an experimental study of blood oxygen saturation...

An Experimental Study of Blood Oxygen Saturation Imagingvia Quantitative Photoacoustic Tomography

Felix Lucka, University College London, [email protected]

joint odyssey with: Lu An, Simon Arridge, Paul Beard, Ben Cox, RobertEllwood, Martina Bargeman Fonseca & Emma Malone.

(Very) Applied Inverse Problems

Hangzhou, June 2, 2017.

Photoacoustic Imaging: Basic Principles

Optical Part

chromophore concentration: ck

optical absorption coefficient: µa(c)

Acoustic Part


Optical Part



pulsed laser excitation: Φ(µa)

Acoustic Part


Optical Part




thermalization: H = µaΦ(µa)

Acoustic Part


Optical Part





Acoustic Part

local pressure increase: p0 = Γ(c)H


Optical Part





Acoustic Part


elastic wave propagation:

∆p − 1

c2

∂2p

∂2t= 0

p|t=0 = p0,∂p

∂t|t=0 = 0


Optical Part





Acoustic Part



∆p − 1

c2

∂2p

∂2t= 0

p|t=0 = p0,∂p

∂t|t=0 = 0

measurement of pressure time courses:

fi (t) = p(yi , t)


Optical Part





Acoustic Part



∆p − 1

c2

∂2p

∂2t= 0

p|t=0 = p0,∂p

∂t|t=0 = 0


fi (t) = p(yi , t)

Photoacoustic effect

I coupling of optical and acousticmodalities.

I ”hybrid imaging”

I high optical contrast can be read byhigh-resolution ultrasound.


Optical Part





Acoustic Part



∆p − 1

c2

∂2p

∂2t= 0

p|t=0 = p0,∂p

∂t|t=0 = 0


fi (t) = p(yi , t)

Inverse problems:

! optical inversion (µa) from boundarydata: severely ill-posed.

X acoustic inversion (p0) from boundarydata: moderately ill-posed.

X optical inversion (µa) from internaldata: moderately ill-posed.

Photoacoustic Imaging: Applications & Properties

I Light-absorbing structures in soft tissue.

I High contrast between blood and water/lipid.

I 3D spatial resolutions of tens of micro meters.

sources: Paul Beard, 2011; Jathoul et al., 2015.

Felix Lucka, [email protected] - Experimental Study of sO2 Imaging via QPAT 9

Photoacoustic Imaging: Spectral Properties

Oxyhemoglobin

Deoxyhemoglobin

Elastin

Collagen

Lipid (a) (b)

Water

(from Beard P, 2011)

I Different wavelengths allow quantitative spectroscopic examinations.

I Gap between oxygenated and deoxygenated blood.

I Use of contrast agents for molecular imaging.


Photoacoustic Imaging: Spectral Properties

(Mallidi S et al, 2011)

I Different wavelengths allow quantitative spectroscopic examinations.

I Gap between oxygenated and deoxygenated blood.

I Use of contrast agents for molecular imaging.


Quantitative Photoacoustic Tomography (QPAT)

Aim: 3D high-resolution, high sensitivity, quantitative information aboutphysiologically relevant parameters such as chromophore concentration.

I Complete inversion (acoustic + optical + spectral).

I Model-based approaches promising.

c µa

µs

�

�

H p0 f

Big gap between simulations and experimental verifications!

Cox, Laufer, Arridge, Beard, 2011. Quantitative spectroscopicphotoacoustic imaging: a review, Journal of Biomedical Optics.


QPAT Experiment: Overview

1. Phantom development

I realistic, stable phantom (matching blood, in-vivo environment).

I characterization of optical, acoustic and thermoelastic properties.

2. Experimental measurements

I accurate, absolute measurements of acoustic field.

I measurement of optical excitation parameters.

3. Acoustic reconstruction

I quantitative, high-res 3D recon of initial acoustic pressure.

4. Optical reconstruction

I quantitative, high-res 3D recon of chromophore concentrations.

Fonseca, Malone, L, Ellwood, An, L, Arridge, Beard, Cox, 2017.Three-dimensional photoacoustic imaging and inversion for accuratequantification of chromophore distributions, Proc. SPIE 2017.

The Phantom

Aim: Similar properties as oxy- and deoxyhemoglobin.

