• 专利附录
  • 专利说明
  • 权利要求
  • 类似技术
  • 同族专利
  • 引用文献
  • 法律状态
  • 优先权
    • 专利摘要:
    A method and system for automatic noninvasive estimation of shear modulus and biological tissue viscosity from shear wave imaging is disclosed. Shear wave images are acquired to evaluate the mechanical properties of an organ of a patient. Shear wave propagation in tissue in shear wave images is simulated based on shear modulus and viscosity values for the tissue using a shear wave propagation calculation model. Simulated shear wave propagation is compared with shear wave propagation observed in tissue shear wave images using a cost function. Patient-specific shear modulus and viscosity values for the tissue are estimated to optimize the cost function by comparing the simulated shear wave propagation to the observed shear wave propagation.
    公开号:FR3035531A1
    申请号:FR1653593
    申请日:2016-04-22
    公开日:2016-10-28
    发明作者:Dorin Comaniciu；Liexiang Fan；Francois Forlot；Ali Kamen；Tommaso Mansi；Saikiran Rapaka
    申请人:Siemens Medical Solutions USA Inc；
    IPC主号:
    专利说明:

    [0001] BACKGROUND OF THE INVENTION The present invention relates to an estimation based on medical images of mechanical properties of tissue and more particularly to an automatic estimation of shear modulus and tissue viscosity from wave imaging. shearing. Shear-wave imaging (SWI) is an ultrasound-based imaging modality that can provide important information about the structure and integrity of a tissue. In the SWI, an ultrasound probe is used to generate and track propagation shear waves in biological tissue. A radiation force from an acoustic radiation force impulse (ARFI) generates the shear waves in the tissue. The propagation velocity of the shear waves in the tissue is measured and a temporal sequence of images showing the shift of the shear wave is captured by the ultrasound probe. Qualitative measurements have been derived from the SWI, for example to highlight more rigid or soft tissues in a region of interest. The clinical applications of SWI are numerous, especially in oncology, where SWI can be used to distinguish between malignant and benign lesions. However, a precise quantitative estimate of fabric elasticity and viscosity from an SWI remains a significant challenge. If the modulus of elasticity can be directly related to the speed of shear waves in homogeneous isotropic solids, this relation does not hold in viscous media such as biological tissues where viscosity also affects the velocity of the wave. shear. It is therefore important to consider both properties in the estimation process in order to arrive at an accurate assessment of tissue mechanics and tissue constitution.
    [0002] SUMMARY OF THE INVENTION The present invention provides a method and system for estimating patient-specific values for shear modulus and viscosity of biological tissue from shear wave imagery ( SWI). Embodiments of the present invention couple a direct model of shear wave propagation in soft media with an optimization algorithm to automatically estimate both shear modulus and viscosity from wave images shearing. Shear wave displacement is calculated from a direct model of shear wave propagation, taking into account shear modulus and viscosity. A cost function, which evaluates the difference between computer shear wave propagation and shear wave propagation observed in shear wave images, is then minimized, for example using a gradientless optimizer, to estimate custom values for shear modulus and fabric viscosity. Embodiments of the present invention may utilize a hierarchical approach, which permits estimation of spatial shear modulus and viscosity maps, which can then be displayed for an end user for diagnostic purposes. A map obtained from an initial estimate of shear modulus from shear wave imagery using the homogeneous tissue approximation can also be used as an initialization of the proposed approach, which estimates both the shear modulus and viscosity.
    [0003] In one embodiment of the present invention, shear wave propagation in tissue of a patient is simulated based on shear modulus and tissue viscosity values using a propagation computation model. of shear waves. The simulated shear wave propagation is compared to a shear wave propagation observed in tissue shear wave images using a cost function. Patient-specific shear modulus and viscosity values for the tissue are estimated to optimize the cost function by comparing the simulated shear wave propagation to the observed shear wave propagation. In a first aspect, a method for estimating a shear modulus and viscosity of tissue of a patient based on tissue shear wave images comprises: simulating a wave propagation of shearing in the fabric based on shear modulus and viscosity values for the tissue using a shear wave propagation calculation model; comparing the simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function; and estimating patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing simulated shear wave propagation with observed shear wave propagation. Depending on the embodiments, the method may include one or more of the following features: - Viewing the estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity. the simulation of shear wave propagation in the tissue based on shear modulus and tissue viscosity values using a shear wave propagation calculation model comprises: computing a shearing the tissue in a spatial domain corresponding to at least one region of the shear wave images at each of a plurality of time steps based on shear modulus and viscosity values for the tissue. calculating a shear displacement of the tissue in a spatial domain corresponding to at least one region of the shear wave images at each of a plurality of time steps based on the shear modulus values and viscosity for the tissue comprises: calculating the shear displacement of the tissue in the spatial domain by solving p + iz = iV2u + λ8V2u at each time step, where p is the shear modulus, q is the viscosity, p is a density of the tissue, and u is the shift in shear of the tissue. simulation of shear wave propagation in the tissue based on shear modulus and tissue viscosity values using a shear wave propagation calculation model comprises: propagation of shear waves in the tissue using the shear wave propagation calculation model with predetermined initialized shear modulus and tissue viscosity values. the simulation of shear wave propagation in the tissue based on shear modulus and tissue viscosity values using a shear wave propagation calculation model comprises: calculating a shear wave initial shear modulus value for the fabric based on a measured shear wave velocity in the shear wave images with an assumption that the tissue is non-viscous; and simulating shear wave propagation in the tissue using the shear wave propagation calculation model with the calculated initial shear modulus value and a predetermined initial viscosity value. the simulation of shear wave propagation in the tissue based on shear modulus and tissue viscosity values using a shear wave propagation calculation model includes: determination of initial conditions limits for shear displacement in the tissue based on a number of first frames of the shear wave images; and simulation of shear wave propagation in tissue from initial boundary conditions for shear displacement in tissue based on shear modulus and viscosity values for tissue using the model of calculation of shear wave propagation. the simulation of shear wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a shear wave propagation calculation model comprises: initial boundary conditions for shear wave propagation using a direct model of an acoustic radiation force pulse (ARFI) used to generate shear waves in shear wave images, in which the model Direct ARFI is adapted to common probe parameters of an ultrasonic probe used to acquire shear wave images; and simulation of shear wave propagation in tissue from initial boundary conditions based on shear modulus and tissue viscosity values using the shear wave propagation calculation model. . the comparison of simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function includes: direct comparison of a wave shift simulated shearing at observed shear wave motion at a particular time frame for a plurality of locations in a spatial domain of shear wave images using the cost function. direct comparison of simulated shear wave displacement with observed shear wave motion at a particular time frame for a plurality of spatial space locations of shear wave images using the function cost method comprises: calculating a cross-correlated normalized cost function that directly compares the simulated shear wave displacement with the observed shear wave displacement at the particular time frame for the plurality of locations in a domain spatial shear wave images. direct comparison of simulated shear wave displacement with observed shear wave motion at a particular time frame for a plurality of spatial space locations of shear wave images using the function method includes: calculating a distance function cost sum squared that directly compares the simulated shear wave displacement with the