Design of Experiments (DOE) in the framework of Analytical ...

1

Profª. Drª Márcia Cristina BreitkreitzLaboratório de Pesquisas Farmacêuticas e Quimiometria (LabFarQui)

Instituto de Química/Faculdade de Ciências Farmacêuticas - UNICAMP

[email protected], www.labfarqui.com.br

Design of Experiments (DOE) in the framework of Analytical

Quality by Design (AQbD):

Case studies

mailto:[email protected]

http://www.labfarqui.com.br/

Supercritical Fluid Chromatography?

Compared to a liquid: lower

viscosity and higher diffusivity.

Efficient mass transfer;

Faster analysis.

Compared to a gas: better

solubilization capabilities.

Supercritical Fluid:

“Convergence

chromatography”

Rebirth of SFC

New equipments with enhanced technology: UHPSFC or “Modern SFC”

Efficient pressure control (ABPR):

Binary pump: FM: CO2 + MeOH, ACN, EtOH,

IPA, 1-30 %) + water + additives (optional)

Detectability

Repeatability, robustness

Analysis of high molecular mass and

hydrophilic compounds

UPC2 (Waters) - Ultra Performance

Convergence Chromatography.

Packed columns with sub-2µm particles

Compatible with the new equipments;

Diverse polarities:

“NP column” “RP column”

Factors to study:

Design of Experiments (DOE) in SFC

INTERACTIONS!!! Stationary phase chemistry;

Organic modifier (type and %);

Sample diluent;

Additives (type and %);

Pressure;

Temperature;

% Gradient time/slope;

Flow rate.

...

Temperature vs % MeOH Pressure vs % MeOH

6

≠ Antihypertensive drugs - SFC

Mostly basic and polar compounds: Very challenging!

They can be prescribed isolated or associated

(combined theraphy):

The goal was to develop a single and fast

method by SFC for the assay of the main

antihypertensives (multiproduct approach)

7


Factors - 1 0 + 1

NH4HCO2 concentration (mmol L-1) 0 10 20

% Binicial (MeOH:H2O 95:5 v/v) 10 15 20

Temperature (°C) 25 40 55

Pressure (psi/MPa) 1595/11.0 1885/13.0 2175/15.0

MeOH necessary to elute

the polar compounds

Step 01:

Full factorial design (24) with five replicates at the central point to study

the influence of:

NH4HCO2 (additive),

Initial concentration of the modifier - MeOH:H2O 95:5 v/v (% Binitial),

Pressure;

Temperature

What we already knew:

8Fixed factors:

Flow rate: 1,0 mL/min; % Bfinal = 45 % Gradient time: 3.0 minutes; Diluent: Isopropanol; Injection volume: 1,0 μL

Without the Additive:

≠ Antihypertensives drugs - SFC

Retention of Propranol (P)

is increased by decreasing

the % B however peak

shape is worsened

Coelution of Atenolol (A)

and Clortalidone (C) in

every condition without the

additive;

Pressure does not

influence much the overal

results.

9

Separation of atenolol and

chortalidone is achieved by

adding 20 mmol NH4HCO2

When we look at 10 % B

(advisable for retention of

propranolol), there is a huge

baseline instability – specially

for lower pressure values

which impairs the

quantification of propranolol

≠ Antihypertensives drugs - SFC

20 mM of NH4HCO2:

10


And what if we increase temperature?

We solve the

problem of

baseline

instability for

high pressure

values!

11


10 mM AmF is

enough to provide

separation of A

and C;

15 % of modifier is

enough to provide

adequate retention

of propranolol;

T = 40 °C and P =

1885 psi

Is enough to avoid

baseline instability

Retention and peak

shape

Separation

@40 °C

Center points results:

RESULTS OF 5

REPLICATIONS!!!

Always check your repeatability!!

Not critical - to be solved

in the next step!

12

The center point region was

adopted as the most

promissing region for the next

optimization step.


Screening step

acomplished its purpose:

Provide understanding of

the influence of the

factors and guidance

towards the Optimization

step

13

Central Composite Design (CCD) as na Optimization Design;

Temperature and gradient strength are key parameters for the separation;

Pressure and flow rate were included as they influence the fluid density and represent a

fine adjustment of the chromatographic parameters.


Factors - α - 1 0 + 1 + α

Temperature (°C) 15 25 35 45 55

Gradient time (min) 1 2 3 4 5

Pressure (psi/Mpa) 1885/13,0 2030/14,0 2175/15,0 2320/16,0 2465/17,0

Flow rate (mL min-1) 0,80 0,90 1,00 1,10 1,20

Final % B = 50 % to garante the elution of all compounds;

14

↓T ↑Rs L/H↓T ↑Rs A/C

Attention: Crossover here!


