Method and system for automatic estimation of shear modulus and viscosity from shear wave imaging

1. A method for estimating shear modulus and viscosity of tissue of a patient based on shear-wave images of the tissue, comprising:

simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation;

comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function; and

estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation.

2. The method of claim 1 , further comprising:

visualizing the estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity.

3. The method of claim 1 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

computing shear displacement of the tissue in spatial domain corresponding to at least a region of the shear-wave images at each of a plurality of time steps based on the shear modulus and viscosity values for the tissue.

4. The method of claim 3 , wherein computing shear displacement of the tissue in spatial domain corresponding to at least a region of the shear-wave images at each of a plurality of time steps based on the shear modulus and viscosity values for the tissue comprises:

calculating the shear displacement of the tissue in the spatial domain by solving ρ∂ t 2 u=μ∇ 2 u+η∂ t ∇ 2 u at each time step, where μ is the shear modulus, η is the viscosity, ρ is a density of the tissue, and u is shear displacement of the tissue.

5. The method of claim 1 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

simulating the shear-wave propagation in the tissue using the computational model of shear-wave propagation with predetermined initialized shear modulus and viscosity values for the tissue.

6. The method of claim 1 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

calculating an initial shear modulus value for the tissue based on a measured shear-wave velocity in the shear-wave images under an assumption that the tissue is non-viscous; and

simulating the shear-wave propagation in the tissue using the computational model of shear-wave propagation with the calculated initial shear modulus value and a predetermined initial viscosity value.

7. The method of claim 1 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

determining initial boundary conditions for shear displacement in the tissue based on a number of first frames of the shear wave images; and

simulating the shear-wave propagation in the tissue starting from the initial boundary conditions for the shear displacement in the tissue based on the shear modulus and viscosity values for the tissue using the computational model of shear-wave propagation.

8. The method of claim 1 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

determining initial boundary conditions for the shear-wave propagation using a direct model of an acoustic radiation force impulse (ARFI) used to generate the shear-waves in the shear-wave images, wherein the direct model of ARFI is adapted to current probe parameters of an ultrasound probe used to acquire the shear-wave images; and

simulating the shear-wave propagation in the tissue starting from the initial boundary conditions based on the shear modulus and viscosity values for the tissue using the computational model of shear-wave propagation.

9. The method of claim 1 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

directly comparing a simulated shear-wave displacement to an observed shear-wave displacement at a particular time frame for a plurality of locations in a spatial domain of the shear-wave images using the cost function.

10. The method of claim 9 , wherein directly comparing a simulated shear-wave displacement to an observed shear-wave displacement at a particular time frame for a plurality of locations in a spatial domain of the shear-wave images using the cost function comprises:

calculating a normalized cross-correlation cost function that directly compares the simulated shear-wave displacement to the observed shear-wave displacement at the particular time frame for the plurality of locations in a spatial domain of the shear-wave images.

11. The method of claim 9 , wherein directly comparing a simulated shear-wave displacement to an observed shear-wave displacement at a particular time frame for a plurality of locations in a spatial domain of the shear-wave images using the cost function comprises:

calculating a sum of squared distance cost function that directly compares the simulated shear-wave displacement to the observed shear-wave displacement at the particular time frame for the plurality of locations in the spatial domain of the shear-wave images.

12. The method of claim 1 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

directly comparing a simulated shear-wave displacement to an observed shear-wave displacement for a particular location in a spatial domain of the shear-wave images frame at each of a plurality of time steps using the cost function.

13. The method of claim 1 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

directly comparing a simulated shear-wave displacement to an observed shear-wave displacement for each of a plurality of locations in a spatial domain of the shear-wave images frame at each of a plurality of time steps using the cost function.

14. The method of claim 1 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

calculating a cost function in a radiofrequency space that compares a measured radiofrequency shift of the observed shear-wave propagation with a computed radiofrequency shift of the simulated shear-wave propagation.