observed shear wave displacement at the particular time frame for the plurality of locations in the spatial domain of shear wave images. The comparison of simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function includes: direct comparison of wave shift shear pattern simulated at a shear wave shift observed for a particular location in a spatial domain of the shear wave image frame at each of a plurality of time steps using the cost function. the comparison of simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function includes: direct comparison of a wave shift shear pattern simulated to observed shear wave displacement for each of a plurality of locations in a spatial domain of the shear wave image frame at each of a plurality of time steps using the function cost. The comparison of simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function includes: calculating a cost function in a radio frequency space which compares a measured radio frequency offset of shear wave propagation observed with a calculated radiofrequency offset of simulated shear wave propagation. the estimation of patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing the simulated shear wave propagation to the observed shear wave propagation comprises: the estimate an initial value of shear modulus and an initial viscosity value for the tissue in a target region of the shear wave images; simulation of shear wave propagation using the shear wave propagation calculation model with the current values for shear modulus and tissue viscosity 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 the observed viscosity and spatial propagation; segmentation of the error map to identify subregions of tissue within the target region based on error values between simulated shear wave propagation using current values for shear modulus and the observed viscosity and spatial spread; and estimating shear modulus and space-change viscosity values for the tissue in the target region by calculating separate values for shear modulus and viscosity for each of the identified tissue subregions to optimize the tissue function. cost using an optimization 15 mu lcriteria. the estimation of patient-specific tissue-specific shear modulus and viscosity values for optimizing the cost function by comparing simulated shear wave propagation with observed shear wave propagation further comprises: repetition steps of simulating shear wave propagation using the shear wave propagation calculation model with the current values for shear modulus and tissue viscosity in the target region, generating a error map, error map segmentation, and estimating shear modulus and space-change viscosity values for the tissue in the target region until a number of subregions in the target region converges. the repetition of the simulation steps of shear wave propagation in the tissue based on shear modulus and tissue viscosity values using a shear wave, comparing simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function, and estimating shear modulus values and viscosity for tissue specific to the patient to optimize the cost function by comparing the simulated shear wave propagation with the observed shear wave propagation until the simulated shear wave propagation converges to the to shear wave propagation observed in shear wave images. the shear modulus values and the estimated patient-specific tissue viscosity values are shear modulus values and spatially varying viscosity values, and visualization of the shear modulus and viscosity values for the Patient-specific tissue estimated by generating spatial maps of shear modulus and viscosity includes: generating a color map of shear modulus by mapping the patient-specific shear modulus values estimated to spatial variations over a spatial domain 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 color viscosity map by mapping the estimated patient-specific viscosity values to spatial variations on the spatial domain of the shear wave images and assigning a color to each pixel in the map in viscosity colors based on the patient-specific viscosity value estimated for that pixel. In another aspect, the invention relates to a computer-readable non-transitory medium storing computer program instructions (code) for estimating a shear modulus and tissue viscosity of a patient based on images. tissue shear waves, the computer program instructions, when executed by a processor, causing the processor to perform operations implementing the steps of the present method.
    [0004] In another aspect, an apparatus for estimating a shear modulus and a tissue viscosity of a patient based on tissue shear wave images comprises: a means for simulating a wave propagation of shearing in the fabric based on shear modulus and viscosity values for the tissue using a shear wave propagation calculation model; means for comparing simulated shear wave propagation with observed shear wave propagation in tissue shear wave images using a cost function; and means for estimating patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing the simulated shear wave propagation with the observed shear wave propagation. Depending on the embodiments, the apparatus may include one or more of the following features: a means for viewing the estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity . the means for simulating shear wave propagation in the tissue on the basis of shear modulus and tissue viscosity values using a shear wave propagation calculation model comprises: means for calculating a shear wave shearing the tissue into a spatial domain corresponding to at least one 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. the means for comparing simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function comprises: a means for directly comparing a shear displacement; Shear waves simulated at observed shear wave motion at a particular time frame for a plurality of locations in a spatial domain of shear wave images using the cost function. The means for comparing the simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: a means for directly comparing a displacement of shear waves simulated at a shear wave shift observed for a particular location in a spatial domain of the shear wave image frame at each of a plurality of time steps using the shear wave function. cost. the means for comparing simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function comprises: means for directly comparing wave motion shear pattern simulated at a shear wave shift observed for each of a plurality of locations in a spatial domain of the shear wave image frame at each of a plurality of time steps using the cost function. the means for comparing simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function comprises: means for comparing a measured radio frequency shift of shear wave propagation observed with a calculated radiofrequency offset of simulated shear wave propagation. The means for estimating patient-specific tissue-specific shear modulus and viscosity values for optimizing the cost function by comparing the simulated shear wave propagation with the observed shear wave propagation comprises: to estimate an initial value of shear modulus and an initial viscosity value for the tissue in a target region of the shear wave images; means for simulating shear wave propagation using the shear wave propagation calculation model with current values for shear modulus and tissue viscosity in the target region; means for 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 the observed viscosity and spatial propagation; means for segmenting the error map 3035531 11 to identify subregions of tissue within the target region based on the error values between the simulated shear wave propagation using the current values for the module shear and viscosity and observed spatial propagation; and means for estimating spatially varying shear modulus and viscosity values for the tissue in the target region by calculating separate values for shear modulus and viscosity for each of the identified tissue subregions to optimize the cost function. These and other advantages of the invention will become apparent to those skilled in the art with reference to the following detailed description and accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 illustrates a method for noninvasive estimation of the shear modulus and viscosity of a biological tissue target region according to an embodiment of the present invention; Figure 2 illustrates an application infrastructure for estimating patient-specific shear modulus and viscosity values from shear wave images using a shear wave mode calculation model in one mode. embodiment of the present invention; Figure 3 illustrates a method for estimating patient-specific shear modulus and viscosity values from shear wave images using a shear wave propagation calculation model according to an embodiment of the present invention. the present invention; Figure 4 illustrates examples of shear wave propagation observed and simulated after an estimate of shear modulus and viscosity parameters; and Figure 5 is a high level block diagram of a computer adapted to practice the present invention.
