Mueller imaging polarimetry for biomedical research

Tatiana Novikova1, Jean Rehbinder1, Stanislas Deby1, Angelo Pierangelo1, Pierre Validire2, Abdelali Benali2, Brice Gayet3, Benjamin Teig4, André Nazac5, François

Moreau1 and R. Ossikovski1

1 LPICM, CNRS, Ecole polytechnique, Université Paris-Saclay, Palaiseau France

2 Département d'Anatomopathologie de l'Institut Mutualiste Montsouris, Paris, France

3 Département médico-chirurgical de pathologie digestive de l’Institut Mutualiste Montsouris, Paris, France

4 Service d’anatomie pathologique, CHU de Bicêtre, Le Kremlin-Bicêtre, France

5 Service de gynécologie et obstétrique, CHU de Bicêtre, Le Kremlin-Bicêtre, France

June 1, 2017, Photonics Summer School, Oulu, Finland

Outline

• Stokes-Mueller formalism

• Mueller matrix images of colon – Early cancer detection

• Mueller matrix images of uterine cervix – Mueller matrix images of fresh specimens

– Mueller matrix images of fixed specimens

• Conclusions

2

Polarization of light

The light propagation in time and space can be fully described by Maxwell’s equations. This varying spatio-temporal field has vectorial nature.

What kind of temporal evolution of the electric field vector E(r,t) occurs in a given point of space?

1. If the temporal evolution does not change in any fixed point of space => light is said to be polarized. NB: it is not necessarily the same in two different points in space.

2. Otherwise the light is said to be partially polarized or non-polarized

S. Huard, Polarization of Light (Wiley, New York, 1997). 3

4

Polarized monochromatic wave

0

)cos(~

)cos(~

0

),( yy

xx

y

x

kztE

kztE

E

E

tz

E

Linear

Circular

Elliptical

)exp(Re),( krErE tjt

Ellipse of

polarization

Monochromatic plane wave

Jones formalism We define the Jones vector E - field

complex amplitudes as:

y

x

yy

xx

E

E

jE

jE

)exp(~

)exp(~

E

Examples of Jones vectors of polarized light

e > 0 e < 0

Jones matrix J describes the transformation

of the Jones vector by the interaction of

the polarized light with an object

iny

inx

yyyx

xyxx

outy

outx

E

E

JJ

JJ

E

E

5

H V 45° -45° Left C Right C Elliptical

Correlation matrix of 2 complex components of electric field

Stokes formalism y

x

θ

ε

Partially polarized light

• « disordered » motion of the electric field vector

• only probability distribution of E can be defined

Linear optics (intensity measurements)

• only the second moments of the probability distribution of E are relevant

**

**

yyxy

yxxx

EEEE

EEEEC

Stokes vector

**

**

**

**

3

2

1

0

xyyx

xyyx

yyxx

yyxx

RL

4545

yx

yx

EEEEj

EEEE

EEEE

EEEE

II

II

II

II

V

U

Q

I

S

S

S

S

S

6

Degree of polarization

)10(

I

VUQ 222

Coherence vector

Tyyxyyxxx EEEEEEEE ),,,(' ****C

in

in

in

in

out

out

out

out

S

S

S

S

MMMM

MMMM

MMMM

MMMM

S

S

S

S

3

2

1

0

44434241

34333231

24232221

14131211

3

2

1

0

Sin Sout

M

Sout=M·Sin

Linear optical system is characterized by the real

4×4 matrix which is called Mueller matrix

Stokes formalism: Mueller matrix

Mueller matrix M

7

General principle of any polarimetric technique

Source

PSG

Sample

PSA Detector

• In order to determine optical properties of the sample one needs to measure

polarization changes occurring in the probing beam light after interaction with the

sample.

• Initial polarization state of the beam is defined by Polarization State Generator

(PSG). The output state is analyzed by Polarization State Analyzer (PSA)

followed by a detector, according to the general schema outlined above.

• Typically, the incident polarizations defined by the PSG and those detected by

the PSA may vary during a given experiment.

8

Interpretation of Mueller matrices

So what to do when a model is not readily available?

Experimental Mueller matrix

EM model relating the physical properties of measured structure to M

Classic physical approach

Phenomenological approach

Experimental Mueller matrix

M1 M2

M3

Lu-Chipman product decomposition represent any depolarizing M as a series combination of three basic blocks: diattenuator, retarder and depolarizer

M = MΔ MR MD 9

…..

