Gaussian kernel based anatomically-aided diffuse optical tomography

reconstruction

Reheman Baikejiang, Wei Zhang, and Changqing Li

SPIE 10059-36, January 31, 2017

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Outline

• Background of DOT• Introduction of kernel method• Simulation Results• Phantom experiment result• Conclusions and future work

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Background of DOTDOT: also known as near-infrared (NIR) tomography, refers tothe optical imaging of biological tissue in the diffusive regime.

Photo courtesy of NIRx

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Background of DOT• Advantages

– Safe, noninvasive and non-ionizing radiation

– Intrinsic molecular sensitivity– Functional imaging– Low cost

• Disadvantages– Low spatial resolution– Very sensitive to noise

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Anatomical guidance by Soft-prior Objective function with priori information:

Soft-prior matrix:1

𝐿𝑖𝑗={ 0 if 𝑖∧ 𝑗 are not∈the same region−1/𝑁 if 𝑖∧ 𝑗 are∈the same region

1 if 𝑖= 𝑗

[1] Phaneendra K. Yalavarthy et al., Opt. Express 15(13), 8176-8190 (2007)).

(1)

(2)

Ω=min𝜇𝑎

{∨¿ 𝑦−𝐹 (𝜇𝑎)∨¿22+𝜆∨¿𝐿(𝜇𝑎−𝜇𝑎0)∨¿2

2 }

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Anatomical guidance by Soft-prior• Advantages Soft-prior method: – Easy to implement when segmented

prior information available

– Fast convergence • Why we introduce the kernel method: – Reduce the image segmentation process– Looking for new method which is robust

to the incorrect prior information

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Outline

• Background of DOT• Introduction of kernel method• Simulation and experimental setup• Results• Conclusions and future work

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Kernel methodThe absorption coefficient at a node can be written as:

Here we use Gaussian kernel:

In a matrix-vector form:

(3)

(4)

(5)

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Kernel methodOnly the k-nearest neighbors() are stored in the kernel matrix:2

Kernelized objective function is obtained as:

Update equation:

where is the data-model misfit,

Once is found, we can obtain

(6)

(7)

(8)

[2] Guobao Wang et al., IEEE Trans. Med. Imag.. (34)1 61-69 (2015).

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Outline

• Background of DOT• Introduction of kernel method• Simulation Results• Phantom experiment result• Conclusions and future work

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Numerical simulation setup

  Diameter HeightBackground 78.0 mm 60.0 mm 0.007 mm-1 1.0 mm-1

Target 10.0 mm 10.0 mm 0.028 mm-1 1.0 mm-1

Optical properties and geometry dimensions of the phantom for the numerical simulation.

Simulation Phantom geometry Source-detector nodes in one projection

A cross section of simulated CT image

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Image quality evaluation metrics• VR = Dice = • CNR = • MSE =

Here: ROI: region of interest , ROB: region of background

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Numerical Simulation Results (I)

Grand truth No prior Soft prior

k = 16, 3×3×3 k = 32, 3×3×3 k = 64, 3×3×3

k = 64, 5×5×5 k = 64, 7×7×7 k = 64, 9×9×9

Kernel Method

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Image quality evaluation metrics

Voxel number VR Dice CNRSoft prior 1.0 1.0 138.57 2.47e-07No prior 1.67 0 2.54 1.39e-07

The calculated VR, Dice, CNR and MSE with the kernel method for k = 16,32,64

k Voxel number VR Dice CNR16 3×3×3 0.52 0.69 16.49 8.55e-0732 3×3×3 0.52 0.69 23.56 6.34e-0764 3×3×3 0.52 0.69 22.16 4.40e-07

k Voxel number VR Dice CNR64 5×5×5 0.52 0.69 22.52 4.12e-0764 7×7×7 0.52 0.69 22.51 3.93e-0764 9×9×9 0.57 0.72 25.48 3.83e-07

The calculated VR, Dice, CNR and MSE with the kernel method for k = 64 and different voxel number

The calculated VR, Dice, CNR and MSE with soft prior method and no prior.

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Numerical Simulation Results(II): Cancer contrast in CT image

Tumor Glandular Adipose SkinMean intensity 74.39 - 3.89 -184.43 - 47.84

Mean intensities of breast compositions in real CT image with iodine contrast injection

One slice of CT image with iodine contrast injection

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Reconstructed DOT images with kernel method: CT contrast effect

CT contrast  VR Dice CNR1:2 0.52 0.69 26.65 3.97e-071:3 0.52 0.69 22.98 4.37e-071:6 0.57 0.72 28.57 3.47e-07

The calculated VR, Dice, CNR and MSE for the reconstructed absorption coefficient images with different background to target CT contrasts.

With CT contrast 1:2 With CT contrast 1:2 With CT contrast 1:6

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Numerical Simulation Results(III): False positive target effect

Grand truth ()simulated CT image

Kernel method (k=64,9×9×9 ) Soft prior

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Numerical Simulation: clinical CT image as guidance

Breast CT image with iodine contrast injection, used in kernel method (without segmentation)

Segmented breast shape and tumor region, used in soft prior method

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Numerical Simulation Results(IV): Source-detector and mesh

Finite element mesh of breast shape generated form CT image

Source-detector nodes in one projection

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Numerical Simulation: Reconstructed DOT image

Reconstructed DOT image by soft prior method Reconstructed DOT image by kernel method with k=64 and voxel numbers of 9×9×9

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Outline

• Background of DOT• Introduction of kernel method• Simulation Results• Phantom experiment result• Conclusions and future work

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DOT prototype system

Prototype DOT system

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Phantom experimental setup and CT image

  Diameter HeightBackground 78.0 mm 60.0 mm 0.007 mm-1 1.0 mm-1

Target 10.86 mm 13.63 mm 0.028 mm-1 1.0 mm-1

Optical properties and geometry dimensions of the experimental phantom.

Phantom geometry. Slice of CT image Target region filled

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Phantom experimental results

  VR Dice CNRNo prior 0.88 0.0 0.48

Soft prior 1.0 1.0 246.20Kernel method 0.65 0.76 16.03

Image quality metrics of reconstructed DOT image

without the structural guidance with soft prior method With kernel method (k=64, voxel number 9×9×9)

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Summary and Future Work• Summary:

• We propose the kernel method to introduce the anatomical guidance into the DOT image reconstruction. Compared with the conventional structural prior guided DOT reconstruction algorithms, such as soft-prior, the proposed method has the advantage of not requiring the image segmentation and region classification. Robust to a false positive target prior.

• Future Work:• Investigating proposed method with a clinical data

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Acknowledgement• Authors thank research support from :

• California Breast Cancer Research Program (IDEA: 20IB-0125)• Startup fund from UC Merced• Travel award from the graduate program of Biological Engineering and

Small Technologies, UC Merced.

• Authors also thank : • Professor John M. Boone, in Department of Radiology, UC Davis for the

phantom CT scan and clinical breast CT data• Professor Ramsey D. Badawi, in Department of Radiology, UC Davis for

helpful discussions.

Thank you for your attention!

Any Questions?