Lensfree diffractive tomography for the imaging of 3D cell cultures

LENSFREE DIFFRACTIVE TOMOGRAPHY
FOR THE IMAGING OF 3D CELL CULTURES
CONTACT :
Anthony Berdeu
[email protected]
A. Berdeu1,2, F. Momey1,2, N. Picollet-D’Hahan1,3,4, S. Porte1,3,4, X. Gidrol1,3,4, T. Bordy1,2, J.M. Dinten1,2, C.Allier1,2
Context
 Apply lensfree microscopy to 3D cell culture


Lack of non-invasive imaging
Difficult to get acquisitions of large volumes
 Rise of lensfree imaging for 2D cell cultures


Experimental prototype (first data on biological culture)
Proof of concept (first algorithms for 3D reconstruction)
 Operational device


Cheap, robust and easy to implement
Label free and time lapse microscopy
Robust to incubator
Suited to living samples
Setup: lensfree in-line holography
𝑈𝑖𝑛𝑐
𝑈𝑑𝑖𝑓
𝑧
𝑈𝑑𝑖𝑓
2𝜋𝑛0
𝑘0 =
𝜆
𝑛0 the medium refraction index
𝐹 𝑟 ′ . 𝑈𝑖𝑛𝑐 𝑟 ′ .
𝑒
𝑂𝑏𝑗𝑒𝑐𝑡
𝐹 𝑟 = −𝑘02
𝑛 𝑟
𝑛0
𝑖𝑘0
𝑟′
𝑦
𝑈𝑡𝑜𝑡 = 𝑈𝑖𝑛𝑐 + 𝑈𝑑𝑖𝑓
rotation
axis for 𝜽
𝑥
𝑖𝑘0 𝑟 ′
with
𝑧 𝑒
𝑈𝑖𝑛𝑐 = 𝑒 𝑖𝑘0 .𝑟
and ℎ𝑧,𝑘0 = .
𝑖𝜆
𝑈𝑑𝑖𝑓 = 𝛿𝑡 ⋆ ℎ𝑧,𝑘0
𝑟′
2
𝒇
𝑧
𝑟
𝑟 ′ −𝑟
−𝑟
∝
Object modelled by a 2D transmission
plane: 𝑡2𝐷 = 1 + 𝛿𝑡
𝑗
𝑘03
𝑦 𝑂
𝑥
𝑗
𝑗
𝑗
𝑝02 , 𝑞02 , 𝑚02
𝑗
𝑘01
𝑟′
𝑈𝑡𝑜𝑡 = 𝑈𝑖𝑛𝑐 + 𝑈𝑑𝑖𝑓
1
𝑟 =−
4𝜋
𝑗
𝑘02
𝜃
𝐹 scattering potential
Digital sensor - 1,67 𝜇𝑚
3840 × 2748 pixels
Phase retrieval
3D Fourier mapping
Acquisition
Semi-coherent
illumination
(about angle 𝜑 // 𝜃 = 45°)
Processing
𝑑3 𝑟 ′
2
−1
2
𝑈𝑑𝑖𝑓
𝑗
3
𝑈𝑑𝑖𝑓
𝑦
𝑥
𝑈𝑡𝑜𝑡
2
⋆ ℎ−𝑧,−𝑘0
data
Lack of phase in the data:
𝑣
𝑢
Simple back
propagation
 Introduction of a phase ramp to take
into account the tilted wavefront
 Twin-image in the data inversion
Solution: inverse problem
3D spatial
3D frequency
−1
domain ℱ3𝐷 domain
Acquisitions & results
𝑗
𝑗
1
𝑈𝑑𝑖𝑓
2D frequency
2D Spatial
Mapping domain ℱ2𝐷 domain
φ
𝜃
Grenoble Alpes, F-38000 Grenoble, France, 2CEA, LETI, MINATEC
Campus, F-38054 Grenoble, France, 3CEA, BIG – Biologie à Grande Echelle,
F-38054 Grenoble, France, 4INSERM, U1038, F-38054 Grenoble, France
Objectives
 Growth of 3D cell culture in organic gel