Effect of temperature:

15

↓tg ↑Rs A/C

↓tg ↓Rs L/H


Effect of gradient time:

16


Effect of the flow rate:

↓F ↑Rs A/CFlow rate does not affect

separation of H/L!!

17


Effect of the ABPR:

ABPR does not influence the separation of

critical pairs, but influences on the peak

width of propranolol

18


-1

-0,75

-0,5

-0,25

0

0,25

0,5

0,75

1

A B C D AB AC AD BC BD CD A² B² C² D²

Separation of A and C

-1

-0,75

-0,5

-0,25

0

0,25

0,5

0,75

1


Separation of L and H

-1

-0,75

-0,5

-0,25

0

0,25

0,5

0,75

1


Propranolol peak width

In red: significant coefficients (and those to support hierarchy). The

bars erros indicate 95 % confidence intervals.

Subtitles:

A = T

B = ABPR

C = tgD = F

The shorter gradient time favors separation of A and C and

reduces the width of P;

The lower temperature favors the separation of L and H;

A higher flow rate improves peak shape of P, although it affects

the separation of A and C.

Coefficients of the models:

19

≠ Antihypertensive drugs - SFCDesign-Expert® Sof twareFactor Coding: ActualSeparation A/C

Design points abov e predicted v alueDesign points below predicted v alue1.0537

1

X1 = A: TemperatureX2 = C: Gradient time

Actual FactorsB: ABPR = 2175D: Flow rate = 1

1

2

3

4

5

15

25

35

45

55

0.98

1

1.02

1.04

1.06

1.08

Se

pa

ratio

n A

/C

A: Temperature (°C)

C: Gradient time (min)

Design-Expert® Sof twareFactor Coding: ActualSeparation L/H

Design points abov e predicted v alue1.07688

0.951447



2

2.5

3

3.5

425

30

35

40

45

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

Se

pa

ratio

n L

/H

A: Temperature (°C)C: Gradient time (min)

Design-Expert® Sof twareFactor Coding: ActualUSP width P

Design points abov e predicted v alueDesign points below predicted v alue0.0992

0.0521

X1 = C: Gradient timeX2 = D: Flow rate

Actual FactorsA: Temperature = 35B: ABPR = 2175

0.9

0.95

1

1.05

1.12

2.5

3

3.5

4

0.05

0.06

0.07

0.08

0.09

0.1

US

P w

idth

P

C: Gradient time (min) D: Flow rate (mL/min)

Separation of A C

(F = 1.00 mL min-1 and ABPR = 2175 psi)

Separtion of L and H

(F = 1.00 mL min-1 and ABPR = 2175 psi)

Peak width (USP) of P (T = 25 °C and ABPR =

2175 psi)

Tg and Temperature interaction

Temperature quadratic coefficient

Tg quadratic coefficient


(T = 25 °C e ABPR = 2117 psi)

Design Space or Method Operabe Design Region:

Design Expert – Overlay plot Fusion - Desirability


(F = 1,00 mL min-1 e tg = 1,50 min)

Design-Expert® Sof twareFactor Coding: ActualOv erlay Plot

Separation A/C CI LowSeparation L/H CI LowUSP width P CI High

X1 = A: TemperatureX2 = B: ABPR

Actual FactorsC: Gradient time = 1.5D: Flow rate = 1

15 25 35 45 55

1943

2059

2175

2291

2407

2523Overlay Plot


B: A

BP

R (

psi)

Separation A/C: 1.042

Separation A/C CI: 1.042

Separation L/H: 1.035

Separation L/H CI: 1.035

USP width P: 0.07USP width P: 0.07

USP width P CI: 0.07

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≠ Antihypertensive drugs - SFCDesign-Expert® Sof twareFactor Coding: ActualOv erlay Plot

Separation A/C CI LowSeparation L/H CI LowUSP width P CI High



15 25 35 45 55

1

2

3

4

5Overlay Plot


C: G

radie

nt tim

e (

min

)

Separation A/C: 1.042Separation A/C CI: 1.042

Separation L/H: 1.035

Separation L/H CI: 1.035

(F = 1.00 mL min-1 ABPR = 2117 psi)

Design-Expert® Sof twareFactor Coding: ActualDesirability

1.000

0.000



15 25 35 45 55

1

2

3

4

5Desirability


C: G

radie

nt tim

e (

min

)

0.2

0.4

0.4

0.6

Final conditions:

T = 25 °C

ABPR = 2117 psi (14,6 MPa)

