value for 8—chloro—6—phenyl-4H-s—triarolo[4.3—al|1,4] benzodiazepine
`(estarolam) was reported to be 2.84 from the UV absorption spectral
`change (23). Considering the structural difference mentioned. the esti-
`mated pKa value for triazolarn, 1.52, is reasonable.
`The bioavailability or the pharmacological effect of a drug would
`greatly depend on the formation rate in the cyclization reaction from the
`opened form to the closed form because only the cyclized 1,4-ben2.odi-
`azepines possess pharmacological CNS activity (24), which are discussed
`in reports on diazepam (8) and desmethyldiazepam (12). The half—time
`of the forward reaction of I at pH 7.4, which was calculated to be 80.6 min
`(Fig. 5), indicates that much time is required to convert I into the closed
`form Il, only if the in viva reaction proceeds chemically.
`
`REFERENCES
`
`(1) H. V. Maulding, J. P. Nazareno,J. E. Pearson, and A. F. Michaelis.
`J. Pharm. Sci, 64, 278 (1975).
`(2) W. W. Han, G. J. Yakatan, and D. D. Maness, ibid., 65. 1198
`(1976).
`lbld. , I55, 573 (1977).
`(3)
`(4) W. Mayer, S. Erbe, and R. Voigt, Pharmazie, 27, 32 (1972).
`(5) W. W. Han, G. J. Yalratan. and D. D. Maness, J. Pharm. Sci.. Eli,
`795 (19,77).
`(6) W. Mayer, S. Erbe. G. Wolf, and R. Voigt, Pharrnazie, 29, 700
`(l974l.
`
`(7) W. H. Hong, C. Jolmston,and D. Szulczewsl:i,J. Phorm. Sci. 56,
`I703 (1977).
`(3) M. Nakano. N. Inotsurne, N. Kohri, and T. Arita, Int. J. Pharm.,
`3, 195 (1979).
`(9) N. Inotsurne and M. Nakano. J. Pharm. Sci.. 69, 1331 (I930).
`(10) N. lnotsume and M. Nakano. Chem. Pharm. Bull. , 28. 2536
`(1980).
`(11) N. Inotsume and M. Nakano, Int. J. Pharm., 6, 147 (1980).
`(12) H. Bundgaard, Arch. Pharm. Chem. Sci. Ed., 8, I5 U930).
`(13) W. P. Jencks, "Catalysis in Chemistry and Enzymology,"
`McGraw—Hill, New York, N.Y., 1969, pp. 153--242, 463---554.
`(14) W. P. Jencks. Prog. Phys. Org. Chem., 2,63 (1964).
`{I5} R. B. Martin. J. Phys.Chem.,li8,1369(1964).
`(16) W. P. Jencks, J. Am. Chem. Suc., 81, 475 (1959).
`(17) E. H. Cordes and W. P. Jencks, ibid.. 84, 4319 (1962).
`(13) Ibid., 84, B32 (1952).
`(19) lbid., 35, 2843 (1963).
`(20) J. Hine, “Physical Organic Chemistry," McGraw—Hill, New York,
`N.‘{., 1962, pp. 141-151.
`(21) J. Barrett. W. F. Smyth, and l. E. Davidson, -J. Pharm. Phar-
`macol., 25, 337 (1973).
`(22) R. ’I'. Hagel and E. M. Debesis, Anal. Chim. Acta, 78, 439
`(1975).
`(23) H. Knvarpa, M. Yamada. and T. Matsuzawa, J. Takecla Res. Lat}.,
`32, 77 (1973).
`(24) M. Fujimoto, Y. Tsulcinolri, K. Hirose, K. Hirai, and T. Ukabay-
`ashi, Chem. Pharm. Bull., 28, 1374 (1980).
`
`Extended Hildebrand Solubility Approach:
`Testosterone and Testosterone Propionate in
`Binary Solvents
`
`A. MARTIN ‘x. P. L. WU *, A. ADJEI§, M. MEHDIZADEH 1,
`K. C. JAMES *, and CARL METZLER ‘ll
`
`Received October 9, 1981, from the ‘Drug Dynamics Institute, College of Pharmacy, University of Texas, Austin, TX 78712 and the ‘Welsh
`School of Pharmacy, University of Wales, Institute of Science and Technology, Cardiff. CF)‘ 3N U , United Kingdom.
`Accepted for
`publication January 28. 1982.
`‘Present address: Abbott Laboratories, North Chicago, IL. “On leave from The Upjohn Co., Kalamazoo, MI.
`
`Abstract El Solubilities of testosterone and testosterone propionate in
`binary solvents composed of the inert solvent, cyclohexane, combined
`with the active solvents. chloroform, octanol, ethyl oleate, and isopropyl
`myristate, were investigated with the extended Hildebrand solubility
`approach. Using multiple linear regression, it was possible to obtain fits
`of the experimental curves for testosterone and testosterone propionate
`in the various binary solvents and to express these in the form of re-
`gression equations. Certain parameters, mainly K and log or-2, were em-
`ployed to define the regions of self-association, nonspecific solvation,
`specific salvation. and strong solvation or cornplexation.
