lamp biomicroscope and by computer assisted image analysis . after satisfactory levels of hair growth are observed , the patient applies the 0 . 2 % w / w bimatoprost composition only twice a week . a 29 year old caucasian healthy female wishes to have fuller hair and more hair growth even though no disease or hair loss condition has been diagnosed by doctors . the patient will apply the 0 . 3 % w / w bimatoprost composition of table 3 once daily until more hair growth is observed after approximately three months of use . the patient continues to apply the composition once a week to maintain the increased hair growth . a 35 year old african american male diagnosed with follicular degeneration syndrome and associated hair loss will apply the 0 . 03 % w / w bimatoprost composition of table 3 . the composition will be applied twice daily , once in the morning after showering and once in the evening . after 46 days of application , increased hair growth will be noticed and easing of the symptoms of follicular degeneration syndrome . the patient continues application for another 6 months . further examples of formulations containing bimatoprost are also possible , and may be used to further stimulate hair growth . in some embodiments , some formulations may be particularly beneficial to stimulate hair growth in the scalp . a formulation of bimatoprost solution containing 0 . 3 % w / w bimatoprost and a penetration enhancer comprising oleyl alcohol may be prepared as follows . the ingredients of table 7 below are weighed and dispensed into a suitable media jar equipped for mixing . preferably , bimatoprost is dissolved into the ethanol , and then combined with oleyl alcohol , propylene glycol and water . the various components are mixed together until homogenously mixed . it will be understood that the formulation provided in table 7 is non limiting and that other formulations are of course possible and envisioned . the bimatoprost solution below had a ratio of bimatoprost to oleyl alcohol of 0 . 06 , a ratio of bimatoprost to ethanol of 0 . 005 , and a ratio of oleyl alcohol to ethanol of 0 . 083 . of course , while the example above comprises oleyl alcohol , which is believed to act as a penetration enhancer , some compositions may nevertheless not comprise this compound . table 8 below illustrates additional non - limiting examples of such formulations . the bimatoprost solutions 8a and 8b below had a ratio of bimatoprost to ethanol of 0 . 005 . in addition to the gel formulation provided in example 1 above , a gel formulation comprising 0 . 3 % w / w bimatoprost may also be manufactured using the ingredients listed in table 9 below . the ingredients in table 9 are formulated into a gel according to the following procedure . first , ascorbic acid and edta are dissolved in a portion of the total water . then , carbopol 974p is added to this solution to disperse and wet the carbopol . next , poloxamer 407 is added to another portion of the total water in a separate container and mixed to disperse . the carbopol portion is then added to this part and mixed . polysorbate 80 , hexylene glycol and peg 400 are next combined in another container and mixed until homogeneous . bha , bht and bimatoprost are weighed into another container , followed by the addition of benzyl alcohol . the ingredients are mixed together until homogeneous . subsequently , this part is added to the polysorbate 80 part and mixed . all parts are mixed together , followed by mixing in the remaining water and tromethamine ( which have been previously mixed together ) so as to neutralize the gel the formulations described in tables 7 , 8 , and 9 above were tested with an in vitro system comprising a 1 . 0 cm 2 franz cell diffusion chamber . during this testing , the franz cell comprises a sample of dermatomized ex - vivo human cadaver posterior trunk skin overlaying a diffusion cell filled with receptor solution fluid configured to simulate body fluid . the tested formulations were applied to the skin samples overlaying the diffusion cell . two donor cadavers were used , the first from a 43 - year old black male , and the second from a 59 - year old white male . testing was performed in triplicate for each donor and formulation tested . ten μl of tested solution was applied per square centimeter of skin . at 2 , 4 , 7 , 24 , and 48 hour intervals , receptor solution fluid was collected at each time point , and the amount of bimatoprost was quantified . to obtain the cumulative receptor solution concentration , the amount of bimatoprost calculated at each time interval above were added together . analysis and bimatoprost quantification for the skin stratum corneum and dermis was performed at the 48 hour endpoint . as shown in table 10 above , the 0 . 3 % bimatoprost formulation described in table 3 was compared to the new formulations of tables 7 , 8 , and 9 . the new formulations ( all containing 0 . 