    [0005] DETAILED DESCRIPTION The present invention relates to an automatic estimation of shear modulus and biological tissue viscosity from shear wave imaging (SWI). Embodiments of the present invention are described herein to provide a visual understanding of the method for estimating patient-specific values for shear modulus and viscosity of a tissue region. A digital image is often composed of digital representations of one or more object (s) 10 (or shapes). The numerical representation of an object is often described here in terms of object identification and manipulation. Such manipulations are virtual manipulations made in the memory or other circuits / hardware of a computer system. Accordingly, it should be understood that embodiments of the present invention may be implemented within a computer system using data stored within the computer system. Embodiments of the present invention utilize an inverse modeling approach to estimate patient-specific shear modulus and viscosity values from shear wave images using a direct model of propagation wave propagation. shear. The direct model of shear wave propagation is used to compute, considering a set of shear modulus and viscosity parameters, and an initial condition, the shear wave shift in a grid lattice multidimensional (2D / 3D) whose extent covers the domain observed. The calculated shear wave propagation is then compared with the shear wave propagation observed in the shear wave images. If the calculated shear wave propagation does not match the observed shear wave propagation, depending on a selected cost function, an optimizer process is used to estimate the optimum shear modulus and viscosity. automatically. For example, in one possible implementation, cross-correlated normalized measurement can be used as a cost function to compare calculated and observed shear wave propagation, but any similarity measure can be used. The optimization process can be performed using a gradientless optimizer, but the present invention is not limited thereto. A hierarchical method can be used to estimate spatially varying values for shear modulus and viscosity on a target tissue region. A first map of shear modulus estimates can be obtained using shear wave velocity, which is related to shear modulus in non-viscous media. This map can be used to initialize the estimation procedure but also to identify regions with variable biomechanical properties. Figure 1 illustrates a method for noninvasive estimation of the shear modulus and viscosity of a biological tissue target region according to an embodiment of the present invention. In step 102, shear wave images are received. Shear wave images are acquired by Shear Wave Imaging (SWI), which uses an ultrasound probe to generate and track shear waves propagating in biological tissue. A radiation force of an acoustic radiation force pulse (ARFI) generates the shear waves in the tissue and a temporal sequence of images showing shear wave motion in the tissue over time is captured by the probe. ultrasound. The shear wave images may be a two-dimensional (2D) time-dependent sequence or a three-dimensional (3D) time-dependent sequence. The shear wave images may be received directly from the ultrasound probe, or may be received by loading shear wave images previously acquired from a memory or storage of a computer system or receiving images. of shear waves acquired previously on a data network. Shear wave images may include a target tissue region of a patient. For example, shear wave images may include a tissue region in which a tumor or lesion is present.
    [0006] In step 104, patient-specific shear modulus and viscosity values for tissue in a target region are estimated on the basis of shear wave images using a computational model for propagation of shear waves. The tissue target region may refer to the entire tissue in the shear wave images or may refer to a particular region of interest within the shear wave images. Figure 2 illustrates an application infrastructure for estimating patient-specific shear modulus and viscosity values from shear wave images using a shear wave propagation calculation model according to a embodiment of the present invention. As shown in Figure 2, model 202 is a direct calculation model of shear wave propagation. Taking into account values for shear modulus and tissue viscosity (p ', rin) in the target region, and an initial condition, model 202 generates a simulation 206 of shear wave propagation in the region. target. The shear modulus and viscosity estimation application infrastructure is initialized with initial shear modulus and viscosity values Po, r 10. A cost function 204 compares the simulation 206 with a field reality shear modulus propagation 208 observed in the shear wave images, and sends the result of the comparison to an optimizer 210. The optimizer 210 computes new parameter values for the shear modulus and the viscosity to minimize the cost function 204 and sends the new parameter values for shear modulus and viscosity to the model 202, which generates another simulation 206 using the new values of parameters. When, on the basis of the result of the comparison calculated by the cost function 204, the optimizer 210 determines that the optimal values for the shear modulus and the viscosity have been found, which minimize the cost function 204, the optimizer 210 outputs optimal values for shear modulus and viscosity. The model 202, the cost function 204 and the optimizer 210 are described in more detail in the description for the method of FIG. 3.