`
`Keyphrases El Testosterone——extended Hildebrand solubility approach,
`solubility in binary solvents El Solubility——extended Hildebrand solu-
`bility approach, testosterone and testosterone propionate in binary sol-
`vents D Binary solvents—solubility of testosterone and testosterone
`propionate, extended Hildebrand solubility approach
`
`Solute—solvent complexes of testosterone and testos-
`terone propionate in binary solvents composed of cyclo-
`hexane with ethyl oleate, isopropyl myristate, and octanol
`have been reported previously (1). These solvents are
`pharmaceutically important; the first two are useful as
`solvents for steroid injectable preparations.
`The calculated complexation constants (1) between the
`steroids and solvents were based on a previous method (2).
`
`The solute-mixed solvent systems are analyzed here with
`the extended Hildebrand solubility approach (3), an ex
`tension of the Hildebrand regular solution theory (4) which
`was introduced to allow the calculation of solubility of
`noupolar and semipolar drugs in mixed solvents having a
`wide range of solubility parameters.
`
`THEORETICAL
`
`Solubility on the mole fraction scale, X 2, may he represented by the
`expression:
`
`-log X2 = —log X2‘ + log L!-2
`
`(Eq. 1)
`
`where X 2‘ is the ideal solu bility of the crystalline solid, and 0'12 is the so-
`lute activity coefficient in mole fraction terms. Scatchard (5) and Hil-
`debrand and Scott (4) formulated the solubility equation for regular
`solutions in the form:
`
`J
`2
`log%=log (I-2:2-303;_l‘_r‘Cl]1+Ug2"2€I12)
`
`where
`
`V 1- X
`(bl=
`l/1(] —Xz)+ 'V2X2
`
`(Eq.2)
`
`{Eq_3)
`
`The activity of the crystalline solid (a-2" ), taken as a supercooled liquid,
`is equal to X 2‘ as defined in Eq. 1. Variable V2 is the molar volume of the
`
`1334 I Journal orPham1aceuri'cal Sciences
`Vol. 71, Na. 12. December 1982
`
`
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 1
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 1
`
`0022-3549)‘ 82:’ 1200- 133450 1. CW0
`© 1982, Arnerican Pharmaceuricamssocfalion
`
`

`
`hypothetical supercooled liquid solute (subscript 2), m is the volume
`fraction of the solvent (subscript 1), R is the molar gas constant, and T
`is the absolute temperature of the experiment.
`The terms a 1 1 and (122 are the cohesive energy densities of solvent and
`solute, and n 12, referred to in other reports (3. 6) and elsewhere in this
`report as W. is expressed in regular solution theory as a geometric mean
`of the solvent and solute cohesive energy densities:
`
`the = W =lB11Cf22l”2
`
`(Eq. 4)
`
`The square roots of the cohesive energy densities of solute and solvent,
`called solubility parameters and given the symbol 6, are obtained for the
`solvent from the energy or heat of vaporization per cubic centimeter:
`
`5; = la.-:1”? = étigtwlm ; ( 1m
`When the solubility parameters and the geometric mean are introduced
`into Eq. ‘.2. the expression becomes:
`
`{Eq. 5)
`
`l0l-K G2 = Aim? ‘l’ 522 ' 25152) =‘- Aldi " 52l2
`
`lEq. El
`
`where
`
`W and obviating the need for 62. The estimated solubility, X g, with this
`method is identical to that obtained with Wm: except for rounding—off
`errors. The entire procedure, referred to as the extended Hildebrand
`solubility approach (3). may be conducted by using a polynomial re-
`gression program and carrying out the calculations on a computer. It is
`useful to include a statistical routine which provides R2, Fisher’s F ratio.
`and a scatter plot of the residuals. Terms of the polynomial (i.e., powers
`of 51) are added sequentially and the values of R2 and F, together with
`the appearance of the residual scatter plot. indicate when the proper
`degree of the polynomial has been reached. A well-known polynomial
`program using multiple regression analysis, SPSS (9), is convenient for
`this purpose.
`Parameters for Solute—Solvent lnteraction——The activity coeffi-
`cient of the solute, 012, may be partitioned into a term, cup, for physical
`or van Cler Waals (dispersion and weak dipolarl forces and a second term,
`(13, representing residual and presumably stronger solute—solvent in-
`teractions (Lewis acid—base type forces). In logarithmic form:
`
`log org = log on; + log on
`
`(Eq. 13)
`
`According to this definition of log (Y2. Eq. 11 may be written:
`
`_ V2¢l2
`2.303}? '1"
`
`(Eq- 7}
`
`where
`
`(log fl2llA = (51 ‘ 3272 + 2(t5if52 — Wl
`
`(ECL 14}
`
`By substituting Eq. 6 into Eq. 1, one obtains:
`
`{log av}!/1 = (51 - 62?