3 % bimatoprost ) all exhibited greater cumulative amounts of bimatoprost permeating through the skin sample and into the receptor solution , with the exception of the gel formulation which exhibited minimal skin penetration . unexpectedly , the formulation from table 7 that contained oleyl alcohol as a skin penetrant showed a surprisingly higher skin penetration ( stratum corneum / epidermis and dermis concentration ), and greater cumulative receptor solution fluid concentration relative to the other tested formulations . additional formulations were prepared in a similar manner to what has already been described . table 11 illustrates examples of such formulations , illustrating that the formulations do not necessarily need to comprise oleyl alcohol . the bimatoprost solution a below had a ratio of bimatoprost to ethanol of 0 . 03 . the bimatoprost solution b had a ratio of bimatoprost to ethanol of 0 . 01 . the bimatoprost solution c had a ratio of bimatoprost to ethanol of 0 . 005 . the bimatoprost solution d had a ratio of bimatoprost to ethanol of 0 . 0167 . the bimatoprost solution e had a ratio of bimatoprost to ethanol of 0 . 05 . the formulations of table 11 were compared to the bimatoprost 0 . 3 % solution formulation of table 3 . testing was done using the same apparatus and general setup as example 20 above . here , however , the cadaver skin samples came from a 44 year old white female , and a 60 year old white female . the results above indicate that the bimatoprost formulations with a higher relative ethanol and propylene glycol content , i . e ., the solutions c , d , and e from table 10 , showed higher receptor solution and dermis concentration relative to the other formulations . further formulations were also prepared using similar manufacturing techniques as have been previously described . here , the formulations described below in table 13 were manufactured comprising oleyl alcohol as a skin penetrating agent . in table 13 , bimatoprost solution a had a ratio of bimatoprost to oleyl alcohol of 0 . 6 , a ratio of bimatoprost to ethanol of 0 . 045 , and a ratio of oleyl alcohol to ethanol of 0 . 076 . the bimatoprost solution b had a ratio of bimatoprost to oleyl alcohol of 0 . 6 , a ratio of bimatoprost to ethanol of 0 . 05 , and a ratio of oleyl alcohol to ethanol of 0 . 083 . the bimatoprost solution c had a ratio of bimatoprost to oleyl alcohol of 0 . 6 , a ratio of bimatoprost to ethanol of 0 . 05 , and a ratio of oleyl alcohol to ethanol of 0 . 083 . an additional gel formulation containing 10 % w / w bimatoprost was also prepared using similar manufacturing techniques as have been previously described . the bimatoprost gel formulation below had a ratio of bimatoprost to ethanol of 0 . 33 . table 14 below describes the specific ingredients comprising this formulation . the formulations of tables 13 and 14 were compared to the bimatoprost 0 . 03 % solution formulation of table 3 . testing was done using the same apparatus and general setup as used in examples 20 and 22 above . here , the cadaver skin samples were from three donor cadavers — a 54 year old white male , a 42 year old black male , and a 26 year old white male . relative to the control formulation of table 3 , the 3 % bimatoprost solutions containing oleyl alcohol demonstrated high skin permeation and permeation into the receptor solution . solution a demonstrated a particularly high receptor fluid concentration relative to the other oleyl alcohol formulations . additionally , the 10 % w / w bimatoprost gel formulation from table 14 , which did not include any oleyl alcohol , showed a high dermal concentration , but did not exhibit as much penetration into the receptor solution as the 3 % w / w bimatoprost solutions . nevertheless , the tested characteristics of all four new formulations were superior compared to the original control formulation . examples of formulations containing bimatoprost and one or more penetration enhancers may be found in table 16 below , and were manufactured in accordance with the techniques described previously . the formulations from table 16 above were tested in an in vitro skin penetration testing method . testing was done using the same apparatus and general setup as used in examples 20 and 22 above . compared to the formulation f - 7 , formulations f - 2 through f - 6 were found to have demonstrated comparable or higher bimatoprost permeation into the receptor fluid . also formulations f - 2 through f - 6 were shown to have a higher amount of bimatoprost in the dermis . formulation f - 6 , which contains oleyl alcohol , had the highest bimatoprost concentration in the dermis and receptor solution , respectively . examples of formulations containing bimatoprost and one or more penetration enhancers may be found in table 18 below , and were manufactured in accordance with the techniques described previously . it will be noted that the formulations f - 1 and f - 2 are the same as those shown in table 11 . the formulations from table 18 above were tested in an in vitro skin penetration testing method . testing was done using the same apparatus and general setup as used in examples 20 and 22 above . compared to the formulation f - 1 ( which has a 3 % bimatoprost concentration ), formulations f - 3 through f - 10 have comparable or higher bimatoprost permeation into the receptor fluid while containing bimatoprost at a 1 % concentration . additionally , formulations