Advanced Image Reconstruction Methods For Photoacoustic .

Advanced Image Reconstruction Methodsfor Photoacoustic TomographyMark A. Anastasio, Kun Wang, and Robert SchoonoverDepartment of Biomedical EngineeringWashington University in St. Louis1

Outline Photoacoustic/thermoacoustic tomography– Very brief review Issues for image reconstruction– Incorporation of transducer effects into imaging model– Incomplete data image reconstruction– Non-uniform acoustic properties of object (layered media)

Schematic of ctionalgorithmTissueabsorbed opticalenergy density

Conventional PAT imaging model Conventional imaging model (assuming point-like transducers)ORwhere

Issue #1 for image reconstruction: Ultrasoundtransducer model Conventional PAT reconstruction algorithms assume theultrasound transducer is “point-like”. In reality, the finite area of the transducer surface will result inan anisotropic detector response. Moreover, the measured pressure signal is degraded by theacousto-electrical response of the transducer. We have developed a methodology for including thetransducer response in the PAT imaging model

An Example of the Degradation Caused by FiniteAperture Size of Transducer Phantom: uniform spheres extendingfrom the center to 10mmZY Transducers: planar transducer ofdimension 4*4mm2 on a sphere ofradius 25mm Forward model: spherical Radontransform (SRT) averaged over thetransducer surface Reconstruction algorithm: filteredback projection (FBP)D. Finch et al., SIAM J Math Anal, 2007X

Ignoring Transducer Size Gives BlurredReconstruction Results Blurring effect is moresignificant for– objects further away fromthe center– tangent direction1A0.50105

Discretization of imaging model Operator form of continuous-to-continuous (C-C) mapping: Digital imaging systems are described by continuous-todiscrete (C-D) mappings:vector of pressuremeasurementsdiscretizationoperator

Discretization of imaging model The discretization operator is defined as:: transducer location index: time sample index Ideal case (Dirac delta sampling):samplingapertures

Discrete-to-discrete (D-D) imaging model To perform iterative image reconstruction, a D-D imagingmodel is required. Obtained by substitution of a finite-dimensional objectrepresentation into the C-D imaging model. Object representation: D-D imaging model:K. Wang, et al, An Imaging Model Incorporating UltrasonicTransducer Properties for Three-Dimensional Optoacoustic Tomography,IEEE TMI, 30, 2011.sphericalexpansionfunctionssystemmatrix

Discrete-To-Discrete Imaging System Explicit form of system matrix:electrical impulseresponse(measured)

Discrete-To-Discrete Imaging System Explicit form of system matrix:spatial impulseresponse

Discrete-To-Discrete Imaging System Explicit form of system matrix:pressure produced byspherical voxel

Computer-Simulation Studies for Noiseless Data Phantom: thin section of depth0.07mm consisting cylindricalstructuresTransducers: planar transducersof size 4*4mm2 on single ring ofradius 25mm lying in the centralplane of the phantom (x-o-yplane).ScanningTrajectoryZ0.07mm Simulation data: of higherresolution (1024*1024*2) Reconstruction: of lowerresolution (512*512*1).YX

Compensation Model Gives Almost ‘Perfect’ Resultsfor Noiseless DataYcompennon compen1XA0.50 8.9251A0.5compen0.035X (mm)non compe

Resolution-Standard Deviation Curves Use of the proposed imagingmodel can enhance spatialresolution in the reconstructedimages. As expect, this comes at thecost of increased noise levels. This reflects that the solutionto the inverse problembecomes less eviation0.10.0500.35Resolution(mm)

Experimental Evaluations (geometry) Phantom: crossing hairs withthe bottom half illuminated(from center to 40mm)Z Transducers: arc scan arraywith radius 65mm consisting of64 transducers of size 2*2 mm2 Reconstruction: bycompensation and noncompensation modelsXtransducerarrayYcrossing hairilluminationCollaborative work with TomoWaveLaboratories Inc.

new imaging modelstandard imaging modelExperimental results

Issue #2 for image reconstruction: Incomplete data For “exact” 3D image reconstruction using analyticreconstruction methods, pressure measurements mustbe acquired on a 2D surface that encloses the object. There remains an important need for robustreconstruction algorithms that work with limited datasets. We are developing/applying iterative imagereconstruction methods for 3D PAT.