`
`(Eli 15)
`
`— log X2 = —logX2i + A05; — 52l2
`
`(Eq. 8)
`
`and
`
`which is the Hilde-brand~Scatchard solubility equation {4} for a crys-
`talline solid compound of solubility parameter 5-,; dissolved in a solvent
`of solubility parameter 6]. Equation 8 may be referred to as the regular
`solution equation; the term regular solution will be defined. The ideal
`solubility term is ordinarily expressed in terms of the heat of fusion of
`the crystalline solute at its melting point:
`
`(log cu;-.-lfA = 2lrS,¢’i-3 — W)
`
`(Eq. 16}
`
`Hildebrand et al. {10} introduced a parameter, i]2, to account for de-
`viations from the geometric mean. In terms of W, in may be written:
`
`W =l1‘l12ll5I52
`
`lECl»17l
`
`Therefore, the second right—hand term of Eq. 14, representing the residual
`activity coefficient, is:
`
`(103 Din}.-"14 ’-' 21125152
`
`'[ECl- l3l
`
`and the modified equation for solubility of a drug in binary polar solvents
`becomes:
`
`-log X2 = -lflg X2‘. + Illa] _ figlz + 2.Afi|gl{d1dg,l
`
`l9}
`
`The variable W may be related to the geometric mean, 5162, by the
`introduction of a proportionality constant, K i 11 }, such that:
`
`W = K(fi1r52}
`
`[Ex]. 20)
`
`From Eqs. 17 and 20:
`
`ll-li2l= W/(did-.al=K
`
`{Eq.2ll
`
`!'];g = I — K
`
`22}
`
`The extended Hildebrand solubility expression (Ed. 11) may now be
`written:
`
`—-log X2 = -log Xzi ‘l’ 1"l(51“d2:|2 ‘l“ 2:4“ — Kll5|52
`
`23)
`
`By employing Eq. 20 to replace W of Eq. 11, another form of the extended
`Hildebrand equation is obtained:
`
`—Iog X2 = -log X3" ‘l’ /H512 ‘l’ 522 — 2K5](l2l
`
`(Eq. 24)
`
`or, with Eq.17:
`
`—log X2 '—‘ -log X2‘. 4* r‘l.l612 + 522 " 2(l " l]2l 5152']
`
`25l
`
`It was found ( l2} that a plot of l 12 against a branching ratio, 1'', provided
`a good linear correlation for testosterone in a number of branched hy-
`drocarbon solvents.
`Variable K was employed (1!) to describe the dissolving power of
`solvents for polyacrylonitrile, and it was concluded that the solvent action
`of organic solvents on the polymer solute was determined “by a very
`delicate balance between the various intermolecular forces involved.“
`Solvent power could not be explained alone in terms of dipolar interaction
`and hydrogen bonding: it depended rather on whether dipolar and hy-
`drogen bonding energies for the solvent—polymer contacts were a few
`percentage points less than, equal to, or greater than the sum of the sol-
`
`—log‘ Xgl 2
`
`(Eq.10l
`
`_,,,,X
`
`lEq. 9}
`
`-T
`T...
`2 ‘ 2.30333"
`although this is an approximation that disregards the molar heat capacity
`difference A{.‘,, of the liquid and solid forms of the solute. An approxi-
`mation involving the entropy of fusion, AS," f. was introduced (1') as:
`I H!’
`m
`M
`T
`R
`103 1.
`to partially correct for the failure to include ACP in Eq. 9, and this form
`of log ideal solubility is employed in the current report. Equations 9 and
`10 are approximations, and currently it has not been determined which
`is more appropriate for use in solubility analysis.
`The Hildebrand- Scatchard equation (Eq. 8) may be used to estimate
`solubility only for relatively nonpolar drugs in nonpolar solvents which
`adhere to regular solution requirements. The molar volumes of the solute
`and solvent should be approximately the same, and the solution should
`not expand or contract when the components are mixed. Dipole—dipole
`and hydrogen bonding interactions are absent from regular solutions,
`with only physical forces being present. In such a system the mixing of
`solvent and solute rwnlts in a random arrangement of the molecules. The
`entropy in a regular solution is the same as that in an ideal solution, and
`therefore, the entropy of mixing is zero. Only the enthalpy of mixing has
`a finite value and it is always positive.