    [0007] FIG. 3 illustrates a method for estimating patient-specific shear modulus and viscosity values from shear wave images using a shear wave propagation calculation model according to one embodiment. of the present invention. The method of Figure 3 can be used to implement step 104 of Figure 1. In step 302, shear wave propagation is simulated in the target region using a propagation computation model. of shear waves. The shear wave propagation calculation model calculates shear wave displacement for a given shear modulus and viscosity. To this end, the following partial differential equation for transverse waves can be used: = little + nateu where p is the shear modulus, q is the viscosity, p is the density (which can be assumed to be 1,070 kg / m3 in biological tissues), and u is the shear displacement of tissue. The wave propagates in a space in 1, 2 or 3 dimensions according to Neumann boundary conditions, 0-Dirichlet, or absorption defined according to the parameterization of the acquisition SWI. In one possible implementation, Neumann or absorption limit conditions may be employed by default. In another embodiment, the organ of interest is segmented from a B mode ultrasound image. The resulting boundaries are used to set appropriate shear wave boundary conditions (eg Neumann), while in areas of SWI where no limit is visible, absorption limit conditions are used. The B and SW mode images are aligned by design if the probe does not move between the two acquisitions. This can be done in a completely transparent way for the user by the hardware. The computational model can compute the shift of shear waves on a multidimensional grid network (2D / 3D) whose extent covers the domain of the target tissue region in. shear wave images. As described above, the target tissue region may be the entire shear wave image or a region of interest defined in the shear wave images. In one possible implementation, generic values, such as values from the literature or average values stored in a database from known cases, can be used for initial values for shear modulus and viscosity of the fabric. In another possible implementation, the shear modulus can be estimated directly from the shear wave velocity in the shear wave images. In this case, the viscosity may be given an initial value of zero or a generic value, such as a value from the literature or an average value in a database of known cases. The initial boundary conditions are determined for the calculation of shear wave propagation. In an advantageous embodiment, the first N frames of the acquired shear wave images are used to establish the initial conditions (eg N = 2). In particular, the displacement of the shear wave observed in the first N frames of the shear wave images gives an initial boundary condition, and then the computational model is used for simulated propagation of the shear wave. This ensures that the observed shear wave of field reality in the shear wave images and the calculated shear wave start in exactly the same state, and protect against a time lag between the observed shear wave and the shear wave. calculated shear wave. In another possible embodiment, a direct model of the ARFI pulse is employed to determine the initial conditions of shear wave propagation. In this embodiment, the parameters of the ultrasonic probe are directly used to calculate the force due to the ARFI pulse. In an advantageous implementation, finite element method (FEM) may be used to calculate shear wave propagation over the 1, 2 or 3 dimensional space. An implicit step-by-step approach can be used for greater stability. However, it should be understood that the present invention is not limited to the FEM method with a time step approach implicit in calculating shear wave propagation, and that other methods, such as FEM methods. explicit or finite differences, can also be used to calculate shear wave propagation. In addition, the present invention is not limited to the use of the differential equation described above for a transverse wave such as the shear wave propagation model, and other wave propagation models. Shearing techniques based on more complex models of viscoelastic materials can also be used.
    [0008] In step 304, the simulated shear wave propagation is compared to the shear wave propagation observed in the shear wave images using a cost function. The shear modulus and viscosity are estimated by minimizing a cost function that calculates a similarity (or difference) between the calculated (simulated) shear wave propagation and the measured (observed) shear wave propagation in shear wave images. In a first embodiment, the calculated shear wave propagation is directly compared with the shear wave displacement observed in the shear wave images. According to one advantageous embodiment, a normalized cross correlation (NCC) can be used as a cost function that measures a similarity between calculated and observed shear wave propagation. However, the present invention is not limited to NCC and any other cost function, such as a sum of squared distance, may be similarly employed to measure the similarity between shear wave propagation. calculated and observed. The cost function NCC can be expressed as: (f (x, Y) - (t (x, Y) - 3035531 18 where at is the standard deviation of the measured shear wave propagation t (x, y ), of is the standard deviation of the calculated shear wave propagation f (X, y), is the mean of the set of measured data, f is the average of the simulation set, and n is In one possible implementation, the NCC is computed at a user-defined time frame (or automatically selected) over the entire domain of the target region. refers to a number of locations (pixels / voxels), denoted as (x, y) in the equation above, to compare simulated shear wave displacement with shear wave displacement observed at a In another implementation, the NCC can be calculated at a position in the user-defined space (or selected automatically) over the entire time domain. In this case, n refers to the number of time steps at which to compare the simulated shear wave displacement with the shear wave displacement observed for a particular spatial location. In another possible implementation, the NCC can be calculated over the entire space-time domain. In a second embodiment, as an alternative for the cost function directly comparing simulated and observed shear wave propagation, an indirect estimate can be performed by working directly in the radio frequency (RF) space. . Intuitively, the shift of shear waves is captured by an offset in the radio frequency signal. By following this shift in time, shear wave motion can be estimated and then displayed to the user. In this mode, the shear modulus and viscosity can be estimated by minimizing the differences between the measured RF offset and a calculated RF offset obtained as the difference in the amplitude of the shear displacement simulated at a specific location. An advantage of working directly in the RF space is that the cost function is not affected by any post-processing performed on the RF signal when estimating shear wave displacement. Another advantage of working directly in the RF space is that the measured shear wave motion can be automatically smoothed through the adjusted model after estimating shear modulus and viscosity (i.e. the propagation of simulated shear waves converges to the measured shear wave propagation).
    [0009] In step 306, it is determined whether the simulated shear wave propagation has converged to the observed shear wave propagation. for example, a difference value between the simulated and observed shear wave propagation, as calculated by the cost function, can be compared to a predetermined threshold value. It is determined that the simulated shear wave propagation has converged to the shear wave propagation observed when the difference value is less than the threshold value. Otherwise, it is determined that simulated shear wave propagation did not converge to the observed shear wave propagation. In addition, in one possible implementation, the simulated shear wave propagation can be considered to have converged to the observed shear wave propagation if a predetermined maximum number of iterations is reached. If it is determined that simulated shear wave propagation has not converged to the observed shear wave propagation, the method proceeds to step 308.