15. The method of claim 1 , wherein estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation comprises:

estimating an initial shear modulus value and an initial viscosity value for the tissue a target region of the shear-wave images;

simulating the shear-wave propagation using the computational model of shear-wave propagation with the current values for the shear modulus and viscosity of the tissue in the target region;

generating an error map showing a spatial distribution of error values between the simulated shear-wave propagation using the current values for the shear modulus and viscosity and the observed spatial propagation;

segmenting the error map to identify sub-regions of tissue within the target region based on the error values between the simulated shear-wave propagation using the current values for the shear modulus and viscosity and the observed spatial propagation; and

estimating spatially-varying shear modulus and viscosity values for the tissue in the target region by calculating separate values for the shear modulus and viscosity for each of the identified sub-regions of tissue to optimize the cost function using a multivariate optimization.

16. The method of claim 15 , wherein estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation further comprises:

repeating the steps of simulating the shear-wave propagation using the computational model of shear-wave propagation with the current values for the shear modulus and viscosity of the tissue in the target region, generating an error map, segmenting the error map, and estimating spatially-varying shear modulus and viscosity values for the tissue in the target region until a number of the sub-regions in the target region converges.

17. The method of claim 1 , further comprising:

repeating the steps of simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation, comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function, and estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation, until the simulated shear-wave propagation converges to the observed shear-wave propagation in the shear wave images.

18. The method of claim 2 , wherein the estimated patient-specific shear modulus values and viscosity values for the tissue are spatially varying shear modulus values and viscosity values, and visualizing the estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity comprises:

generating a shear modulus color map by mapping the estimated spatially varying patient-specific shear modulus values to a spatial domain of the shear-wave images and assigning a color to each pixel in the shear modulus color map based on the estimated patient-specific shear modulus value for that pixel; and

generating a viscosity color map by mapping the estimated spatially varying patient-specific viscosity values to the spatial domain of the shear-wave images and assigning a color to each pixel in the viscosity color map based on the estimated patient-specific viscosity value for that pixel.

19. A non-transitory computer readable medium storing computer program instructions for estimating shear modulus and viscosity of tissue of a patient based on shear-wave images of the tissue, the computer program instructions when executed by a processor cause the processor to perform operations comprising:

simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation;

comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function; and

estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation.

20. The non-transitory computer readable medium of claim 19 , wherein the operations further comprise:

visualizing the estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity.

21. The non-transitory computer readable medium of claim 19 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

computing shear displacement of the tissue in spatial domain corresponding to at least a region of the shear-wave images at each of a plurality of time steps based on the shear modulus and viscosity values for the tissue.

22. The non-transitory computer readable medium of claim 21 , wherein computing shear displacement of the tissue in spatial domain corresponding to at least a region of the shear-wave images at each of a plurality of time steps based on the shear modulus and viscosity values for the tissue comprises:

calculating the shear displacement of the tissue in the spatial domain by solving ρ∂ t 2 u=μ∇ 2 u+η∂ t ∇ 2 u at each time step, where μ is the shear modulus, η is the viscosity, ρ is a density of the tissue, and u is shear displacement of the tissue.

23. The non-transitory computer readable medium of claim 19 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

simulating the shear-wave propagation in the tissue using the computational model of shear-wave propagation with predetermined initialized shear modulus and viscosity values for the tissue.

24. The non-transitory computer readable medium of claim 19 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

calculating an initial shear modulus value for the tissue based on a measured shear-wave velocity in the shear-wave images under an assumption that the tissue is non-viscous; and

simulating the shear-wave propagation in the tissue using the computational model of shear-wave propagation with the calculated initial shear modulus value and a predetermined initial viscosity value.

25. The non-transitory computer readable medium of claim 19 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

determining initial boundary conditions for shear displacement in the tissue based on a number of first frames of the shear wave images; and

simulating the shear-wave propagation in the tissue starting from the initial boundary conditions for the shear displacement in the tissue based on the shear modulus and viscosity values for the tissue using the computational model of shear-wave propagation.