f - 3 , and f - 5 through f - 10 demonstrate a higher amount of bimatoprost in the dermis versus formulation f - 1 . this study shows that glycerol monooleate and oleic acid , respectively , may be useful in enhancing the penetration of bimatoprost into and through the skin in an in vitro study compared to formulations f - 1 and f - 2 . examples of formulations containing bimatoprost and one or more penetration enhancers may be found in table 20 below , and were manufactured in accordance with the techniques described previously . it will be noted that the formulations f - 1 and f - 2 are the same as those shown in table 11 . the formulations from table 20 above were tested in an in vitro skin penetration testing method . testing was done using the same apparatus and general setup as used in examples 20 and 22 above . compared to the formulation f - 1 , formulations f - 3 through f - 9 have comparable or higher bimatoprost permeation into the receptor fluid while using a comparatively lower percentage of bimatoprost ( 1 % versus 3 %). a combination of gmo and oleic acid ( formulation f - 4 ) and linoleic acid ( formulation f - 9 ), showed the highest permeation of bimatoprost into the receptor solution . examples of formulations containing bimatoprost and one or more penetration enhancers may be found in table 22 below , and were manufactured in accordance with the techniques described previously . it will be noted that the formulation f - 1 is the same as those shown in table 11 . the formulations from table 22 above were tested in an in vitro skin penetration testing method . testing was done using the same apparatus and general setup as used in examples 20 and 22 above . compared to the formulation f - 1 , formulations f - 2 through f - 9 have demonstrated comparable or higher bimatoprost permeation into receptor solution and into the dermis , even with a lower overall concentration of bimatoprost . examples of formulations containing bimatoprost and one or more penetration enhancers may be found in table 24 below , and were manufactured in accordance with the techniques described previously . it will be noted that the formulation f - 1 is the same as those shown in table 11 . in some embodiments , several possible formulations capable of superior skin penetration may be manufactured as set forth in the two following tables . using a base formulation set forth in table 25 , a mixture of one or more fatty acids or fatty esters ( as set forth in table 26 ) may be added thereto . preferably , a base formulation from table 25 will be combined with at least two ingredients from table 26 . even more preferably , the at least two ingredients from table 26 are one fatty acid and one fatty ester . of course , it will be understood that these formulations do not presume any particular order of manufacture , and are only presented thusly for ease of understanding . while the base formulations may be prepared with any appropriate concentration of bimatoprost , this concentration is preferably between about 0 . 3 % w / w and about 5 % w / w , more preferably about 1 % w / w to about 3 % w / w , and even more preferably about 3 % w / w . in a phase 2 multicenter trial , men 18 - 49 years of age with mild to moderate androgenic alopecia ( aga ) were randomized in a 1 : 1 : 1 : 1 : 1 ratio to receive in a double - blind manner bimatoprost ( bim ) 0 . 3 %, 0 . 1 %, 0 . 03 %, or vehicle applied once daily , or open label over - the - counter minoxidil 5 % solution ( min ) applied twice daily to the vertex area of the scalp for 6 months . subjects were evaluated every 2 months during treatment and at 2 months after completing treatment . the bim formulations used in this study were as described in table 3 above . the following assessments were made with digital image analysis ( dia ; macrophotographs of a prespecified 1 - cm 2 circular area at the anterior leading edge of the vertex thinning area of the scalp identified by microdot tattoo ) using customized validated software : target area hair count ( tahc ) measured in terminal hairs / cm 2 ; target area hair width ( tahw ) measured in mm / cm 2 ; and , target area hair darkness ( tahd ) measured in intensity units ; other assessments included subject self assessment ( ssa ), investigator global assessment ( iga ), and global panel review ( gpr ) by an independent panel of 3 dermatologists while viewing standardized global photographs of the scalp at baseline ( day 1 ) and at the current visit ( or live assessment at the current visit in the case of iga ) change in scalp hair growth was measured on 7 - point ordinal scale from − 3 ( greatly decreased ) to + 3 ( greatly increased ). co - primary efficacy endpoints measured included the change from baseline in tahc and the ssa of change in scalp hair growth . secondary efficacy endpoints included changes from baseline in tahw and tahd , and iga / gpr of changes in scalp hair growth . safety measures included adverse event monitoring , local tolerability assessment , clinical laboratory testing , vital signs , 12 - lead electrocardiograms ( ecgs ), and physical examinations . statistical efficacy analyses were performed on the modified