`In most solutions encountered in pharmacy. interactions and selective
`ordering of molecules occur; these systems are referred to as irregular
`solutions. in pharmaceutical solutions, the geometric mean rule [Eq. 4)
`is too restrictive, and Eq. 6 or 8 ordinarily provides a poor fit to experi-
`mental data in irregular solutions. Instead, 615-; is replaced in Eq. 6 by
`W = a .3. which is allowed to take on values as required to yield correct
`mole fraction solubilities:
`
`—log X2 = —log /Y2" ‘l’ M6.” ‘l' 522 —
`
`lEq.11)
`
`It is not possible at this time to determine W by recourse to funda-
`mental physical chemical properties of solute and solvent. It has been
`found, however, for drugs in binary solvent mixtures (3, 6. 3) that W may
`be regressed in a power series on the solvent solubility parameter:
`
`Wcaic = Cg ‘l’ (‘[5] ‘l’ C2151?’ + C3513 ‘l’ .
`
`. .
`
`lEq. 12)
`
`A reasonable estimate, W,.,,;,,, is obtained by this procedure, and when
`I-l/M1,, is substituted in Eq. II for W, mole fraction solubilities in polar
`binary solvents are obtained ordinarily within 320% of the experimental
`results. Log rrg/A may also be regressed directly on powers of 51, bypaming
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 2
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 2
`
`Journal of Hiarmaceutfcal Sciences I 1 335
`Vol. 71, Na. 12. December 1932
`
`

`
`
`
`
`
`0.0002530.000311-22.90.000426
`
`0.000618
`
`0.000957
`
`0.001410.001780.00649 0.02110.0577 0.1020.163 0.1800.204 0.217 0233
`
`venl.—solvent and po[ymer—polymer interaction energies. The same
`conclusions can be reached for steroids in the various solvents in the
`present study and are elaborated.
`The various extended solubility equations {Eqs. 11. 24, and 25) are
`equivalent, and the deviation of polar {or nonpolar) systems from regular
`solution behavior may be expressed in terms of (log oglf/l, (log cmlfil,
`W, 112, or K. Any one of the parameters may be regressed on a polynomial
`in 6; to obtain values of solubility, X 2. These quantities may also be re-
`gressed against the volume fraction or percent. of one of the solvents in
`the mixture or against the mean molar volume of the binary solvent
`mixture (3l. Volume percents and mean molar volumes of chloroform in
`mixtures ofcyclohexane and chloroform are given in Table I. The X2(¢.;¢;
`values may be converted to molal solubility units and, if densities of the
`solutions are available. to molar or gram per milliliter concentration.
`Solubility Parameters for Crystalline SIJIi(l.'i—ll. is not possible to
`obtain solubility parameters of crystalline drugs by vaporization using
`Eq. 5. because many organic compounds decompose above their melting
`points. Instead. it has been shown (13) that the solubility parameter of
`solid drugs can be estimated from the point of maximum solubility in a
`binary solvent such as ethyl acetate and ethyl alcohol. The solubility
`parameter of the solute must lie between the :5 values of the two solvents
`for this technique to be successful. In a regular solution, when:
`
`log X2 = log Xgl
`
`{EC}. 25)
`
`the system represents an ideal solution, and the maximum solubility is
`obtained. excluding specific solvation effects. When a pure solvent or
`solvent mixture is found that yields a peak in the solubility profile for
`a regular solution, 51 is assumed to equal 52, and the final term of Eq. 8
`becomes zero, then Eq. 26 holds.
`In an irregular solution, these relations do not hold exactly as in a
`regular solution. Equation 24 may be written as:
`
`(E0. 27)
`£003 X2‘ - loe X2) = ID?” * 5:’ + 62 - ZK5152
`The partial derivative of (log or2l;"A then is taken with respect to 15; and
`the result set equal to zero to obtain the value of ($2 at the peak in the
`solubility profile:
`
`F0003 com)
`
`0051}
`
`= 251 - 2KI5g = 0
`
`5-2
`01 = K02
`
`(Eq. 28}
`
`(Eq. 2.90)
`
`or, from Eq. 5 and the corresponding equation for the solute:
`
`I3” = K2022
`
`[El].
`
`Thus, 51 55 5-2 at the maximum in the solubility curve. but rather is equal
`to K6; (11). In irregular solutions, K is slightly greater than unity (~l.01)
`when solvation occurs between the solute and solvent; K is slightly less
`than unity (~0.93) when the species of the solution self-associate; and
`K = 1.00 when the solution is regular. As pointed out (11), a very small
`change in K can bring about large changes in solvent action; this phe-
`nomenon is considered in another report (8). Since K is nearly unity, even
`for highly solvated solutions, 62 is almost equal to (5; at the point of peak
`solubility in the system. This gives the researcher a good method for as-
`timating soluhility parameters of crystalline drugs. A differentiation
`method was introduced to obtain this value more precisely (12). Methods
`for calculating the solubility parameters of solid drugs, involving a re-
`gression of {log crglfli on 0; in a second degree power series. have been
`introduced (14. 15). Satisfactory values of 622 and K are obtained‘ by use
`of the coeflicients of the polynomial in moderately polar systems. but the
`technique is inadequate for highly irregular solutions. Another approach
`was introduced I16} to calculate 52 of solid compounds. Solubility pa-
`rameters for solutes may also he obtained by a group contribution method
`(17).