S. Y. Lu R. Chipman, JOSA A 13(5) 1106 (1996)

Mueller matrix imaging polarimeter

Multi-spectral visible wavelength Mueller matrix imaging system installed and tested at IMM Anatomopathology Department, Paris, France

10

Cancer evolution

11

Source: http://www.ndhealthfacts.org/wiki/Oncology_%28Cancer%29

Epithelial cancer > 80%

• Epithelial tissues line the cavities and surfaces of organs throughout the body

• Epithelial layers contain no blood vessels, so they receive nourishment via

diffusion of substances from the underlying connective tissue

11

Colon specimens: early stage cancer

Colon

Cancer

Healthy

tissue

Mueller matrix images taken at 550 nm

Common features

•Mueller matrices are diagonal :

tissues exhibit depolarization, wihout

signifiant retardation nor diattenuation

•M22=M33>M44, meaning that circularly

polarized light is more depolarized

than linearly polarized light. This

behaviour is typical of « small »

scatterers (Rayleigh regime)

•Depolarization increases with

wavelength in the visible, probably

due to decrease of absorption

•Tumoral tissue is less depolarizing

than healthy tissue, at all wavelenghts

from 500 to 700 nm. T. Novikova et al., OPN, OSA, October 2012

12

5 c

m

htt

p:/

/ca

ncerq

uest

.em

ory.e

du

/in

dex.c

fm?

pa

ge=

4062

Normal CIN I CIN II CIN III

Larger

and

more dense

nuclei!!

Histological

slides

of cervical

tissue

Cervical

Intraepithelial

Neoplasia

Diagnosis of cervical cancer

300 µm

• Cervical cancer is the second most frequent cancer affecting women, and causes 275 000 deaths per year worldwide mostly in developing countries

.

• In the vast majority (95 to 98%) of cases the disease is due to infection by various types of Human Papillomavirus (HPV)

13

(Medical diagnostic procedure

to examine an illuminated,

magnified view of the cervix)

(Cytology) (Histology)

Diagnosis of cervical cancer

Colposcopy: Precancerous (CIN2+) lesions are very difficult to visualize. Results are very operator dependent.

Conization : the surgical margins are poorly defined

Screening : Systematic Pap smear cannot be implemented in low income countries.

14

15

Polaimetric images of cervical specimens 2 c

m

Intensity image

A. Pierangelo et al., Opt. Express 21 (12), 14120 (2013)

Mueller matrix images of uterine cervix

Pathology map

16

Lu Chipman product decomposition M = MΔ MR MD

Ex vivo images of uterine cervix specimen

A. Pierangelo et al., Opt. Express 21 (12), 14120 (2013)

Depolarization @500nm Pathology map Scalar retardance @500nm

Healthy

CIN3

Healthy

CIN3

Healthy

CIN3

50°

0°

1

0

(a) (b) (c)

2 c

m

• Intensity and polarimetric images of a healthy cervix (the positions of histological cuts, which confirmed that the sample was healthy, are shown with white lines)

Depolarization @550nm

Intensity image

Scalar birefringence @550nm

Ex vivo images of fresh cervical specimen

A. Pierangelo et al., Opt. Express 19 (2), (2011) 17

18

Typical experimental trends

• Healthy cervical tissue exhibits a significant birefringence

• Birefringence disappears already at stage CIN1

• Depolarization values: glandular < CIN3 < CIN2 < CIN1 <

healthy squamous epithelium

Ex-vivo studies of fixed cervical specimens

Mueller matrix

Fixed conization

specimen

19

17 patients

Tag Type of tissue

HSE Healthy squamos epitelium

SEM Squamous epithelium metaplasia

GE Glandular epithelium

CIN1 Cervical intraepitelial neoplasia (mild)

CIN2/3 Cervical intraepitelial neoplasia (moderate-severe)

Histological diagnosis mapping

CIN1

CIN2/3

HSE

SEM

GE

Scalar retardance (550nm)

Conization specimen

20

Sensitivity and specificity

Test of MP technique with gold standard histological diagnosis

Disease No disease

Postive test TP FP

Negative test FN TN

Se = 𝑇𝑃

𝑇𝑃 + 𝐹𝑁 Sp =

𝑇𝑁

𝑇𝑁 + 𝐹𝑃

Ability of test technique to correctly detect disease

Classical colposcopy: Se~60-70%

Ability of test technique to correctly detect healthy conditions

Classical colposcopy: Sp < 50%

21

Scalar retardance treshold = 5°

22

First statistical evaluation

Scalar retardance treshold = 10°

23

First statistical evaluation

Scalar retardance treshold = 15°

24

First statistical evaluation

25

Scalar retardance treshold = 20°

First statistical evaluation

26

Scalar retardance treshold = 25°

First statistical evaluation

J. Rehbinder et al J. Biomed. Opt. 21(7) (2016) 27

First statistical evaluation

AUC = 0.9

Conclusions

• Enhancement of contrast between healthy and cancerous zones on polarimetric images using Lu-Chipman decomposition of Mueller matrices

• Light is mainly backscattered by small scatterers in our experiments

• Dumping of scattering and increase of absorption better preservation of backscattered light polarization from cancerous zone

• Depolarizing and birefringent healthy uterine cervix

28

T. Novikova et al., OPN, OSA, October 2012

Thank you for your attention

29

Acknowledgement for funding: • PAIR Gyneco project of INCa • French ANR TWIST4NET project • CampusFrance POLHIS project

Dr Tatiana Novikova gratefully achowledges the sponsorship of OSA Traveling Lecturer Program