intent - to - treat population , which included all randomized subjects who received study treatment and had baseline measurements the co - primary efficacy analyses were conducted at month 6 . percent changes from baseline in tahc , tahw , and tahd were analyzed using the wilcoxon rank - sum test . frequency distributions of ssa , iga , and gpr scores were analyzed using a cochran - mantel - haenszel test stratified for age group ( 18 - 34 vs 35 - 49 years ), and missing data were imputed to month 6 using a last - observation - carried - forward approach . safety measures were evaluated in all subjects who received study medication ; among - group and pairwise comparisons of the incidence of adverse events were performed using a chi - square or fisher &# 39 ; s exact test a total of 307 men with aga received study treatment and were included in the efficacy and safety analyses . treatment arms were generally well balanced with respect to demographic and baseline characteristics digital image analysis ( dia ) showed that bimatoprost 0 . 3 % produced a significantly greater mean percentage change from baseline to month 6 in tahc compared with vehicle ( 11 . 1 % vs 3 . 3 %; p = 0 . 008 ). dia also revealed a significant improvement in tahw , but not in tahd , with bimatoprost 0 . 3 % in comparison to the vehicle at month 6 ; significant improvements were also seen at month 4 for tahw . two months after stopping treatment , the changes in tahc and tahw with bimatoprost were no longer significantly different from vehicle . the distribution of ssa scores at month 6 did not differ between bimatoprost and vehicle . gpr assessments at month 6 , but not iga assessments , showed that the percentage of subjects with ≧ 1 - grade improvement ( i . e ., scores of + 3 , + 2 , or + 1 ) was significantly greater with bimatoprost 0 . 3 % compared with vehicle ( 21 . 1 % vs 8 . 9 %; p = 0 . 030 ). the improvement in gpr assessment with bimatoprost 0 . 3 % was maintained at 2 months post - treatment ( 16 . 4 % vs 0 %; p = 0 . 017 ) in the open - label minoxidil 5 % treatment arm with twice - daily application , treatment resulted in an increase in tahc of 18 . 4 % from baseline at month 6 . this was higher than published reports of an ≈ 13 % increase in tahc after 4 and 12 months of treatment . a majority of subjects ( 67 . 3 %) on minoxidil 5 % indicated ≧ 1 - grade improvement in hair growth . at the doses tested , the efficacy of any bimatoprost group was less than that of the min group with reference to table 27 below , the incidence of treatment - related adverse events was slightly higher with bimatoprost compared with vehicle , but lower than the rate with minoxidil . with reference to table 28 below , the most common dermal tolerability symptoms were itching based on subject report and dryness / scaling based on dermatologist report ; both were less frequent with bimatoprost 0 . 3 % compared with minoxidil . however , folliculitis was more common with bimatoprost 0 . 3 % than with minoxidil on the dermatologist report . the study demonstrated that topical bimatoprost 0 . 3 % applied once daily significantly increased scalp hair growth compared with vehicle in subjects with mild - to - moderate aga . topical minoxidil 5 % applied twice daily in an open - label manner showed efficacy higher than any of the bimatoprost doses tested . topical bimatoprost exhibited a safety and tolerability profile that was consistent with that of an established topical treatment for scalp hair growth while the above detailed description has shown , described , and pointed out novel features as applied to various embodiments , it will be understood that various omissions , substitutions , and changes in the form and details of the device or process illustrated may be made without departing from the spirit of the disclosure . additionally , the various features and processes described above may be used independently of one another , or may be combined in various ways . all possible combinations and subcombinations are intended to fall within the scope of this disclosure . many of the embodiments described above include similar components , and as such , these similar components can be interchanged in different embodiments . although the invention has been disclosed in the context of certain embodiments and examples , it will be understood by those skilled in the art that the invention extends beyond the specifically disclosed embodiments to other alternative embodiments and / or uses and obvious modifications and equivalents thereof . accordingly , the invention is not intended to be limited by the specific disclosures of preferred embodiments herein .
methods and compositions for stimulating the growth of hair are disclosed wherein said compositions include a cyclopentane heptanoic acid , 2 - cycloalkyl or arylalkyl compound represented by the formula i wherein the dashed bonds represent the presence or absence of a double bond which can be in the cis or trans configuration and a , b , z , x , r 1 and r 2 are as defined in the specification and a penetration enhancer . such compositions are used in stimulating hair growth of human or non - human animals .