    [0010] If it is determined that the simulated shear wave propagation has converged to the observed shear wave propagation, the method proceeds to step 310. In step 308, the shear modulus parameters and viscosity of the tissue in the target region are estimated by minimizing the cost function. A gradientless optimizer can be used to calculate new values for shear modulus and viscosity that minimize the cost function. In an advantageous embodiment, shear modulus and tissue viscosity values in the target region can be calculated using a coarse-to-fine hierarchical approach to estimate spatially varying parameters for shear modulus and viscosity. . In such a hierarchical approach, in a first step, it is assumed that the tissue in the target region is homogeneous and a single value is calculated for each of the shear modulus and viscosity for the entire target region. Next, the spatial domain of the target region is divided into sub-regions based on the spatial distribution of a simulation error (eg, sum of high distances squared or NCC error measurement between wave propagation shear rate calculated and measured at each point in the spatial domain), shear modulus and viscosity values are estimated separately for each of the subregions. In particular, after initial estimation of the shear modulus and viscosity with the assumption of homogeneous tissue, another simulation of shear wave propagation is performed by the computational model using the modulus values of the shear modulus. Updated shear and viscosity and error (eg sum of high squared difference or NCC) between calculated and observed shear wave propagation. In an advantageous implementation, the same measurement as that used to calculate the cost function (e.g., NCC, squared difference sum, etc.) may be used to calculate the error, but the present invention is not It does not limit, and it is also possible that different measures can be used for the cost function evaluation and the error calculation at this step. An error map can be generated by mapping the computed error value at each point in the spatial domain to an image of the spatial domain. For example, the error map may be an image in which the intensity or color at each pixel depends on the error calculated at that pixel. The error map is segmented to identify regions of the error map with similar error values. The error map can be segmented using any automated or semi-automated image segmentation technique, such as creating an intensity threshold, region growth, graphical slices, random segmentation of Walker, etc. Once the different regions are identified in the error map, a multicriteria optimization can be used to estimate different shear modulus and viscosity parameters of each of the identified spatial regions to best minimize the cost function that compares the Calculated shear wave propagation to the observed shear wave propagation. In a possible implementation, this optimization can only be performed for regions having high error values (for example greater than a threshold). The steps of generating an error map, segmenting the error map to identify regions with different error values, and calculating the shear modulus and viscosity parameters for the identified regions can be to be repeated, and at each iteration, regions identified at the previous iteration can be divided into smaller regions. These steps may be iterated until the number of different regions identified in the spatial domain converges, i.e., the overall average or maximum error is below a certain threshold. Once the spatially variable shear modulus and viscosity parameters for the tissue in the target region are estimated, the process returns to step 302, and 302, 304 and 306 are repeated with the shear modulus and viscosity updated. In particular, the computational model is used to simulate shear wave propagation with updated shear modulus and viscosity values (step 302), simulated shear wave propagation is compared to propagation. of shear waves observed in the shear wave images using the cost function (step 304), and it is determined whether simulated shear wave propagation has converged to the propagation of the shear waves. observed shear (step 306). In step 310, once it is determined that the simulated shear wave propagation has converged to the shear wave propagation observed in the shear images, the method of FIG. and the final estimated values of the shear modulus and viscosity parameters are returned. Returning to Figure 1, in step 106, the estimated shear modulus and viscosity values for the target region are output. The estimated shear modulus and viscosity values can be output by viewing the shear modulus and viscosity values on 1, 2 or 3 dimensional boards, which can be displayed on a display device. a computer system. For example, the shear modulus values identified for each spatial location of the target tissue region may be mapped to an image of the target region, which is displayed on the display device. The shear modulus values and the viscosity values can be visualized using respective color maps, in which the color (or intensity) at each pixel or voxel in the spatial domain depends on the shear modulus value. or the viscosity value calculated at this location. In one possible implementation, the error maps generated in step 308 of Figure 3 can be used to generate these 10 color maps, since they are already divided into regions for which common values of shear modulus and viscosity were calculated. Space maps of shear modulus and viscosity can be displayed for a user (eg physician, technician, etc.) for diagnostic purposes. For example, in oncology applications, the target region in the shear wave images may include a lesion or tumor and the patient-specific shear modulus and viscosity values estimated for the lesion or tumor may allow the user to diagnose the lesion or tumor as malignant or benign. In a possible application, the values of shear modulus and viscosity for a lesion or tumor and / or the surrounding region can be used as features and fed into a machine-learning-based classifier, such as a support vector machine (SVM), which can then automatically classify the lesion or tumor. For example, based on the estimated shear modulus and viscosity values, the machine-based trained classifier can classify the lesion or tumor as malignant or benign, can classify the lesion / tumor as a particular type of lesion. or tumor, or may classify the lesion / tumor to assign a particular grade to the lesion / tumor. It should be understood that the oncology applications described herein are not intended to limit the present invention, and that the method of Figure 1 may also be applied to other applications.
    [0011] In addition to spatial maps of shear modulus and viscosity, simulated shear wave propagation and shear wave images showing the observed shear wave propagation can also be displayed, for example on a shear wave device. display of a computer system, as well as the error maps generated in step 308 of Fig. 3. Fig. 4 illustrates examples of observed and simulated shear wave propagation. As shown in Figure 4, image 402 shows the measured (observed) shear wave propagation in the shear wave images for the entire spatial range of the shear wave images, and the image 404 shows the measured (observed) shear wave propagation for a region of interest used for a cost function evaluation. image 406 shows simulated shear wave propagation throughout the spatial domain and image 408 shows the simulated shear wave propagation in the region of interest used for cost function evaluation. In the example of Figure 4, the first two frames of the shear wave images are used as initial conditions for the simulation of shear wave propagation, and only a part of the space (region of interest) is used to evaluate the cost function to minimize the effects of boundary conditions.
