Approaches to measure equilibrium (intrinsic) and “transient” solubility, and the

impact on dissolution and membrane transport kinetics.

Lynne S. TaylorPurdue University

Outline

• Thermodynamics of solubility, crystalline and amorphous• Solubility measurement

• Experimental approaches• Media effects• Common issues in measurement

• Supersaturation – defining based on solubility measurements versus thermodynamic considerations

• Dissolution of different solid state forms and controlling factors• Factors impacting membrane transport• Supersaturation evaluation in different media and membrane transport

Solubility – Conventional Definition

Thermodynamically Stable FormSaturated Solution Concentration = X mg/mL

Solubility – extended definition

Saturated Solution Concentration = X mg/mL

Y mg/mLZ mg/mL

Polymorph x

Polymorph y

Amorphous z

What Factors Determine Crystal Solubility?

crystal at MP

heating

liquid at RT

cooling

liquid at MP

melting

crystal at RT

+ solvent

ln𝑎𝑎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = ln 𝑥𝑥𝛾𝛾 = −∆𝐺𝐺𝑓𝑓𝑓𝑓𝑐𝑐𝑓𝑓𝑓𝑓𝑓𝑓

𝑅𝑅𝑅𝑅

ln 𝑥𝑥 = −∆𝐺𝐺𝑓𝑓𝑓𝑓𝑐𝑐𝑓𝑓𝑓𝑓𝑓𝑓

𝑅𝑅𝑅𝑅− ln 𝛾𝛾

solute-solvent interactionsSolid state properties

)298(01.0log5.0log −−−= fsolidw TPS

Simplified Thermodynamic Description

Yalkowsky’s General Solubility Equation

Jain and Yalkowsky J. Pharm. Sci. 2001

-20

-15

-10

-5

0

5

Ibuprofen Griseofulvin Telaprevir Ritonavir SucroseLn

sol

ubilit

y (m

ole

fract

ion)

LN Xideal/crystallinity

LN (gamma)/Hydrophobicity

Relative Contributions of Crystal Lattice and Hydrophobicity to Aqueous Solubility

Polymorph X

Polymorph Y

Amorphous Z

Concentration Free energy

Changing the Solid State Form Changes Thermodynamic Activity and Solubility

RTG

X

Z

eSS ∆

≈

(Supersaturation)

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

Atazanavir

TelaprevirRitonavir Warfarin

Obs

erve

d En

hanc

emen

t Rat

io

Predicted Enhancement Ratio

IbuprofenPhenylbutazone

Diclofenac

Griseofulvin

Sorafenib

4x

65x

Amorphous:Crystalline Solubility Ratios

Taylor, L. S.; Zhang, G. G. Z., ADDR. 2016 doi:10.1016/j.addr.2016.03.006

Large ΔGHigh Mpt

Small ΔGLow Mpt

Key Points

• Solubility depends on solid properties • The solubility also depends on the solvent• The solvent does not impact the thermodynamic activity of the

crystal*

*true as long as the solvent does not mix with the crystal, e.g. solvate formation

Membrane flux depends on solute activity not concentration

Twist and Zatz J. Soc. Cosmet. Chem. 1986

Increasing crystal solubility = constant flux

Saturated solutions of methyl parabens in different solvents

Large variations in concentrationSame flux value

Why?

saturated

activity solid = activity solution

3 mg/mL

300 mg/mL

Solubility measurement

• Top down• Early phase solubility• Amorphous solubility• Risks

• Unknown solid form• Solvent effects• True equilibration may not be reached

• Bottom up• Crystalline solubility• Concerns

• Equilibration time• Solid phase at end of experiment• Separation of solid and supernatant• pH

Conc

entr

atio

n

Time

Top down

Bottom up

conc

entr

atio

n

subsaturated (1 phase)

supersaturated(metastable, 1 phase)

Crystal solubility

L-L coexistance

(amorphous solubility)

“Fast” crystallizer

“Slow” crystallizer

Spinodal

time

supersaturated(unstable,2 phase)

LLPS

crystallization

Metastable boundary

Phase Transitions in Supersaturated Solutions

Media Effects

• pH• Ionic strength• Buffer species• Solubilizing components (most commonly micelles)

pH-dependent Solubility –Crystalline Drug

PosaconazolepKas: 3.6 and 4.6

)101( )( pHpKBtot

aSS −+=

Crystalline solubility

pH-dependent Solubility –Amorphous Drug

PosaconazolepKas: 3.6 and 4.6

)101( )( pHpKBtot

aSS −+=

Amorphous solubility

pH Solubility Profiles for Amorphous and Crystalline Posaconazole

Concentration of unionized form as a function of pH

0.27

9.08

33.6x

Supersaturation is ~ 33

Solubilizing Media Components

Some comments about solubility measurement• Magnetic stirrers can grind material. This may reduce particle size and

allow small particles to pass through a filter. • Chemical stability in medium should be checked for equilibration

period.• Separation method should be carefully considered• Ionic strength matters! Keep constant when measuring solubility as a

function of pH.• Check pH and adjust if necessary prior to equilibration point.• Check solid state form of drug in equilibrium with solution

(polymorph, salt, free form etc).