`
`EXPERIMENTAL
`
`The solubility analyses of testosterone and testosterone propionate
`in solvent mixtures ti.-9., cyclohexane—chloroform, cyclohexane—octar1ol.
`cyclohexane—isopropyl myristate, and cyclohexanenethyl oleatel were
`reported earlier (1), and the reported values were used in this study.
`
`1 The K value reported in Rel’. 15 is constant over the ran a of solvent solubility
`parameters used. It differs from K introduced 111 the extend HIldebrand_solLIb1l.1ty
`approach which has a different value for each solvent used. The term [11 Ref. 15
`apps.
`ihould properly be differentiated from K by use of another symbol, such as K,
`
`1338 I Journalo!Pham1aceurr'calSc1'ences
`Vol. N. No. 12. December 1982
`
`
`
`TableI———TestosteroneinChlorofor-m—Cyclohexaneat25°*
`
`RESULTS
`
`Testoaterone in CycIollexa.ne—Cl1lorofol-rI:1—The solubilities of
`testosterone at 25" in mixtures of cyclohexane and chloroform are found
`in Table I. The AH,,,I" value for testosterone is 6190 calfmole and Tm is
`42’l'.2°K. The —log X2‘ value is 1.1388 (X2‘ = 0.072264), and :5; is 10.90
`(cal/cm3l”2. The solubility parameter for cyclohexane is 8.19 and for
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 3
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 3
`
`
`
`
`
`
`
`«Parameters:mm!=6190caifmole;T...=42'i'.2°K,5,=10.9tcaixcmom:V2-254.5crrfi’.-‘mole;X2*=0.0?264:—logX2*"=1-1338«"Equation33‘"Equation32-
`
`

`
`chloroform is 9.14. The molar volume of testosterone is 254.5 cmsimole
`(12). The log activity coefficients are calculated using the expression:
`
`log (X2 = log X2" — log X;
`
`{Eq. 30)
`
`The values of W for the various mixtures are obtained directly from the
`solubility data. using a rearranged form of Eq. 11:
`
`1,1/=1}; 5]2+522_ ]
`A
`{Eq. 31}
`= 115 [1512 + 5-12 — (log or-2).o"A]
`Also included in Table I are the calculated values of (log a2)/A and W
`obtained by regressing (log or-2}/A and W on B1 in athird degree polyno-
`mial:
`
`W = -3298.82 + 1084,5651 - 116.90-1512 + 4267421513
`
`n = 15, R2 = 0.999, F = 6702, I~'{3,11,0.01)9 = 6.22
`
`(Eq. 32)
`
`0.0
`
`O .
`
`1.
`1:; X:
`I 11 1
`logo, nugativu
`_—
`..
`
`Solution
`kn, no-u.1u / K ‘ l“"\\
`.
`/:32 D0l'|t.lvI
`nun‘ Polunm
`
`-
`
`3
`K1-U .0726-l
`1
`2
`‘ K,
`I
`‘
`5
`1
`\‘ It
`xkfulyl: n:;lt.tvI
`
`tl
`
`12.0
`
`.
`
`14.0
`
`1
`
`"'5 "2 = 6716.38 ~ 2169.126. + 234.ao915.2 — a.534e5a.3
`
`n =15.R2 = 0.998, F = 2352, F13. 11,001} = 6.22
`
`The observed mole fraction solubilities, and the calculated values (ob-
`tained with Eqs. 30 and 33}, together with percent differences between
`calculated and observed solubilities, are given in Table I. Variables K,
`l12, and [log ah-l/A were also regressed on 51 and the equations are:
`
`(Eq. 33}
`
`Figure 1—Mole fraction solubility of testosterone (62 = 10.9) at 25° in
`cyciohexone and chloroform. Key: (0) experimental points: {—) solu-
`bility calculated by extended Hildebrand solubility approach; (- - — -)
`solubility curve calculated using regular solution theory.