I 4 polythene tubes (580µm inner diameter, 190µm wall thickness).

I copper sulphate (CuSO4.5H2O) and nickel sulphate (NiSO4.6H2O):photostable, absorption linear with concentration.

I mixtures with Q % ratio of NiSO4.6H2O mother solution.

I background intralipid and india ink solution as scattering medium

I spectra measured with spectrophotometer

The Phantom

Aim: Similar properties as oxy- and deoxyhemoglobin.

800 900 1000 1100Wavelength [nm]

0

0.01

0.02

0.03

0.04

0.05

0.06

µa [m

m-1

]

India Ink M10b*0.04

H2O

Background

I 4 polythene tubes (580µm inner diameter, 190µm wall thickness).

I copper sulphate (CuSO4.5H2O) and nickel sulphate (NiSO4.6H2O):photostable, absorption linear with concentration.

I mixtures with Q % ratio of NiSO4.6H2O mother solution.

I background intralipid and india ink solution as scattering medium

I spectra measured with spectrophotometer

Photoacoustic Efficiency / Gruneisenparameter

I p0 = Γ(c)H

I Linear dependence found by photoacoustic spectroscopy:

Γ = ΓH2O (1 + βCuSO4 cCuSO4 + βNiSO4 cNiSO4) (range: 1− 1.72)

Stahl, Allen, Beard, 2014. Characterization of the thermalisation efficiency andphotostability of photoacoustic contrast agents, Proc. SPIE.

High Resolution PAT Scanner

I Fabry-Perot sensors: wide bandwidth, small element size, low noise,almost omni-directional

I data acquisition gets faster and faster

I two orthogonal sensors to reduce limited view artefacts

Ellwood, Ogunlade, Zhang, Beard, Cox, 2017. Photoacoustictomography using orthogonal Fabry Perot sensors, Journal of BiomedicalOptics.

sources: Paul Beard, 2011; Jathoul et al., 2015, Ellwood et al., 2017.

Experimental Setup

I excitation: 7ns pules at 10Hz with 19mJ at 800nm

I spatial sampling 100µm, temporal sampling: 8ns


Scanner Calibration

I spatial alignment with registration phantom

I V to Pa conversion by characterisation with calibrated transducer

I Pa corrected for pulse energy variations with integrating sphere


Acoustic Reconstruction

fi (t) = p(yi , t), ∆p − 1

c2

∂2p

∂2t= 0, p|t=0 = p0,

∂p

∂t|t=0 = 0

f = Ap0

I pre-processing & sound speed calibration

I model-based inversion:

p = argminp>0

‖Ap − f ‖22

via projected gradient-descent-type scheme (iterative time reversal):

pk+1 = Π(pk − A/(Apk − f )

)I numerical wave propagation simulation.

I 50µm voxel resolution: N = 264× 358× 360 (up to 4003!)

Arridge, Betcke, Cox, L, Treeby, 2016. On the Adjoint Operator inPhotoacoustic Tomography, Inverse Problems 32(11).


Acoustic Wave Propagation: Numerical Solution

k-Wave♣ implements a k-space pseudospectral method to solvethe underlying system of first order conservation laws:

I Compute spatial derivatives in Fourier space: 3D FFTs.

I Modify finite temporal differences by k-space operator anduse staggered grids for accuracy and robustness.

I Perfectly matched layer to simulate free-space propagation.

I Parallel/GPU computing leads to massive speed-ups.

♣ B. Treeby and B. Cox, 2010. k-Wave: MATLAB toolboxfor the simulation and reconstruction of photoacoustic wavefields, Journal of Biomedical Optics.

We gratefully acknowledge the support of NVIDIA Corporation

with the donation of the Tesla K40 GPU used for this research.

Acoustic Inversion Results

Maximum intensity projection for 1060nm excitation.


Acoustic Inversion Results

volume rendering for 1060nm excitation.


