Simulations

Intro
Simulations
Validation
Applications
Fluorescence Cross-Correlation
for Flow Mapping:
to monitor dynamics in parallel
on extended field of views
direct applications to:
-hemodynamics in microcapillary bed
-neurophysiology
-chaotic dynamics in soft matter.
Giberto Chirico
Università degli Studi di Milano-Bicocca
Dipartimento di Fisica G. Occhialini
Intro
Validation
Simulations
Applications
Fluorescence Correlation Spectroscopy
(FCS)
open
confocal
volume
Fluorescence
Intensity I(t)
Information from Noise
Time
• Brownian diffusion
• Directional flow
• (Photophysical reactions)
Auto- and cross-correlation functions
Intro
Simulations
Validation
Applications
Auto-correlation Function
1.0
V=100 µm
G()
0.8
0.6
0.4
0.2
beam waist
0.0
1E-5
1E-4
1E-3
0.01
Lag time  (s)
D = diffusion coefficient
Diffusion & Drift
two relaxation times
V = drift velocity
0.1
Validation
Simulations
Intro
Applications
Cross-correlation Function
I1(t)
flow
t
Time
Detector1
Detector2
t
R
Time
τV,R
I2(t)
flow
t+τ
Detector1
Detector2
Cross-correlation
t
t+τ
Time
Intro
Validation
Simulations
Applications
Cross-correlation Function
R
flux
ω0
1
ω0
V
2
For a stationary flow with drift speed
V:
Quasi-Gaussian
component
de-coupled
Brownian diffusion
Drift
Intro
Validation
Simulations
Applications
Simulations: Auto vs Cross