`
`where the solubility parameter of testosterone is 10.9 (calfcm3]”2. Log
`X2‘ is equal to —1.1388 for testosterone at 25°. and A from Table I is
`0.1096 at 50% by volume chloroform. Continuing with Eq. 25, one ob-
`tains;
`
`K = -41.1320 + 13.768561 - 1.5035151’ + 0,05it9512513
`
`—log X2 = 1.1388 + (0.1096l{*l.8691l = 0.9340
`
`rt =15, R2 = 0.997, F = 1476, F(3,11, 0.01} = 5.22
`
`X21,;.,1¢1= 0.116 {-13.71% error}
`
`(Eq- 34}
`
`X-3.[¢.h3) = 0.102
`
`(12 = 42.1320 — 13.768561 + 150351612 — 00549512613
`
`(Eq. 35)
`
`11. = 15, R2 = 0.9911? = 1476, H3, 11, 0.01) = 5.22
`
`'‘’g‘'" = 913.4736. — 300.13.41.51? + 3237765513 — 1.1s79415.4
`
`= 15.1%? = 0.997,}? = 1476,F(4,10,0.01}= 5.99
`
`(Ec1.36)
`
`Since K = 1—1'12from Eq. 21 and {log oral/A = 23125152 from Eq. 18, any
`one of the regression equations for K, £111, and (log cm }/A can be obtained
`from the others. For example, replacing K in Eq. 34 by (1 - I12) yields
`Eq. 35 for £111. It is seen that the only differences are in the constant terms,
`-41.1320 in Eq. 34 and +42.1320 in Eq. 35, and the change in sign of each
`coefficient. Equation 36 for (log cr_o}i'A is observed to take on an inter-
`esting form: no constant term exists and the polynomial is carried to the
`fourth rather than the third power.
`Once the calculated value for one of these parameters is obtained from
`the regression equation, it may be substituted in the appropriate ex-
`pression given earlier to obtain X 21.1.1.1. For example, t121,.,,1,.1 for testos-
`terone solubility in 50% chloroforrn—50% cyclohexane Iv/V} (51 = 8.67}
`is obtained with Eq. 35:
`
`112...... = 42.1320 — 13.7es5(s.s7) + 1.5o35{s.s7)2
`—0.05495l.2(3.67l3 = -0.0362
`
`Then, from the second right hand term of Eq. 25:
`
`1°’: "9 = 5.2 + 5.2 — 2(1 — 1.21.5.5. = 13.5712 + (10.91?
`
`— 2{1 + 0.0362] (8.67) (10.9) = —l.8691
`
`9 H3, 11, 0.01) is the tabulated F value with ,o degrees of freedom in the numer-
`ator and n —
`-1 degrees of freedom in the denominator, where p = 3 is the number
`of indepen ent variables and n = 15 is the total number ofsamples. The value 0.01
`signifies that the F ratio is compared with the tabular value obtained at the 99%
`level of confidence.
`
`Variables K, .!'12, and log org are three different means of expressing
`deviation from regular solution behavior. Log org (Column 12, Table I}
`is a measure of the residual activity coefficient. due to dipolar interactions
`between solvent and solute, inductive effects, and hydrogen bonding.
`Variables K and £12 are also used to represent solution irregularities.
`When log org is negative, I12 (Column 11) becomes negative and K (Col-
`umn 10} becomes greater than unity, indicating that X 2 is greater than
`the mole fraction solubility in a regular solution. As observed in Table
`I, this effect occurs at 20% chloroform in cyclohexane. Above this con~
`centration ofchloroform, it may he assumed that the predominant factor
`promoting the solubility of testosterone is solvation of the drug by
`chloroform, most probably in this case through hydrogen bonding. At
`50% chloroform in cyclohexane, the interaction between testosterone and
`chloroform has increased sufficiently to elevate the drug solubility above
`the ideal mole fraction solubility, X 2‘ = 0.0726. At this point the total
`logarithmic activity ooefficient, log org, as well as log cm, is negative, in-
`dicating the beginning of strong solvation. It is suggested that the term
`cornplexation is appropriate for interactions between solute and solvent
`when X 2 :9) X 2‘. observed in Table I for testosterone in pure chloro-
`form.
`The various parameters, and the manner in which they may be used
`to express self-association (K < 1), nonspecific solvent effects or regular
`solution (K ; 1), weak solubilization [K > 1 and X 2 < X2‘), and com-
`plexation or strong solubilization (K > 1 and X2 > X2‘), are depicted in
`Fig. 1 for testosterone in a mixture of chloroform and cyclohexane. As
`the real or irregular solubility line crosses the regular solution line at the
`lower left side of Fig. 1, K changes from -(1.0 to > 1.0. Then, as the ir-
`regular solution line crosses the ideal solubility line, If remains > 1.0, X 2
`becomes greater than X2‘, and log 0151 becomes negative. At 100% chlo-
`roform, log or-3 = -0.506, which means that the ratio of X 2 to X2" is ~3:l.
`The curve for testosterone propionate in cl1loroform—-cyclohexane (not
`shown} is similar to Fig. 1 for testosterone, demonstrating complexation
`between the steroid ester and chloroform >3{)'3’o by volume chloroform
`in the chloroforrn—cyclohexane mixture.