    [0012] The field reality for tissue properties in the region of interest is a shear modulus of 4 kPa and a viscosity of 0 Pa.s. The results of the estimation using the methods of Figures 1 and 3 for this example are a shear modulus of 4.01 kPa and a viscosity of 4.4 e-1 ° Pa.s. The total space (images 402 and 406 of FIG. 4) shows a difference for wave propagation, but the method nevertheless manages to estimate values close to field reality values since the evaluation was carried out in one region. of interest (images 404 and 408 of Figure 4) remote from the boundary conditions. The methods described above for noninvasive estimation of patient-specific shear modulus and viscosity values for biological tissue based on shear wave imaging (SWI) can be performed on a computer using computer processors, memory units, storage devices, computer software, and other well-known components. A high level block diagram of such a computer is illustrated in Figure 5. The computer 502 contains a processor 504, which controls the entire operation of the computer 502 by executing computer program instructions that define such operation. . The computer program instructions may be stored in the storage device 512 (for example a magnetic disk) and loaded into the memory 510 when execution of the computer program instructions is desired. Thus, the steps of the methods of Figures 1, 2 and 3 can be defined by the computer program instructions stored in the memory 510 and / or storage 512 and controlled by the processor 504 executing the computer program instructions. An ultrasonic acquisition device 520, such as an ultrasonic probe, may be connected to the computer 502 to acquire shear wave images and input the shear wave images into the computer 502. It is possible that the ultrasonic acquisition device 520 and the computer 502 communicate wirelessly through a network. In one possible embodiment, the computer 502 may be located away from the ultrasonic acquisition device 520, and the method steps may be performed by the computer 502 as part of a server-based service. or the cloud. Computer 502 also includes one or more network interface (s) 506 for communicating with other devices over a network. The computer 502 also includes other input / output devices 508 that allow user interaction with the computer 502 (e.g., a display, keyboard, mouse, speakers, buttons, etc. .). Such input / output devices 508 may be used in conjunction with a set of computer programs as an annotation tool for annotating volumes received from the ultrasonic acquisition device 520. Those skilled in the art will recognize that the The implementation of an actual computer may also contain other components, and Figure 5 is a high-level representation of some of the components of such a computer for illustrative purposes.
    [0013] The foregoing detailed description should be understood to be illustrative and illustrative in all respects but not restrictive. It should be understood that the embodiments shown and described herein are merely illustrative of the principles of the present invention and that various modifications may be practiced by those skilled in the art without departing from the spirit of the present invention. the invention. Those skilled in the art can implement various other combinations of features without departing from the spirit of the invention.
    权利要求:
    Claims (27)
    [0001]
    REVENDICATIONS1. A method of estimating shear modulus and tissue viscosity of a patient based on tissue shear wave images, comprising: simulating a shear wave propagation in the tissue on the basis of shear modulus and viscosity values for the tissue using a shear wave propagation calculation model; comparing the simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function; and estimating patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing the simulated shear wave propagation to the observed shear wave propagation.
    [0002]
    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.
    [0003]
    The method of claim 1, wherein simulating a shear wave propagation in the tissue based on shear modulus values and tissue viscosity using a wave propagation calculation model. shearing method comprises: computing a shear displacement of the tissue in a spatial domain corresponding to at least one region of the shear wave images at each of a plurality of time steps based on the shear modulus values and viscosity for the fabric.
    [0004]
    The method of claim 3, wherein calculating a shear shift of the tissue in a spatial domain corresponding to at least one region of the shear wave images at each of a plurality of time steps on the basis of shear modulus and viscosity values for tissue comprises: calculating shear displacement of tissue in the spatial domain by solving little - = fire + riatV 2u at each time step, where p is the shear modulus , q is the viscosity, p is a density of the fabric, and u is the shift in shear of the fabric.
    [0005]
    The method of claim 1, wherein simulating a shear wave propagation in the tissue based on shear modulus and viscosity values for the tissue using a propagation computation model of Shear waves include: simulation of shear wave propagation in the tissue using the shear wave propagation calculation model with predetermined initialized shear modulus and tissue viscosity values.
    [0006]
    The method of claim 1, wherein simulating a shear wave propagation in the tissue based on shear modulus values and tissue viscosity using a propagation computation model. Shear waves include: calculating an initial shear modulus value for the fabric based on a measured shear wave velocity in the shear wave images with an assumption that the tissue is non-viscous; and simulating a shear wave propagation in the tissue using the shear wave propagation calculation model with the calculated initial shear modulus value and a predetermined initial viscosity value.
    [0007]
    The method of claim 1, wherein simulating shear wave propagation in the tissue based on shear modulus values and tissue viscosity using a propagation computation model of Shear waves include: determining initial boundary conditions for shear displacement in the tissue based on a number of first frames of the shear wave images; and simulating shear wave propagation in the tissue starting from the initial boundary conditions for shear displacement in the tissue based on shear modulus values and tissue viscosity using the calculation of shear wave propagation. 10
    [0008]
    The method of claim 1, wherein simulating a shear wave propagation in the tissue based on shear modulus values and viscosity for the tissue using a wave propagation calculation model. shearing comprises: determining initial boundary conditions for shear wave propagation using a direct model of an acoustic radiation force pulse (ARFI) used to generate shear waves in the wave images shear, in which the ARFI direct model is adapted to current probe parameters of an ultrasonic probe used to acquire shear wave images; and simulation of shear wave propagation in tissue from initial boundary conditions based on shear modulus and tissue viscosity values using the shear wave propagation calculation model. . 25
    [0009]
    The method of claim 1, wherein the comparison of simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: the comparison Directly from a shear wave motion simulated to observed shear wave motion at a particular time frame for a plurality of locations in a spatial domain of shear wave images using the cost function. 3035531 29
    [0010]
    The method of claim 9, wherein the direct comparison of simulated shear wave displacement with observed shear wave displacement at a particular time frame for a plurality of locations in a spatial domain of the image of the shear wave. Shear waves using the cost function include: calculating a cross-correlated normalized cost function which directly compares the simulated shear wave displacement with the observed shear wave displacement at the particular time frame for the plurality of locations in a spatial domain of shear wave images.