F = 1.00 mL min-1

tg = 1.50 min

D = 0,746

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VITAMINA NOME GENÉRICOFÓRMULA

MOLECULAR

MASSA

MOLAR (g/mol)pKa LogP ESTRUTURA

A Palmitato de Retinol C36H60O2 524,86 7,04 13,60

D3 Colecalciferol C27H44O 384,64 18,38 7,50

E Acetato de a-tocoferol C31H52O3 472,74 10,80 7,59

B1 Tiamina C12H17N4OS 265,35 15,50 -2,11

B2 Riboflavina C17H20N4O6 376,37 6,97 -1,46

B3 Nicotinamida C6H6N2O 122,13 13,39 -0,45

B6 Cloridrato de Piridoxina C8H11NO3 169,18 9,40 -0,57

B12 Cianocobalamina C63H88CoN14O14P 1355,29 1,84 0,67

CÁcido Ascórbico C6H8O6 176,09 4,36 -1,58

B9 Ácido Fólico C20H23N7O7 441,37 3,37 -1,20

Liposoluble vitamins

(LSV)

Hydrosoluble

vitamins (HSV)

Very different

characteristics!

ACQUITY UPC2 BEH 1.7 µm. 2.1mm x 100mm;

ACQUITY UPC2 HSS C18 SB, 1.8 µm, 2.1mm x 50mm;

ACQUITY UPC2 CSH Fluoro-Fenil, 1.7 µm, 2.1mm x

50mm;

ACQUITY UPC2 Torus 2-PIC (2-Picolilamina) 1.7 µm,

2.1mm x 50mm;

SP Screening:

Retention curves for all SPs, with different

modifiers: MeOH, ACN, isopropanol (IPA);

With and without additives: NH4HCO2, H2O, NaOH,

NH4OH, triethylamine;

≠ Vitamins - SFC

The screening step is a very

flexible step, sometimes there is

no need for a formal DOE.

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Fato

r d

e R

ete

nção

% MeOH

Vitamin A - Metanol

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Fato

r d

e R

ete

nção

% Acetonitrila

Vitamin A - Acetonitrile

0

10

20

30

40

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

Fato

r d

e R

ete

nção

% 2-Propanol

Vitamina A - 2-Propanol

Adequate retention

only in C18 column for

LSV no matter the

modifier used!

MeOH was selected

due to the higher

chromatographic strength

to elute the HSV;

NH4HCO2 was

important for HSV.

≠ Vitamins - SFC

ACQUITY UPC2 BEH

ACQUITY UPC2 HSS C18 SB

ACQUITY UPC2 CSH Fluoro-Fenil

ACQUITY UPC2 Torus 2-PIC

Retention curves:

Factor Level - Central Point Level +

MeOH at the end of

gradient (%)20 25 30

Pressure (psi) 1500 2000 2500

Temperature (°C) 30 40 50

Responses: Retention factors (to understand the

system); Assymmetry factors; Resolution; Number of

Plates; Area.

Optimization – Central Composite Design: Study of the fluid density:

≠ Vitamins - SFC

Important interaction between

pressure and %B

Retention of LSV: low significance regression: not much affected by the

experimental variables, except the pressure:

≠ Vitamins - SFC

Higher regression significance for HSV!

Temperature Effect

Interaction!

No lack of fit!

≠ Vitamins - SFC

50 °C

DOE tells you when it is not ssible to achieve the a

certain value, no matter what you do!!

30 °C

≠ Vitamins - SFC

Asymmetry:

Area: Unchanged for Vit A, E, D, B2, B3, B6

Significant regression for Vit B1 e Vit C

Vit B1: Not detected in some conditions

Vit C: 30 °C

50 °C

Degradation?

≠ Vitamins - SFC

Number of plates: Important for HSV;

% MeOH and Temperature are the most importante variables:

Vit. C:

30 °C 50 °C

≠ Vitamins - SFC

Desirability: Selected conditions: 30% of MeOH, 30°C. Pressure

does not influence the responses when working with

30 % of MeOH = Subcritical conditions: MP has the

density of a liquid.

Vitamins that never eluted:

(Limitation of the technique)

B12 B9

≠ Vitamins - SFC

1. Vit. E, 2. Vit. A, 3. Vit. D,

4. Vit. B3, 5. Vit. B6, 6. Vit.

B2, 7. Vit. C.

33

≠ Losartan and Amlodipine - HPLC

Development of a stability indicating method for the association of the drugs

Losartan Potassium and Amlodipine Besylate by High Performance Liquid

Chromatography Design of Experiments.

