crystals, cameras, and chemical engineering: new tools for ...jbr · crystals, cameras, and...

Crystals, Cameras, and Chemical Engineering: NewTools for Monitoring Particulate Processes

Paul A. Larsen and James B. Rawlings

Department of Chemical and Biological EngineeringUniversity of Wisconsin–Madison

CBE Department Seminar – May 10, 2007

Larsen, Rawlings (Wisconsin) Imaging-based crystallization monitoring 1 / 31

Process understanding through imaging

Examples from UW-CBE

Abbott, de Pablo, Palecek groups: Polarized and fluorescence microscopy toinvestigate stem cell cultures on liquid crystal interfaces.

Kuech and Nealey groups: SEM imaging to characterize size distributionand number density of quantum dot arrays.

Yin group: Quantifying viral propagation rates.

de Pablo and Graham groups: Flourescence microscopy to characterizeconfined DNA molecules.

quantum dots confined DNA virus infection


Extracting information from images

Segmentation: Separating objects of interest from the background


Challenges for automatic image segmentation

Challenges for thresholding andedge detection-based methods:1

Non-uniform color/intensity.

Poorly-defined outline.

Challenges for template-matching:

Non-uniform size and shape.

Random orientation in 3-Dspace.

Other challenges:

Motion blur, out-of-focus blur.

Agglomeration, attrition,breakage.

1Calderon De Anda, Wang andRoberts, ChE Sci, 2005


SHARC: 2-D model-based image analysis for needles2,3

Original image

Linear feature detection Collinearity identification

Parallelism identification Cluster properties

2Larsen, Rawlings, and Ferrier, ChE Sci, 20063Patent filed by WARF, P05340US



Original image Linear feature detection

Collinearity identification





Original image Linear feature detection Collinearity identification






Parallelism identification

Cluster properties



M-SHARC: 3-D models for more complex shapes 4,5

Parameterized, wireframe model.

Viewpoint-invariant groups used as cues for location and size ofcrystals in image.

t

t

h

y

x

z

w

w

Junction Parallel pair

Symmetric pair Arrow



M-SHARC: 3-D models for more complex shapes 4,5

Parameterized, wireframe model.Viewpoint-invariant groups used as cues for location and size ofcrystals in image.

t

t

h

y

x

z

w

w

Junction Parallel pair

Symmetric pair Arrow4Larsen, Rawlings, and Ferrier, ChE Sci, 20075Patent filed by WARF, P06449US


M-SHARC example: α-glycine crystal

(a) Original image

(b) Linear features (c) Salient line group

(d) Model initialization (e) Further matches (f) Optimized Fit



(a) Original image (b) Linear features

(c) Salient line group




(a) Original image (b) Linear features (c) Salient line group





(d) Model initialization

(e) Further matches (f) Optimized Fit




(d) Model initialization (e) Further matches

(f) Optimized Fit


Low solids concentration


Medium solids concentration


High solids concentration


What we want to measure

Crystal shape

Needles glycine, α polymorph glycine, γ polymorph

Particle size distribution (PSD)

0 100 200 300 400 500

num

ber

dens

ity,

[1/m

m3]

particle length, L, [µm]

PSD


PSD estimation: definitions

ntot : Total number ofparticles

V : Total system volume

ni : Total number of particlesin size class i

ρi = ni/V : PSD, number ofparticles of size class i perunit volume of crystallizer.

0 100 200 300 400 500

num

ber

dens

ity,

[1/m

m3]


PSD


PSD estimation: definitions

ntot : Total number ofparticles

V : Total system volume

ni : Total number of particlesin size class i

ρi = ni/V : PSD, number ofparticles of size class i perunit volume of crystallizer.

0 100 200 300 400 500

num

ber

dens

ity,

[1/m

m3]


PSD a

b

d


Sampling bias by occlusion and orientation effects

Occlusion effects

Orientation effects

Projected particle lengths are less than true lengths unless particles areoriented in the plane perpendicular to camera’s optical axis.


Sampling bias by edge effects

“Clean tile” and the Buffon-Laplace needle problem

a a a

b

b

b

clean

Double

Intersection

Single

Intersection

Solomon,H., Geometric Probability, SIAM 1978


Result of ignoring edge effects

PSD estimated by counting non-border particles

Uniform distribution Normal distribution

0 0.2 0.4 0.6 0.8 1

PSD

particle length (normalized)

True PSDEstimated PSD

0 0.2 0.4 0.6 0.8 1PSD

particle length (normalized)

True PSDEstimated PSD


Maximum likelihood estimation of PSD

Definitions

ρ = arg maxρ

pX (x1, x2, . . . , xT |ρ)

ρ = (ρ1, . . . , ρT ): maximum likelihood estimate of absolute PSD

xi : number of observations of non-border particles in size class i

pX : joint probability density for X

X = (X1, . . . ,XT ): random vector in which Xi gives the number ofnon-border particles of size class i observed

Solution

Assuming X1, . . . ,XT independent (occlusion effects negligible) . . .