2


τ
G (τ ) ≅ exp  −

2

τ
(
)
τ
ω
+
1

D 0 
τ D  




2

R − Vτ 
G (τ ) ≅ exp −

2

τ
 ω0 1 + τ  
D 


τD=2-4-30 ms
τD=4ms
τV<ττD
V=500 – 125 µm/s
τ max − τ V ,R = ατ D
0.3 ms < τV < 12 ms
10µm
20µ
µm
|R|=10µm
V=2000 – 125 µm/s
Sampling time
4 ms
Vmax ≈ 8000 µm/s
τ V ,R
R
=
V
Large diff times
…. are «better»
Validation
Simulations
Intro
Applications
Implementation of
Fluorescence Correlation Spectroscopy
on Imaging
Intra-image
(correlate over an image)
RICS….
Drilling through
a stack
STICS….
or a line
SLICS….
Intro
Simulations
Validation
Applications
Fluorescence Correlation Imaging
(SFCS)
Gratton, J.Biom. Opt. 2010
Digman, Biophys. J, 2009
Intro
Simulations
Validation
Applications
Fluorescence Correlation Imaging
(RICS)
Diffusion coefficients
on
uniform Region of Interest
Correction for the
Immobile fraction of
Fluorophores.
Intro
Simulations
Validation
Applications
Fluorescence Correlation Imaging
(STICS)
Velocity map of EGFP/α-actin
flux on retracting lamellar extension
of CHO cell plated on fibronectin
Herbert 2005, Biophys. J.
Intro
Simulations
Validation
Applications
Fluorescence Correlation Imaging
ON PIXELATED DETECTORS
• Hardware implementations
Blood Flow
•
Software implementations
Cell-cell interaction map
•
Validation on STICS
Validation
Simulations
Intro
Applications
Hardware Implementations:
dedicated multispot CCD system
Flux in
Flow out
EM-CCD Detector
Image stack
Advantages:
• variable interspot distance R
• pixelated detector for two
spots detection
• dual spot scanning
NIR LASER
Twyman-Green
Interferometer
250 fps
Intro
Simulations
Validation
Test of the dual spot system: - linearity vs. R
- detection of D
Rodamine D=300±30um2/s
(V=310±10um/s)
Gold Nanorods D=12±1um2/s
(V=195±2um/s)
gold nanorods (16x48 nm)
in square microcapillary at
different spots distances:
R=3-4-14-17 um
V=270±10um/s
Applications
Intro
Validation
Simulations
Applications
Scanning along the capillary:
velocity profile
|R|
100 nm fluorescent microbeads
d=720±20 um
d
flow
1 2 3 4 5 6 7 8 9 10 11 12 13
1 2 3 4 5 6 7 8 9 10 11 12 13
F
L
O
W
Pozzi, Chirico, Mapelli, Gandolfi, D’Angelo et al. JBO, 2014
fimage=200Hz, pixel=7.4 um
N=42 pixels
Intro
Simulations
Validation
Zebrafish
Model system: Zebrafish embryo
- Cold-blooded tropical freshwater teleost with two-chamber heart morphology
- Simple and regenerative heart and circulatory system
- Modeling of blood clotting, blood vessel development, heart failure
- Two main vessels:
dorsal aorta, cardinal vein
(typical diameter ≈ 15-20 υm)
Endothelial Cells expressing GFP
Red Blood Cells expressing DsRed
Intro
Validation
Simulations
Zebrafish
Dual-Spot Cross-correlation Spectroscopy
FLOW ACROSS VEIN AND ARTERY
embryos 4 dpf
vein 50%
F
L
O
W
0.03
GX1,2(τ)
0.00
artery 20%
0.04
V(vein) = 630±70 um/s
0.00
V(s20%)= 980±120 um/s
V(d20%)= 420±40 um/s
V(s50%)= 1420±200 um/s
V(d50%)= 380±20 um/s
artery 50%
0.03
0.00
10
0.03
1000
Lag time [ms]
0.00
10
Pozzi JBO 2014
100
100
Lag time [ms]
Validation
Simulations
Intro
Zebrafish
Dual-Spot Cross-correlation Spectroscopy
vessel
scan
SPEED PROFILES ACROSS VEIN AND ARTERY
4dpf, 50half-way heart-tail
1400
R=40υm
0.06
(D)
(C)
0.04
1200
1000
0.25d
V [µ m/s]
GX1,2(τ)
flow
400
0.02
300
0.125d
(B)
(A)
0.08
700
650
V [µm/s]
GX1,2(τ)
0.00
0.04
600
0.125d
0.25d
0.00
10
100
lag time [ms]
0
10
20
30
vessel radialcoordinate [µm]
550
Pozzi et al., JBO 2014
Validation
Simulations
Intro
Zebrafish
Dual-Spot Cross-correlation Spectroscopy
vessel
F
L
O
W
scan
SPEED PROFILES: SENSITIVITY TO THE FLUX DIRECTION
(i,i)
Method
strength
(i-1,i)
(i,j)
GX1,2 (τ)
0.08
i-2
i-1
flow
i
i+1 i+2
0.04
(i+1,i)
i-2
i-1
i
(i+2,i)
i+1 i+2
(i-2,i)
0.00
0
50
100
lag time [ms]
150
200
Intro
Simulations
Validation
Zebrafish
Software Implementations: raster scanning fluorescence
correlation spectrometer
Two galvanometric mirrors:
the sample is raster scanned by the
excitation laser beam
x
y
Laser scanning confocal
microscope
Scan frequency:
2 Hz – 8000 Hz
( 0.5 s – 125 µs / line)
Validation
Simulations
Intro
Zebrafish
Scanning Laser Image Cross-correlation
(SLIC)*
x
A
B
C
D
E
A1
B1
C1
D1
E1
A2
B2
C2
D2
E2
A3
B3
C3
D3
E3
A4
B4
C4
D4
E4
A5
B5
C5
D5
E5
A6
B6
C6
D6
E6
v
x
t
* Rossow, Mantulin, Gratton, Jbiom Optics 2010
8000
lines
1s
t
x
t
x
t
Validation
Simulations
Intro
Zebrafish