Amlodipine Besylate Losartan Potassium

= Combined theraphy

+

34

Stability indicating method:

RDC 53/2015 (ANVISA): "Validated methods, capable of detecting, over the time,

low concentrations of degradation products and properly

separate all substances present in the sample"

Step 1: Column, modifier and pH screening for both

drugs;

Step 2: Optimization with the degraded sample -

mixture of the main degradation products of the two

drugs!

Forced degradation studies

Potencial Profile

Real Profile

Without

standards


35

Columns:

XTerra MS C18 3.5 µm - 3.0x100 mm

XSelect HSS C18 µm 5 µm – 4.6x150 mm

Nova-Pak C18 4 µm – 3.9x150 mm

CORTECS C18+ 2.7 µm – 4.6x150 mm

XSelect CSH Fluoro-Phenyl 3.5 µm – 4.6x150 mm

pH range from 2.5 to 6.0.

Organic modifiers: ACN and MeOH.

Low resolution and high asymmetry for amlodipine peak with both modifiers in

the whole pH range.

pH


36


37

Zoom

Zoom Zoom


38

Amlodipine forced degradation:

Degradation routes: acidic and oxidative.

(Basic to a lesser extent)

Basic degradation (0,1 mol L-1)


Acidic degradation (0,1 mol L-1)

Oxidative degradation (3%)

Control

90% assay

80% assay

The same degradation products were formed

by acidic and oxidative degradation!


39

Main degradation route: oxidative

Losartan forced degradation:

Control

Acidic degradation (0,1 mol L-1)


Oxidative degradation (3%)


40

“Worst scenario sample”: mix

of samples degraded under

acidic/ basic (Amlodipine) and

oxidative conditions (Losartan).

Acidic degradation (Amlodipine)

Basic degradation (Amlodipine)

Oxidative degradation (Losartan)


4141

Central Composite Design:

Factors (-1) (+1) - α + α Responses

pH 3 4 2,5 4,5Peak purity; Tailing

factor; Number of

plates; Resolution

Temperature (°C) 28,8 36,3 25 40

Flow rate (mL min-1) 0,8 1 0,7 1,1

Data treament:


42

Source SSQ DF MSQ Fcal P-value Interpretation

Modeo 6,70E+08 9 7,44E+07 26,36 0,0011Significant

A-Flow rate 1,01E+08 1 1,01E+08 36,01 0,0018Significant

B-pH 4,03E+07 1 4,03E+07 14,3 0,0129Significant

C-Temperature 8,19E+07 1 8,19E+07 29,05 0,0030Significant

AB 1,09E+08 1 1,09E+08 38,64 0,0016Significant

AC 4,08E+05 1 4,08E+05 0,14 0,7192Not significant

BC 6,43E+05 1 6,43E+05 0,23 0,6532Not significant

A² 1,29E+07 1 1,29E+07 4,56 0,0857Not significant

B² 3,21E+08 1 3,21E+08 113,89 0,0001Significant

C² 2,74E+07 1 2,74E+07 9,73 0,0263Significant

Residuals 1,41E+07 5 2,82E+06

Lack of fit 5,84E+06 3 1,95E+06 0,47 0,7333Not significant

Pure Error 8,26E+06 2 4,13E+06

Total 6,83E+08 14

The importance of Design

selection

Regression is significant

Model is adequate

Ex: ANOVA - peak purity of losartan:


43

T = 28°C 32°C 36°C

Conditions selected for validation within the

DS: Flow rate: 0.95 ml min-1; pH 3.2;

Temperature 28 °C.


Peak purity of Losartan: 99.67

Peak Purity of Amlodipine: 99.33

Tailing Factor of Losartan: 1.46

Tailing factor of Amlodipine: 1.39

44 Method was validated according to RDC 166/2017.

0

50000

100000

150000

200000

250000

300000

350000

0 5 10 15 20 25 30 35 40 45

Tempo (min)

Potencial degradation profile –

worst case scenario


Very interesting application:

Considering Monte Carlo simulation:

≠ From literature

Average predictions:

Final remarks

Systematic way for method development;

Identification of interactions. Cause and effect

understanding; modelling of the chromatographic

parameters as functions of the experimental variables;

Knowledge of the method: Best performance

conditions, edges of failure. Robustness brought into

development;

Commercial software integrated with the chromatographs:

Recognition by Regulatory Agencies (validation concepts

are being revised!).

DOE in chromatography:

Profª. Márcia Cristina Breitkreitz

Chemistry Institute/Faculty of Pharmaceutical Sciences - UNICAMP

[email protected], www.labfarqui.com.br

Acknowledgments

mailto:[email protected]

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