Transmission ultrasound data simulated using the k-Wave toolbox as a benchmark for biomedical quantitative ultrasound tomography using a ray approximation to Green's function

Transmission ultrasound data simulated using the k-Wave toolbox as a benchmark for biomedical quantitative ultrasound tomography using a ray approximation to Green's function 

The folder ‘’simulation’’ includes the transmission ultrasound data sets used in the project:https://github.com/Ash1362/ray-based-quantitative-ultrasound-tomography. In the Github link, the associated project can be found in the branch master in the folder r-Wave #V1.1. (The folder ‘’data_ust_kWave_transmission.zip’’ is deprecated.)

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The ultrasound data were simulated using the k-Wave toolbox (version 1.3.)  [5] and using a digital breast phantom [4]. In k-Wave version 1.4., no changes have been reported that affects the simulations. The simulations were done assuming isotropic point sources.

The folder ‘’simulation’’  must be added to the path:

''…r-Wave/data/simulation/…''

For running the Matlab example scripts in the project in the github, the user has two choices: 

Simulate the k-Wave ultrasound data by setting data_sim=true; in the examples in the project.

Upload the already simulated k-Wave ultrasound data according to the description below and load them by setting  data_sim=false; in the examples in the project.

Please read the description in the example scripts!

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The folder simulation includes 2 subfolders, ‘’phantom’’ and ‘’data_ust_kWave_transmission’’.

1) The subfolder ‘’simulation/phantom’’  includes ‘’OA-BREAST’’. 

In the project: https://anastasio.bioengineering.illinois.edu/downloadable-content/oa-breast-database/,

the user must upload the folder ‘’Neg_47_Left’’ , and add it as  ‘’r-wave/data/simulation/phantom/OA-BREAST/Neg_47_Left/’’.

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2) The subfolder ‘’simulation/data_ust_kWave_transmission’’  includes 2 subfolders, ‘’2D’’  and ‘’3D’’ .

The subfolder ‘’2D’’  includes:

data_ust_kWave_transmission/2D/PulsePammoth_1_dx4_cfl1_Nr256_Ne64_Interpoffgrid_Transgeompoint_Absorption1_CodeMatlab/data4_sphere_nonsmooth.mat

Two transmission ultrasound data sets were simulated using the k-wave for only water and breast in water according to section ‘’6.1. data simulation’’ in [1]. 64 emitters and 256 receivers are simulated as off-grid points which are placed on a 2D circular ring. (The characters ‘’_sphere_’’  are added to indicate that the transducers are placed on a ring.) To simulate the data, each emitter was individually driven by an excitation pulse, and the induced acoustic pressure time series were recorded on all the receivers. The k-Wave simulation was performed on a grid with grid spacing 0.4 mm, and the time spacing was set using a CFL number 0.1. The acoustic absorption and dispersion were accounted for based on the frequency power law. This data set is used for the purpose of image reconstruction, and therefore, the sound speed and absorption coefficients maps are not smoothed, i.e., the original maps are used for simulations. This data set can be used for image reconstruction using the time-of-flight-based approach and then the Green's approach.

data_ust_kWave_transmission/2D/PulsePammoth_1_dx4_cfl1_Nr256_Ne64_Interpoffgrid_Transgeompoint_Absorption1_CodeMatlab/data4_plane_nonsmooth.mat

Two transmission ultrasound data sets were simulated using the k-wave for only water and breast in water. 64 emitters and 256 receivers are simulated as off-grid points which are placed on 16 planar arrays which are all aligned with a circle. Each planar array includes 4 emitters and 16 receivers. Therefore, in contrast with the data mentioned above, the ray linking is performed using the line equations defining the 2D geometry of the linear arrays. (The characters ‘’_plane_’’  are added to indicate that the transducers are placed on line.) To simulate the data, each emitter was individually driven by an excitation pulse, and the induced acoustic pressure time series were recorded on all the receivers. The k-Wave simulation was performed on a grid with grid spacing 0.4 mm, and the time spacing was set using a CFL number 0.1. The acoustic absorption and dispersion were accounted for based on the frequency power law. This data set is used for the purpose of image reconstruction, and therefore, the sound speed and absorption coefficients maps are not smoothed, i.e., the original maps are used for simulations. This data set can be used for image reconstruction using the time-of-flight-based approach, but ahs not been extended to the Green's approach yet. The image reconstruction should be slower than the circular array. the reason is for circular array, for each emitter, the raylinking problem is solved for all receivers once using the equation of circle. However, for this data set, for each emitter, the ray linking problem is solved for each receiver array separately, because receiver arrays are defined with different line equations.