2


R − V fitτ
G fit (τ ) ≅ G0 exp −



2
 ω 1 + τ

τ D , fit  
 0 
Scanning Laser Image
Cross-correlation
(SLIC)
changing the distance between the columns
x
t
A
B
C
D
0.025
τv (s)
0.020
G(τ)
0.015
E
v
0.020
0.018
0.016
0.014
0.012
0.010
0.008
4
0.010
6
8
10
R (µm)
0.005
0.000
0.01
0.1
τ (s)
x
t
x
t
Validation
Simulations
Intro
Zebrafish
Scanning Laser Image Cross-correlation
ARTERY
80 υm
<V>
= 714±43 υm/s
8VEIN0
VEIN
R = 10, 20 …υm
90 pixels= 1.6, 3.2 … 14.4 υm
80 υm
1.5
double component
in the carpet:
systolic and diastolic
velocities.
GXab(t)
1.0
0.5
R = 2.5, 5 … 22.5 µm
0.0
2.0
(vein)
1.5
-0.5
1.0
1E-4
1E-3
0.01
0.1
1.4
Lag time(s)
0.5
8000 Hz / line
125 µs / line
512x8192
100 nm / pixel
Single component
In the carpet:
<V> = 715±40 µm/s
GXab(τ)
0.0
1E-4
1E-3
0.01
0.1
(artery)
0.7
0.0
1E-4
1E-3
0.01
Lag time τ (s)
0.1
Intro
Validation
Simulations
Zebrafish
Scanning Laser Image Cross-correlation
short time lapse analysis:
Method
Strength
3750
50 υm
v (µ m/s)
3000
2250
1500
750
0
0.0
0.5
1.0
Time (s)
ROI size ≈
512x300 pixels
≈ 30 ms
1.5
2.0
Estimate of the
cardiac output:
CO ≈ 30 nL/min
Intro
Simulations
Validation
Neurophysiology
Hardware Implementations:
Spatial Ligth Modulator + CCD
CMOS or
CCD
Advantages:
• Variable spot array
LCOS-SLM optical
phase
modulator
• pixelated detector for
parallel spots detection
• Possibility of space mapping
sample
Gandolfi, Pozzi, Chirico, Mapelli, D’Angelo Frontiers in Cell. Neurosci. 2014
Intro
Simulations
Validation
Neurophysiology
Sliding grid Two-photon imaging
Desired
Excitation
pattern
Single
acquired
images
SLM
holograms
reconstructed
image
cerebellar slice
bulk-loaded
with Fura-2AM
Intro
Simulations
Sliding grid TPE
Method
strength
Validation
Neurophysiology
Selected neurons
Calcium signal
from selected neurons
Signal variation from the
soma of granule cells
in response to mossy fiber
stimulation (10 pulses/50Hz)
Intro
Simulations
Validation
Epathite Virology
Software Implementations:
pair correlation on full raster scanned image
flowing fluorescent objects…
Cross-correlation
On x-y images
1000 Hz
1 ms/line
Zebrafish
DsRed signal
(red blood cells)
vein
8000 Hz - 125 µs/line
10 µm
Typical pixel size ≈ 30-100 nm
Typical field of view ≈ 30-100 µm
10 µm
The scan speed is chosen so that
flowing objects produce diagonal
lines: vscan > vflow
Simulations
Intro
Validation
Epathite Virology
How to extract dynamic information from a single xy-image?
Cross-correlation is computed among pairs of columns of the image:
a
15 µm
2
3
4
1
400
6
col. I col. J
500
5
300
200
7
2000
1000
0
0
200
400
600
800
8
1000
12
3000
FJ (y)
100
9
10
11
2000
1000
0
0
200
400
600
y (pixel)
800
1000
94a.u.
12508a.u.
5-nm quantum dots; λexc=900 nm
G (τ)
FI (y)
3000
0
|v| (µm/s)
10 µm
Intro
Simulations
Validation
Applications
the biophotonics people @ UNIMIB…
Paolo Pozzi
Margaux Bouzin
Maddalena Collini
Laura D’Alfonso
Laura Sironi
Cassia Marquezin
Mykola Borzenkov
Egidio D’Angelo
Jonathan Mapelli
Daniela Gandolfi
Dept. of Human Physiology
Univ. Pavia
Piersandro Pallavicini
Dept. of Chemistry
Univ. Pavia
Franco Cotelli
Efrem Foglia
Dept. of Lifesciences
Univ. Milano
Luca Guidotti
Matteo Iannacone
Donato Inverso
San Raffaele Scientific
Institute, Milano