ρi =Xi

αi, i = 1, . . . ,T


Distribution of PSD estimates

x-y plane: PSD

01234567

02

46

8100

0.050.1

0.150.2

0.250.3

probability

PSD size class

probability



100 images

01234567

02

46

8100

0.050.1

0.150.2

0.250.3

probability

PSD size class

probability



1000 images

01234567

02

46

8100

0.01

0.02

0.03

0.04

0.05

probability

PSD size class

probability


Characterizing measurement reliability

Measurement reliability depends on a variety of factors:

Imaging conditions:

Camera resolution, R

Field of view, a,b

Depth of field, d

Process conditions:

Solids concentration (w/v), Sw

Particle length, L

Particle width, w

Factors can be lumped into single parameter denoting number of crystalsappearing in the image:

Nc =Swabd

ρcw2L

. . . but what’s really important is the amount of overlap

D = ρΩd


Constant solids concentration versus constant D

Constant solids Constant overlap (D)

0

2

4

6

8

10

3 4 5 6 7 8 9 10 11 12

Ave

.no

.of

over

laps

Solids Concentration, Sw

0.1a

0.4a0.7a

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

Ave

.no

.of

over

laps

Image difficulty, D

L = 0.1a, AR=5L = 0.7a, AR=5L = 0.1a,AR=20L = 0.7a,AR=20


Estimation of number density in presence of overlap

Number of particles identified by image analysis (IA):

n = ρα

0

20

40

60

80

100

0 100 200 300 400 500 600 700

num

ber

iden

tified

byIA

number of particles per image

Per

fect

IA




n = ρα exp(−ρΩ)

0

20

40

60

80

100

0 100 200 300 400 500 600 700

num

ber

iden

tified

byIA


Per

fect

IA

Worst-case IA




n = ρα exp(−ρΩ)

0

20

40

60

80

100

0 100 200 300 400 500 600 700

num

ber

iden

tified

byIA


Per

fect

IA

Worst-case IA

SHARC data




n = ρα exp(−ρΩθ)

0

20

40

60

80

100

0 100 200 300 400 500 600 700

num

ber

iden

tified

byIA


Per

fect

IA

Worst-case IA

SHARC dataθ = 0.4

θ = 0

θ = 1


Estimation

D = 0.1 D = 1.0 D = 3.0 D = 6.0

0

0.5

1

1.5

2

0 1 2 3 4 5 6

ρ/ρ

Image difficulty, D

MLE including overlapMLE ignoring overlap


Example: Batch crystallization of photochemical6

Simulation methods

Simulate PSD using populationbalance model.

At t = 0, 1, . . . , 7 hours,generate images correspondingto process state.

Estimate PSD from image data.

Batch Crystallizer.(Image courtesy of Ferro Pfanstiehl

Laboratories, Inc.)6Matthews and Rawlings, AIChE J., 1998


Conventional solid-phase measurement

Mirror

FiberopticProbe

00.10.20.30.40.50.60.70.80.9

1

0 1 2 3 4 5 6 7Tra

nsm

itta

nce

Time, [hours]

Surface area

Transmittance


Photochemical crystallization, t = 0 hrs

True vs measured PSD (500 images) Example image

0

0.01

0.02

0.03

0.04

0.05

0.06

0 50 100 150 200 250 300 350

wei

ght

PSD

,f w

,[g

/cm

3]

Length, L, [µm]

TrueMeasured


Photochemical crystallization, t = 1 hr


0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200 250 300 350

wei

ght

PSD

,f w

,[g

/cm

3]

Length, L, [µm]




00.10.20.30.40.50.60.70.80.9

1

0 50 100 150 200 250 300 350

wei

ght

PSD

,f w

,[g

/cm

3]

Length, L, [µm]




0

2

4

6

8

10

12

0 50 100 150 200 250 300 350

wei

ght

PSD

,f w

,[g

/cm

3]

Length, L, [µm]




0

5

10

15

20

25

0 50 100 150 200 250 300 350

wei

ght

PSD

,f w

,[g

/cm

3]

Length, L, [µm]




0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350

wei

ght

PSD

,f w

,[g

/cm

3]

Length, L, [µm]


Conclusions

Image Analysis

SHARC and M-SHARC can segment noisy, in situ images.

The algorithms enable real-time measurement of crystal shape andsize distributions.

SHARC licensed by Mettler-Toledo.

Statistical Estimation

Sampling bias due to edge effects and imperfect image analysis canbe corrected using maximum likelihood estimation.

An easy-to-implement, computationally inexpensive method forestimating PSD has been developed.


Acknowledgment

Professor Nicola Ferrier, Mech. Eng. Dept.

Image analysis consulting.

Professor Lian Yu, School of Pharmacy

Polymorphism expertise.XRPD and Raman analysis for initial glycine studies.

Dr. Philip C. Dell’Orco, GlaxoSmithKline

Imaging equipment.

National Science Foundation.


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