Acoustic Inversion Results: Different Inversion Approaches

iTR

0 10y [mm]

0

5

10

15

z [m

m]

0

5

10

p0 [P

a]

×105 TR

0

2

4

p0 [P

a]

×105 TR, system 1

0

1

2

p0 [P

a]

×105

Inset

5 10y [mm]

2

4

6

8

z [m

m]

0

5

10

p0 [P

a]

×105

0

2

4

p0 [P

a]

×105

0

1

2

p0 [P

a]

×105

Acoustic Inversion Results: Simulation vs Experiment


Optical Inversion: Overview

c µa

µs

�

�

H p0 f

q

I mapping from c to (µa, µs , Γ): measured spectra

I q: light source properties

I mapping from (µa, µs , q) to Φ: non-linear.


Optical Reconstruction: Beam Characterization

I PA image at water absorption peak to determine surface

I PA image with acetate sheet to determine center and radius


The RTE and Toast++

Radiative transfer equation:

(s · ∇+ µa + µs)φ(x , s) = q + µs

∫Θ(s, s ′)φ(x , s ′)ds ′

Φ(x) =

∫φ(x , s)ds

! (x , s) ∈ R5 direct FEM infeasible.

Diffusion approximation:

(µa −∇ · κ(x)∇) Φ(x) =

∫q(x , s)ds, κ =

1

3(µa + µs(1− g))

source moved one scattering wave-length into volume.

Toast++:I time-resolved light transport in highly scattering mediaI FEM, different elements and basis functions, 2D and 3D

Schweiger, Arridge, 2014. The Toast++ software suite for forward andinverse modeling in optical tomography, Journal of Biomedical Optics.


Model Based Inversion

c µa

µs

�

�

H p0 f

q

c = argminc∈C

Nλ∑λ=1

∫ROI

(precon0,λ − p0,λ(c)

)2dx

I solve via iterative first order method (L-BFGS)

I derivatives of Φ(µa, µs) via adjoint method: two solves of lightmodel per iteration (per wavelength).

I additional data interpolation and rotation into FEM mesh

I addition of global scaling factor.

Malone, Powell, Cox, Arridge, 2015. Reconstruction-classificationmethod for quantitative photoacoustic tomography, JBO.

Optical Inversion Results

(a)

0

0.5

1

c NiS

O4, n

orm

. [a.

u.]

Ground-truth(c

k)

LU

Tube

1 (to

p)

Tube

2

Tube

3

Tube

40

0.5

1

c CuS

O4, n

orm

. [a.

u.]

(b)


Estimated

0

1

2

3

[M]

CuSO4

0

0.2

0.4

0.6

0.8

[M]

Ground truth

0

0.5

1

1.5

2

[M]

NiSO4

-4 -2 0 2Y [mm]

-10

-5

0

Z [m

m]

0

0.2

0.4[M

]

0

1

2

3

c NiS

O4 [M

]

Surface BottomDistance

0

0.2

0.4

0.6

0.8

c CuS

O4 [M

]

Estimated, (ck)

Ground-truth



tube 1 (top) tube 2 tube 3 tube 40

25

50

75

100R

atio

Q (

%)

Results for ratio Q, the sO2 analogue.


Effect of Inaccuracies

δNiSO4 =‖c(norm)

true − c(norm)est ‖

‖c(norm)true ‖

Source of explicit uncertainty/error δNiSO4

None 6.5%

µs : 20% overestimation 7.4%

Gruneisen: Γ = ΓH2O 39.6%

No acoustic pressure calibration 14.4 %

non-iterative time reversal 26.5%

non-iterative time reversal + sensor 1 only 26.4 %


Summary & Outlook

What we wanted to do:

I highly-res, 3D chromophore distributions from exp. PAT data.

I ratio between two chromophores (sO2 analogue)

What we learned and achieved:

I promising estimates of normalized chromophore concentrations.

I promising ratio estimates

I sensitivity to in-accuracies

What we need to improve:

I experimental set-up & beam characterization

I acoustic reconstruction

I light model

I coupling of acoustic and optical models

I optimization


Thank you for your attention!

Fonseca, Malone, L, Ellwood, An, L, Arridge, Beard, Cox, 2017.Three-dimensional photoacoustic imaging and inversion for accuratequantification of chromophore distributions, Proc. SPIE 2017.

Arridge, Betcke, Cox, L, Treeby, 2016. On the Adjoint Operator inPhotoacoustic Tomography, Inverse Problems 32(11).

We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla

K40 GPU used for this research.


an experimental study of blood oxygen saturation...

Documents