1Univ.
 𝑙1 -norm minimization: sparse objects
 𝑇𝑉 minimization: sparse gradient
 ℜ 𝛿𝑡 < 0: non-emissive objects
𝛽
spherical
caps
𝛼
data fidelity
𝑭
𝛾
𝛿𝑡0 = min
𝛿𝑡
ℜ 𝛿𝑙 <0
𝐼𝑑𝑎𝑡𝑎 − 𝑈𝑖𝑛𝑐 + 𝛿𝑡 ⋆ ℎ𝑧,𝑘0
+𝜇𝐿1 𝛿𝑡
𝑦
𝐿1
+ 𝜇 𝑇𝑉 𝛻 𝛿𝑡
2 2
…
𝐿1
Residual artifacts
(twin image, …)
𝑥
𝑧
𝑗
𝐹 𝛼 𝑗 , 𝛽 𝑗 , 𝛾 𝑗 = 4𝑖𝜋𝑤. 𝑒 −2𝑖𝜋𝑤𝑧𝑠 𝑈𝑑𝑖𝑓 𝑢, 𝑣; 𝑧𝑠
Matrigel® capsules data
𝜑 = 0°, 84.6°, 169.2°
The arrows point on special features
𝜆 = 630 𝑛𝑚
𝑗
𝑗
𝑗
with 𝛼 , 𝛽 , 𝛾
𝑗
𝑗
𝑗
𝑛0 𝑝0
𝑛0 𝑞0
𝑛0 𝑝0
= 𝑢−
,𝑣 −
,𝑤 −
𝜆0
𝜆0
𝜆0
and 𝑤 =
𝑛02
− 𝑢2 − 𝑣 2
𝜆20
Retrieved phase
𝑡2𝐷 = 1 + 𝛿𝑡0
Conclusions
 Working prototype with 3D biological samples acquisitions
 2D slantwise phase retrieval on real data acquisitions
 First 3D reconstructions on several 𝒎𝒎𝟑 volumes
Perspectives
 Incubator-proof prototype for 3𝐷 + 𝑡 acquisitions
Reconstruction of 5123 × 3.343 𝜇𝑚3 = 5𝑚𝑚3 volumes without/with phase retrieval on
the 2D dataset. 31 angles 𝜑 = 0°: 9.4°: 282° , 𝜃 = 45°. Cell-sized beads can be
resolved both on 𝑥𝑦-plane and 𝑧-axis.
References
[1] Momey F. & al., Lensfree
diffractive tomography for the
imaging of 3D cell cultures,
Biomed. Opt. Express 7, 949-962
(2016)
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analysis of prostate acini-like 3D
structures by lensfree imaging.
Biosensor and Bioelectronics, 49,
176-183, 2013.
[3] Kesavan S. V. & al., Highthroughput monitoring of major cell
functions by means of lensfree video
microscopy. Nature Scientific
Reports, 4, n°5942, 2014.
[4] Gabor D., A new microscopic
principle. Nature, 161, 777-778,
1948.
[5] Wolf E., Three-Dimensional
structure determination of semitransparent objects from holographic
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n°14, pp. 153-156, 1969.
[6] Kak, A., Slaney, M. Principles of
computerized tomographic imaging.
IEEE Press, 1988.
[7] Sung, Y. Optical, diffraction
tomography for high resolution live
cell imaging. Optics express, vol.
17, n°11, pp. 266-277, 2009.
[8] Haeberlé, O. & al., Tomographic
diffractive microscopy : basics,
techniques and perspectives. Journal
of Modern Optics, 2010.
 Improve data alignment

Inverse problem algorithms on the 3D volume
[9] Isikman S. O. & al., Lens-free
optical tomographic microscope
with a large imaging volume on a
chip, Proc. Natl. Acad. Sci. U.S.A.
108(18), 7296-7301. (2011).
[10] Rudin, L.I. & al., Nonlinear
total variation based noise removal
algorithms. Journal of Modern
Optics, 2010.
Journée de l’école doctorale EDISCE
Grenoble – Faculté de pharmacie – 6 Juin 2016