    [0011]
    The method of claim 9, wherein the direct comparison of simulated shear wave displacement with observed shear wave displacement at a particular time frame for a plurality of locations in a spatial domain of the image of a shear wave. Shear waves using the cost function include: calculating a sum of squared distance cost function which directly compares the simulated shear wave displacement with the observed shear wave displacement at the time frame particularly for the plurality of locations in the spatial domain of shear wave images.
    [0012]
    The method of claim 1, wherein the comparison of simulated shear wave propagation with shear wave propagation observed in tissue shear wave images using a cost function comprises: direct comparison of simulated shear wave displacement with observed shear wave motion for a particular location in a spatial domain of the shear wave image frame at each of a plurality of time steps using the cost function. 303 5 5 3 1 30
    [0013]
    The method of claim 1, wherein comparing the simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: direct comparison of simulated shear wave displacement with observed shear wave displacement for each of a plurality of locations in a spatial domain of the shear wave image frame at each of a plurality of locations plurality of time steps using the cost function. 10
    [0014]
    The method of claim 1, wherein comparing the simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: calculating a cost function in a radio-frequency space that compares a measured radio frequency offset of the observed shear wave propagation with a calculated radiofrequency offset of the simulated shear wave propagation. 20
    [0015]
    The method of claim 1, wherein estimating patient specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing simulated shear wave propagation to wave propagation. observed shearing comprises: estimating an initial value of shear modulus and an initial viscosity value for the tissue in a target region of the shear wave images; the simulation of shear wave propagation using the shear wave propagation calculation model with the usual values for shear modulus and tissue viscosity 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 the observed viscosity and spatial propagation; Mapping the error map to identify subregions of tissue within the target region based on error values between simulated shear wave propagation using current values for shear modulus and the observed viscosity and spatial spread; and estimating shear modulus and space-change viscosity values for tissue in the target region by calculating separate values for shear modulus and viscosity for each of identified tissue subregions to optimize the function. cost using a multicriteria optimization. 15
    [0016]
    The method of claim 15, wherein estimating patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing simulated shear wave propagation with wave propagation. The observed shearing error further comprises: repeating the simulation steps of the shear wave propagation using the shear wave propagation calculation model with the current values for the shear modulus and the tissue viscosity in the shear wave. the target region, generating an error map, segmenting the error map, and estimating shear modulus values and spatially varying viscosity for the tissue in the target region to a number of subregions in the target region converge.
    [0017]
    The method of claim 1, further comprising: repeating the steps of simulating shear wave propagation in the tissue based on shear modulus values and tissue viscosity using a model calculating shear wave propagation, comparing simulated shear wave propagation to shear wave propagation observed in tissue shear wave images using a cost function, and estimating patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing the simulated shear wave propagation with the observed shear wave propagation, until Simulated shear wave propagation converges to the shear wave propagation observed in shear wave images. 10
    [0018]
    The method of claim 2, wherein the shear modulus values and the estimated patient-specific tissue viscosity values are shear modulus values and spatially varying viscosity values, and viewing the values of Apparent patient-specific tissue shear and viscosity modulus estimated by generating spatial maps of shear modulus and viscosity includes: generating a color map of shear modulus by mapping the shear modulus values specific to the shear modulus. Patient estimated spatial variations on a spatial domain of shear wave images and assigning a color to each pixel in the shear modulus color map based on the patient specific shear modulus value estimated for this pixel; and generating a color viscosity map by mapping the estimated patient-specific viscosity values to spatial variations over a spatial range of shear wave images and assigning a color to each pixel in the map in viscosity colors based on the patient-specific viscosity value estimated for that pixel.
    [0019]
    Apparatus for estimating a shear modulus and tissue viscosity of a patient based on tissue shear wave images, comprising: a means for simulating shear wave propagation in the patient; fabric based on shear modulus and viscosity values for tissue using a shear wave propagation calculation model; means for comparing simulated shear wave propagation with observed shear wave propagation in tissue shear wave images using a cost function; and means for estimating patient-specific tissue-specific shear modulus and viscosity values to optimize the cost function by comparing the simulated shear wave propagation with the observed shear wave propagation.
    [0020]
    The apparatus of claim 19, further comprising: means for viewing estimated patient-specific shear modulus and viscosity values by generating spatial maps of shear modulus and viscosity.
    [0021]
    Apparatus according to claim 19, wherein the means for simulating shear wave propagation in the tissue based on shear modulus values and tissue viscosity using a propagation computation model. Shear wave comprises: means for calculating a shear displacement of the tissue in a spatial domain corresponding to at least one region of the shear wave images at each of a plurality of time steps based on the modulus values of Shear and viscosity for the fabric. 25
    [0022]
    Apparatus according to claim 19, wherein the means for comparing simulated shear wave propagation with observed shear wave propagation in the tissue shear wave images using a cost function comprises: means for directly comparing simulated shear wave motion with observed shear wave motion at a particular time frame for a plurality of locations in a spatial domain of the shear wave images using the function cost.
    [0023]
    Apparatus according to claim 19, wherein the means for comparing simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: means for directly comparing a simulated shear wave shift with observed shear wave displacement for a particular location in a spatial range of the shear wave image frame at each of a plurality of shear waves. temporal steps using the cost function.
    [0024]
    24. Apparatus according to claim 19, wherein the means for comparing the simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: means for directly comparing a simulated shear wave motion with an observed shear wave shift for each of a plurality of locations in a spatial range of the shear wave image frame at each a plurality of time steps using the cost function.
    [0025]
    Apparatus according to claim 19, wherein the means for comparing simulated shear wave propagation with shear wave propagation observed in the tissue shear wave images using a cost function comprises: means for comparing a measured radio frequency offset of the observed shear wave propagation with a calculated radiofrequency offset of the simulated shear wave propagation. 3035531
    [0026]
    Apparatus according to claim 19, wherein the means for estimating patient-specific tissue-specific shear modulus and viscosity values for optimizing the cost function by comparing simulated shear wave propagation with propagation of Shear waves observed include: means for estimating an initial shear modulus value and an initial viscosity value for the tissue in a target region of the shear wave images; means for simulating shear wave propagation using the shear wave propagation calculation model with current values for shear modulus and tissue viscosity in the target region; means for 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 the observed viscosity and spatial propagation; means for segmenting the error map to identify subregions of tissue within the target region based on the error values between the simulated shear wave propagation using the current values for the shear and viscosity and observed spatial propagation; and means for estimating spatially varying shear modulus and viscosity values for the tissue in the target region by calculating separate values for shear modulus and viscosity for each of the identified tissue subregions to optimize the cost function.