Avdeef A, Fuguet E, Llinàs A, Ràfols C, Bosch E, Völgyi G, Verbić T, Boldyreva E, Takács-Novák K. Equilibrium solubility measurement of ionizabledrugs–consensus recommendations for improving data quality. ADMET and DMPK. 2016 Jun 29;4(2):117-78.

21

Impact of solid state form on dissolution rate

Noyes-Whitney equation: ( )hCDACC

hDA

dtdM s

s

≈−=

Iopanoic acid

• Comparison of intrinsic dissolution rates of three solid forms: two polymorphs and amorphous solid

• IDRs are reflecting (apparent) solubility values of the solids

Stagner & Guillory, 1979, J Pharm Sci

Amorphous Form has a Faster Dissolution Rate than Crystal

0

5

10

15

20

25

0 10 20 30 40 50 60

Itrac

onaz

ole

conc

entr

atio

n µg

/ml

Time (min)

Cryst AmoQM

( )hCDACC

hDA

dtdM s

s

≈−=

Slope of amorphous form ~ 20X crystal

Bhardwaj et al. (2018). Int J Pharm 540(1-2):106-119.

Dissolution of Amorphous Solid Dispersions

23

-5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

0

10

20

30

40

50

60

70

crystalline drug controlled

Crystalline ITZ Amorphous ITZ SD HME

Rel

ativ

e D

isso

lutio

n R

ate

% Polymer

amorphous drug controlled

24

Dissolution rate of drug from an ASD can be much faster than from pure amorphous drug

Itraconazole-PVPVA system0 10 20 30 40 50 60 70 80 90

0

10

20

30

40

50

60

70

crystalline drug controlled

Crystalline ITZ Amorphous ITZ SD HME

Rel

ativ

e D

isso

lutio

n R

ate

% Polymer

amorphous drug controlled

No predictive models for these systems

supersaturated

activity solid < activity solute

S ∝ 𝐶𝐶𝑠𝑠𝑠𝑠𝐶𝐶𝑒𝑒𝑒𝑒

0 2 4 6 8

0.00

0.04

0.08

0.12

0.16

Flux

( µg/

min

)

C/Ceq

Flux ∝ Supersaturation

Supersaturation and Membrane Transport

Defining Supersaturation

eqeqeqeq cc

cc

aaS ≈==

γγ

eqeqccS γγ ≈≈ when only valid is

We can check this relationship by performing flux measurements

Supersaturation (activity based)

J is the diffusive flux across a membrane and a is activity of the solute in the solution.

D is the diffusion coefficient of the solute, h is the thickness of the membrane and γm is the activity coefficient of the solute in the membrane.

y = 0.0715x + 0.2324R² = 0.999

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70 80 90 100

Conc

entr

atio

n (u

g/m

l)

Time (minutes)

Receiver Cell BufferJ = Slope

Impact of Solubilizing Media on Crystalline and Amorphous Solubility

PosaconazoleMwt: 701 g/mol

Log P: 4.6pKa: 3.6 and 4.6

0

5

10

15

20

25

30

35

40

45

Blank Buffer V1 FaSSIF V1 FaSSIF V2 FaHIF Composite-FaSSIF

Solu

bilit

y (μ

g/m

L)

Crystalline Solubility Amorphous Solubility

0

5

10

15

20

25

30

Blank Buffer V1 FaSSIF V1 FaSSIF V2 FaHIF Composite-FaSSIF

Extent of increase in solubility

0

5

10

15

20

25

30

35

40

45

FaSSIF Buffer 1 FaSSIF V1 FaSSIF Buffer 2 FaSSIF V2 FaHIF Composite-FaSSIF

Supe

rsat

urat

ion

ratio

Media

a/a*c/c*

Activity versus Concentration-Based Supersaturation

Flux measurements are similar for the different media. Concentration-based estimates are much lower in solubilizing media

Medium Km/w at crystalline solubility Km/w at amorphous solubilityFaSSIF-V1 13.9 5.3

Composite-FaSSIF 7.4 1.9FaHIF 11.3 1.6

Explanation – Micelle-water Partition Coefficient is not Constant with Solute Concentration

Supersaturation Duration Also Depends on the Medium

0

20

40

60

80

100

120

140

Buffer FaSSIF-V1 FaSSIF-V2 FaHIF

Indu

ctio

n tim

e (m

inut

es)

Posaconazole Atazanavir≈ 2.2 fold increase

≈ 4 fold increase

Summary

• Solubility is dictated by the solid and the solvent properties• Many different values of solubility can be measured depending on

experimental set-up. Which value is important?• Current approach of defining supersaturation in complex medium is

unlikely to be predictive of transport behavior• Better estimates of supersaturation are also vital to understand

crystallization kinetics. Impact of media components on crystallization kinetics are not well understood.

Acknowledgements

• Ahmed Elkhabaz• Dana Moseson• Anura Indulkar• Geoff Zhang• Gao Yi• Tu van Duong• Patrick Augustijns• Joachim Brouwers• Vivek Bhardwaj

• FDA• NSF• AbbVie

And for fun – some cool pictures!

Posaconazole crystallized from buffer and FaSSIF-V1(with polymer)

Amorphous posaconazole precipitated in HIF