`Testosterone Propionate in Mixed Solvents—The solubilities of
`the steroidal ester, testosterone propionate, at 25° in octa.nol—cyclohex—
`ane, ethyl oleate—cyclohexane, and isopropyl myristate—cyclohexane are
`plotted in Figs. 24! as a function of the solubility parameter of the mixed
`solvent. The logarithmic ideal solubility of testosterone propionate, log
`X 115, is —0.8l 356 at 25°: X2‘ = 0.15362. The solubility parameter, 5;», and
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 4
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 4
`
`Journal of Phamiaceorical Sciences 1’ 1337
`Vol. 71, No. 12. December 1982
`
`

`
`0.16
`
`0.12
`
`>3 0.03
`
`0.04
`
`
`I
`°-°°r.5
`3.0
`3.5
`9.0 as
`9.5
`10.0
`10.5
`
`11.0
`
`Figure 2—Mole fraction solubility of testosterone propionate (152 = 9.5)
`at 25° in cyclohexane and octanol. Key: (0) experimental points; (—)
`solubility calculated by extended Hildebrand solubility approach; (— - —J
`solu bility curoe calculated using regular solution theory.
`
`0.16
`
`x;=o.1sJ6
`
`0.12
`
`0.04
`
`0.0
`
`7.0
`
`0.0
`
`9.0
`
`51
`
`10.0
`
`11.0
`
`12.0
`
`13.0
`
`Figure 3-—-Mole fraction solubility of testosterone propionate (152 = 9.5)
`at 25° in cyclohexane and ethyl oleate. Key: (0) experimental points;
`(——,l solubility calculated by extended Hildebrand solubility approaclz;
`(- - -) solubility curve calculated using regular solution theory.
`
`0.16
`
`,go.oa
`
`0.12
`
`0.04
`
`°'°°6.0
`
`11.0
`
`3.0
`
`9.0
`
`10.0
`
`11.0
`
`12.0
`
`13.0
`
`Figure 4—Mole fraction solubility of testosterone propionate (52 = 9.5)
`at 25° in cyclohexane and isopropyl myristate. Key: (OJ experimental
`solubility; (——) solubility calculated by extended Hildebrand solubility
`approach;
`t'—— -) solubility curve calculated using regular solution
`theory.
`
`the molar volume. V2. of testosterone propionate are, respectively, 9.5
`(cal,-‘cm*‘)1l2 and 294.0 cm3,lmole. The solubility parameter is 8.19 for
`cyclohexane, 10.30 for octanol, 8.63 for ethyl oleate. and 8.85 for isopropyl
`myristate.
`Use of the extended Hildebrand solubility approach to calculate
`soluhilities yields good results for these systems as observed by the fit
`of the calculated line to the points in Figs. 2-4.
`As seen by comparing the regular solution curve {calculated using Eq.
`8) with the extended Hildebrand solubility line {calculated using Eq. 11,
`24, or 25}, the observed solubilities are smaller than those predicted for
`a regular solution over most of the range of 51 values of the mixed solvents,
`as contrasted to the ch]oroform—cyc-lohexane mixture. At no composition
`of mixed solvent do the solubilities exceed the ideal solubility, as observed
`
`earlier in chloroform—cyclohexane (Fig. l). The regression equations used
`to calculate solubilities in these systems are:
`Octanol—Cyclohexane Mixtures (Fig. 2):
`log (‘(2
`
`= 1142.47 - 356.23’1'51 + 37.035761? - 128137613
`
`{Eq. 37}
`
`n = 15,R2 = 0.965, F = 101, F(3. ] l. 0.01) = 6.22
`
`Ethyl 0leate—Cyclohexane Mixtures (Fig. 3):
`
`mg "2 = 27333.99 — 9367.305. + 11s4.77a.= — 45.86176.“
`
`(Eq. 38}
`
`n = 11. R2 = 0.999,F = 2589, F[3. 7. 0.01) = 3.45
`
`lsopropyl Myristate-Cyclohexane Mixtures {l“ig. 4):
`
`1°’; "2 = 157348.62 — 56733.35. + $321,486.? ~ 213.4395.“
`
`(Eq. 39)
`
`n = 11,192 = 0.999, F = 3970. F(3, 7, 0.01) = 8.45
`
`Nonlinear Regl'ession—'I‘l‘1e solubility of testosterone in octane]-
`cyclohexane and in ethyl oleate—cyc-lohexane are plotted in Figs. 5 and
`6. The extended Hildebrand solubility approach with polynomial re-
`gression. used with success for the other systems, failed to provide a
`satisfactory fit of the data. as shown by the dotted lines in Figs. 5 and
`6.
`
`The polynomial regression method contains potential nurncrical dif-
`ficulties which show themselves only in certain applications. The source
`of these difficulties may be seen by recognizing that to date the extended
`
`0.00
`
`lI;‘0. 0726!
`
`0.02 0.00
`
`0.06
`
`56 0.04
`
`‘L0
`
`0.0
`
`9.0
`
`10.0
`
`51
`
`11.0
`
`12.0
`
`13.0
`
`14.0
`
`Figure 5—Mole fraction solubility of testosterone 1'09, = I09) at 25° in
`cyclohexane and octanol. Key: I'D) experimental points; 1'-—) extended
`Hildebrand solubility curoe based on NONLlN polynomial regression;
`(.