26. The non-transitory computer readable medium of claim 19 , wherein simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation comprises:

determining initial boundary conditions for the shear-wave propagation using a direct model of an acoustic radiation force impulse (ARFI) used to generate the shear-waves in the shear-wave images, wherein the direct model of ARFI is adapted to current probe parameters of an ultrasound probe used to acquire the shear-wave images; and

simulating the shear-wave propagation in the tissue starting from the initial boundary conditions based on the shear modulus and viscosity values for the tissue using the computational model of shear-wave propagation.

27. The non-transitory computer readable medium of claim 19 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

directly comparing a simulated shear-wave displacement to an observed shear-wave displacement at a particular time frame for a plurality of locations in a spatial domain of the shear-wave images using the cost function.

28. The non-transitory computer readable medium of claim 27 , wherein directly comparing a simulated shear-wave displacement to an observed shear-wave displacement at a particular time frame for a plurality of locations in a spatial domain of the shear-wave images using the cost function comprises:

calculating one of a normalized cross-correlation cost function or a sum of squared distance cost function that directly compares the simulated shear-wave displacement to the observed shear-wave displacement at the particular time frame for the plurality of locations in a spatial domain of the shear-wave images.

29. The non-transitory computer readable medium of claim 19 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

directly comparing a simulated shear-wave displacement to an observed shear-wave displacement for a particular location in a spatial domain of the shear-wave images frame at each of a plurality of time steps using the cost function.

30. The non-transitory computer readable medium of claim 19 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

directly comparing a simulated shear-wave displacement to an observed shear-wave displacement for each of a plurality of locations in a spatial domain of the shear-wave images frame at each of a plurality of time steps using the cost function.

31. The non-transitory computer readable medium of claim 19 , wherein comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function comprises:

calculating a cost function in a radiofrequency space that compares a measured radiofrequency shift of the observed shear-wave propagation with a computed radiofrequency shift of the simulated shear-wave propagation.

32. The non-transitory computer readable medium of claim 19 , wherein estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation comprises:

estimating an initial shear modulus value and an initial viscosity value for the tissue a target region of the shear-wave images;

simulating the shear-wave propagation using the computational model of shear-wave propagation with the current values for the shear modulus and viscosity of the tissue in the target region;

generating an error map showing a spatial distribution of error values between the simulated shear-wave propagation using the current values for the shear modulus and viscosity and the observed spatial propagation;

segmenting the error map to identify sub-regions of tissue within the target region based on the error values between the simulated shear-wave propagation using the current values for the shear modulus and viscosity and the observed spatial propagation; and

estimating spatially-varying shear modulus and viscosity values for the tissue in the target region by calculating separate values for the shear modulus and viscosity for each of the identified sub-regions of tissue to optimize the cost function using a multivariate optimization.

33. The non-transitory computer readable medium of claim 32 , wherein estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation further comprises:

repeating the operations of simulating the shear-wave propagation using the computational model of shear-wave propagation with the current values for the shear modulus and viscosity of the tissue in the target region, generating an error map, segmenting the error map, and estimating spatially-varying shear modulus and viscosity values for the tissue in the target region until a number of the sub-regions in the target region converges.

34. The non-transitory computer readable medium of claim 19 , where the operations further comprise:

repeating the operations of simulating shear-wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a computational model of shear-wave propagation, comparing the simulated shear-wave propagation to observed shear-wave propagation in the shear-wave images of the tissue using a cost function, and estimating patient-specific shear modulus and viscosity values for the tissue to optimize the cost function comparing the simulated shear-wave propagation to the observed shear-wave propagation, until the simulated shear-wave propagation converges to the observed shear-wave propagation in the shear wave images.

35. The non-transitory computer readable medium of claim 20 , wherein the estimated patient-specific shear modulus values and viscosity values for the tissue are spatially varying shear modulus values and viscosity values, and visualizing the estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity comprises:

generating a shear modulus color map by mapping the estimated spatially varying patient-specific shear modulus values to a spatial domain of the shear-wave images and assigning a color to each pixel in the shear modulus color map based on the estimated patient-specific shear modulus value for that pixel; and

generating a viscosity color map by mapping the estimated spatially varying patient-specific viscosity values to the spatial domain of the shear-wave images and assigning a color to each pixel in the viscosity color map based on the estimated patient-specific viscosity value for that pixel.