Example of real-data study: 3D Mouse Scanner Arc-shaped transducer array with 64 elementsThe mouse was rotated about z-axis over 2π‘Full-data’: 180 view angles‘Half-data’: 90 view anglesReconstruction algorithms– FBP algorithm– PLS algorithmCollaborative work with TomoWaveLaboratories Inc.

3D Rendering of Reconstructed ImagesFBP using ‘full-data’PLS using ‘half-data’

2D Slices across Blood VesselsFBP from ‘full-data’FBP from ‘half-data’PLS from ‘half-data’

Compressive sensing-inspired approaches Optimization problem:θˆ arg min θθTVs.t. p H θ εθ 0 We implemented the ASD-POCS to solve the optimizationproblem. (Sidky and Pan, Phys. Med. Biol., 7, 2008)Collaborative work with Drs. E. Sidky and X. Pan (UChicago)

Computer-simulations Scanning radius: 65mm Sampling rate: 20MHz3D phantomTransducers on a sphere

FBP Requires Data to be Densely Sampled over Space ‘Full-data’: 128*360 transducers ‘Limited-data’: 8*15 transducersFull-dataLimited-dataImage profiles

TV Algorithm Outperforms Conventional Algorithms(noisy) Reconstructed images from limited-data contaminated by0.5% Gaussian noise.ARTTVImage profiles

Issue #3 for image reconstruction: Acousticinhomogeneities Conventional PAT reconstruction algorithms assume the object ofinterest is acoustically homogeneous. In medical imaging applications this assumption is often notwarranted. We have developed an analytic reconstruction formula for usewith layered acoustic mediaR.W. Schoonover and M.A. Anastasio, “Image reconstruction inphotoacoustic tomography involving layered acoustic media,” J. Opt.Soc. Am. A 28, 1114–1120 (2011).

Generic Layered Medium

Imaging Model for Layered MediumDevelop a Green function for layered medium through use ofAngular Spectrum decomposition:Imaging model:determined from B.C.s

Acoustic boundary conditionsB.C.s enforced at each layerA linear system of equations can be established todetermine Green function.- Algebraic solution

Solution: Three-Layered MediumFor a three layer medium with the object located in the layer furthest fromthe detection plane:The label m refers to the first layer (muscle), the label f refers to thesecond layer (fat) and the label s refers to the third layer (skin).The thicknesses of the layers are df (fat layer) and ds (skin layer).

Image Reconstruction Model for Three-Layered MediumReflection and transmission coefficients:

Images reconstructed from noiseless data

Images reconstructed assuming a homogenous medium

Incorporation of shear waves in PAT Acoustic solids support twotypes of propagating waves Longitudinal waves (alsosupported in fluids) andtransverse waves (shearwaves) We have extended our analysis to include shear wavephysics-- PAT reconstruction formula for layered media including elasticsolids

Summary Incorporation of the transducer response into the imaging modelfacilitates accurate solution of the acoustic inverse problem. Use of accurate image models with iterative methods can facilitatelimited data image reconstruction. For planar measurement geometries and layered media close-forminversion formulas are available– shear wave production in elastic solids– dispersion and attenuation

Acknowledgements NIH award EB010049(Development of Thermoacoustic Tomography Brain imaging) NIH award EB09719For more information contact:Mark Anastasioanastasio@wustl.edu

Issue #2 for image reconstruction: Incomplete data For “exact” 3D image reconstruction using analytic reconstruction methods, pressure measurements must be acquired on a 2D surface that encloses the object. There remains an important need for robust reconstruction algorithms that work with limited data sets.