`.
`. .) extended Hildebrand solubility curve based on ordinary p0ly~
`nomial regression; {- - - -) regular solution curoe.
`
`0.040
`
`0.032
`
`0.003
`
`0'00“ 0.1
`
`3.2
`
`3.3
`
`3.4
`
`3.5
`
`51
`
`8.6
`
`3.7
`
`8.8
`
`Figure 6-—-Mole fraction solubility of testosterone (52 = 10.9) at 25° in
`cyclobexane and ethyl oleate. Key.‘ (0) experimental points; (—) ex-
`tended Hildebrand solubility curoe based on NONLIN polynomial re-
`gression; f extended Hildebrand solubility curoe based on ordinary
`polynomial regression; ( - - -) regular solution curoe.
`
`1338 I Journal o!Pbarrr1acau1‘icsl Sciences
`Vol. 7'1. No. 1'2. December 1982
`
`
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 5
`
`MYLAN PHARMS. INC. EXHIBIT 1046 PAGE 5
`
`

`
`loglX2‘lX2l-
`
`Hildebrand solubility approach has fitted observed values of X2 W 3
`model that defines X2 as a function of :5 and other variables and constants.
`That is, the relations expressed by Eq. 11 may be Wfll-l»9Tl 353
`V2
`Vil1— Xel
`3
`..: _———- us =0 (E .40)
`2.30331" v,u-X-_»)+v,,X.,,
`I
`l
`q
`where {(6) is a polynomial in 6. Thus, Eq. 40 defines the‘ dependent
`variable X 2 as an implicit function of the independent variables 6 and
`V1, The terms X 2" , R, '1", and V-_; are known constants, and the parameters
`to be estimated are the coefficients of {(6}.
`The polynomial regression method contains a circular element in that
`it uses the observed values of X 2 in W or (log org)/A to estimate the
`coefficients of I(6), and then uses these values of fill) to obtain calculated
`values of X 2. This circular process can be thought of as the first step in
`an iteration; the conditions necessary for this process to converge are not
`known. In many applications the iteration gives acceptable results; in
`some cases. as shown in Figs. 5 and 8. the results are poor.
`Another potential source of difficulty is that the values of W or (log
`org}./A are lit by least squares to the polynomials of 5. Thus, the coeffi-
`cients are estimated by minimizing the squared deviations between ob-
`served and predicted (model) values of functions of X 2 [W or (log aglfn ].
`When X2 then is calculated, this is equivalent to weighted least squares,
`wil.h the weights being complicated functions of the constants in W or
`in (log cr2la"A.
`To use Eq. 40 as a model for predicting X -3 as a function of ii and VI,
`it must be determined that there is a unique value of X2 that satisfies the
`equality. Writing the expression in Eq. 40 as F(X 2}, it can be verified that
`lim F(Xg)x._, ..r. = w and F{X2lXg-~fl = log X-2*" < 0. Thus. F(X2l has a root
`between 0 and 1. It can also be shown that if _f(5l ‘> 0 than F ‘(X 2) < 0 for
`0 5 X 3 S 1. Thus, F (X 2) is monotonic decreasing on [0,1] and has one,
`and only one, root.
`Equation 40 can be used in any nonlinear regression program that
`accepts the model defined as an implicit function. In this application good
`inital estimates are important; they can be obtained as the coefficients
`of the polynomial in :5 used in the polynomial regression method.
`The regression equations for testosterone in ocl.anol—cyclohexane and
`in ethyl oleateecyclohexane were obtained by fitting Eq, 40 with the
`nonlinear regression program NONLIN (18). The results are:
`Testosterone in Octanol—Cyclohexanc ll-‘ig. 5):
`log or;
`
`= 395.34 - 254.0335, + 26.121751? — 0.3656035,‘-*
`
`(Eq. 41)
`
`A combination of X 25 and K may be used to define various classes of
`interaction between solute and solvent. As observed in Fig. 1, when a
`solubility point falls on or near the regular solution line, it is defined as
`a regular solution (4). Referring to Eq. 24, when K ; 1, the geometric
`mean obtains, and the solution may be considered to be a regular system.
`However, it is conceivable that W equals 5152 (i.e., K 2 1) in polar systems
`by cancellation ofsolvating and self-associating effects, rather than be-
`cause of the criteria layed down (4) for regular solution behavior.
`When K < 1, the solubility points in a graph such as Fig. 2 fall below
`the regular solution line. The solute, solvent, or both are ordinarily con-
`sidered to be sell'—associated when X «C 1, resulting in decreased solu-
`bility.
`When K > 1 and Xg > X 2‘, association of a specific nature {i.e., hy-
`drogen bonding, dipolar interaction, or charge transfer oomplexation)
`is considered to exist between solute and solvent.
`Finally. when K > 1 but X 2 < X9‘, an intermediate situation