data_ust_kWave_transmission/2D/PulsePammoth_1_dx4_cfl1_Nr256_Ne64_Interpoffgrid_Transgeompoint_Absorption1_CodeMatlab/data4_sphere_smooth_17_1.mat

Two transmission ultrasound data sets were simulated using the k-Wave for only water and breast in water  as the benchmark for validation of ray approximation to Green’s function in homogeneous and heterogenous media, respectively. The simulation was performed according to section ‘’6.2. Numerical validation of the ray approximation to the Green’s function’’ in [1].

64 emitters and 256 receivers are simulated as off-grid points which are placed on a 2D circular ring. (The characters ‘’_sphere_’’  are added to indicate that the transducers are placed on a ring.) The pressure field was produced by emitter 1 (of the 64 emitters) and was recorded in time on all 256 receivers. The k-Wave simulation was performed on a grid with grid spacing 0.4 mm, and the time spacing was set using a CFL number 0.1. The acoustic absorption and dispersion were accounted for based on the frequency power law. The sound speed and absorption coefficient maps were smoothed by an averaging window of size 17 grid points. This data set is used as the benchmark for measuring accuracy of ray approximation to Green’s function for computing phase and amplitude of the pressure field on the receivers.

data_ust_kWave_transmission/2D/PulsePammoth_1_dx4_cfl1_Nr256_Ne64_Interpoffgrid_Transgeompoint_Absorption1_CodeMatlab/data4_sphere_smooth_17_20.mat

 This data set is the same as data4_smooth_17_1 except the pressure field is produced by emitter 20.

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The subfolder ‘’3D’’  includes:

data_ust_kWave_transmission/3D/PulsePammoth_1_dx5_cfl1_Nr4096_Ne1024_Interpnearest_Transgeompoint_Absorption0_CodeCUDA/data5_sphere_nonsmooth_tof_singram.mat

The discrepancy of time-of-flight data for two transmission ultrasound data sets simulated by the k-wave for breast in water and only water according to section 5.2 in [3]. The pressure fields were produced by 1024 emitters separately and were recorded on 4096 receivers. The emitters and receivers were simulated as points which are placed on a 3D hemispherical surface, and are interpolated onto the grid using a neighboring interpolation.  The k-Wave simulations were performed on a grid with grid spacing 0.5 mm, and the time spacing was set using a CFL number 0.1. The time-of-flight data were computed and will be used for a refraction-corrected image reconstruction of the sound speed based on the inversion approach proposed in [3].

References

1 - A. Javaherian, ❝Hessian-inversion-free ray-born inversion for high-resolution quantitative ultrasound tomography❞, 2022, https://arxiv.org/abs/2211.00316/ .

2 - A. Javaherian and B. Cox, ❝Ray-based inversion accounting for scattering for biomedical ultrasound tomography❞, Inverse Problems vol. 37, no.11, 115003, 2021.  https://iopscience.iop.org/article/10.1088/1361-6420/ac28ed/

3- A. Javaherian, F. Lucka and B. T. Cox, ❝Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast❞, Inverse Problems, 36 125010.  https://iopscience.iop.org/article/10.1088/1361-6420/abc0fc/  

4- Y. Lou, W. Zhou, T. P. Matthews, C. M. Appleton and M. A. Anastasio, ❝Generation of anatomically realistic numerical phantoms for photoacoustic and ultrasonic breast imaging❞, J. Biomed. Opt., vol. 22, no. 4, pp. 041015, 2017. https://anastasio.bioengineering.illinois.edu/downloadable-content/oa-breast-database/

5 - B. E. Treeby and B. T. Cox, ❝k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields❞, J. Biomed. Opt. vol. 15, no. 2, 021314, 2010. http://www.k-wave.org/