    [0027]
    27. A computer-readable non-transitory medium storing computer program instructions for, when the computer program instructions are executed by a computer, implementing the method of any one of claims 1 to 18.
    类似技术:
    公开号 | 公开日 | 专利标题
    FR3035531A1|2016-10-28|
    KR101805619B1|2017-12-07|Apparatus and method for creating optimal 2-dimensional medical image automatically from 3-dimensional medical image
    US20170322309A1|2017-11-09|Specular reflection removal in time-of-flight camera apparatus
    Marin et al.2016|Reliable fusion of tof and stereo depth driven by confidence measures
    JP6239594B2|2017-11-29|3D information processing apparatus and method
    McGuinness et al.2011|Toward automated evaluation of interactive segmentation
    Haller et al.2011|Design of interpolation functions for subpixel-accuracy stereo-vision systems
    CN102246206B|2015-07-22|Vessel analysis
    KR20150047315A|2015-05-04|Apparatus and method for computer aided diagnosis
    KR102128325B1|2020-07-01|Image Processing System
    FR2936889A1|2010-04-09|METHOD FOR REPLACING A SET OF POINTS IN IMAGES
    CN106683176A|2017-05-17|Visceral organ three-dimensional model construction method and device
    US20150063649A1|2015-03-05|Method and System for Blood Flow Velocity Reconstruction From Medical Images
    WO2010037850A2|2010-04-08|Image processing method for estimating a brain shift in a patient
    Agresti et al.2018|Combination of spatially-modulated ToF and structured light for MPI-free depth estimation
    Cai et al.2012|Automated extraction of three-dimensional cereal plant structures from two-dimensional orthographic images
    Georgiev et al.2018|Time-of-flight range measurement in low-sensing environment: Noise analysis and complex-domain non-local denoising
    Kang et al.2015|Progressive 3D model acquisition with a commodity hand-held camera
    CN104463825A|2015-03-25|Apparatus and method for detecting objects in three-dimensional volumetric image
    Maki et al.2017|3d model generation of cattle using multiple depth-maps for ict agriculture
    CN104685542B|2017-09-22|Method and system for detecting and characterizing channel system
    EP3314572B1|2019-08-07|Edge detection on images with correlated noise
    Wang et al.2008|Artifact removal and texture-based rendering for visualization of 3D fetal ultrasound images
    JP4432495B2|2010-03-17|Object shape estimation method, object shape estimation device, object shape estimation program, and storage medium storing object shape estimation program
    Kadmin et al.2022|Improvement of Disparity Measurement of Stereo Vision Algorithm Using Modified Dynamic Cost Volume
    同族专利:
    公开号 | 公开日
    KR20160125910A|2016-11-01|
    US9814446B2|2017-11-14|
    DE102016107220A1|2016-10-27|
    CN106073824B|2019-04-23|
    CN106073824A|2016-11-09|
    US20160310107A1|2016-10-27|
    KR101874053B1|2018-07-04|
    DE102016107220B4|2018-10-25|
    引用文献:
    公开号 | 申请日 | 公开日 | 申请人 | 专利标题
    KR100868551B1|2007-04-04|2008-11-13|경희대학교 산학협력단|Apparatus and method for imaging shear modulus within a body|
    US8197408B2|2008-02-27|2012-06-12|Siemens Medical Solutions Usa, Inc.|Sparse tissue property measurements in medical ultrasound imaging|
    US8187187B2|2008-07-16|2012-05-29|Siemens Medical Solutions Usa, Inc.|Shear wave imaging|
    CN102469989B|2009-07-07|2014-04-16|株式会社日立医疗器械|Ultrasonic diagnosis apparatus and ultrasonic measurement method|
    US8469891B2|2011-02-17|2013-06-25|Siemens Medical Solutions Usa, Inc.|Viscoelasticity measurement using amplitude-phase modulated ultrasound wave|
    US10338203B2|2011-09-09|2019-07-02|Siemens Medical Solutions Usa, Inc.|Classification preprocessing in medical ultrasound shear wave imaging|
    US8801614B2|2012-02-10|2014-08-12|Siemens Medical Solutions Usa, Inc.|On-axis shear wave characterization with ultrasound|
    US9468421B2|2012-02-16|2016-10-18|Siemens Medical Solutions Usa, Inc.|Visualization of associated information in ultrasound shear wave imaging|
    US9332962B2|2013-03-13|2016-05-10|Siemens Medical Solutions Usa, Inc.|Ultrasound ARFI displacement imaging using an adaptive time instance|
    US10743814B2|2013-03-15|2020-08-18|Siemens Medical Solutions Usa, Inc.|Fat fraction estimation using ultrasound with shear wave propagation|
    CN103431874B|2013-09-06|2015-06-03|中国科学院深圳先进技术研究院|Method and system for estimating acoustic radiation force pulse imaging|
    US10376242B2|2015-04-16|2019-08-13|Siemens Medical Solutions Usa, Inc.|Quantitative viscoelastic ultrasound imaging|KR102287021B1|2014-10-28|2021-08-09|수퍼소닉 이매진|Imaging Methods and Apparatuses for Performing Shear Wave Elastography Imaging|
    US10537305B2|2015-09-30|2020-01-21|General Electric Company|Detecting amniotic fluid position based on shear wave propagation|
    US10610302B2|2016-09-20|2020-04-07|Siemens Healthcare Gmbh|Liver disease assessment in medical imaging|
    US11154277B2|2017-10-31|2021-10-26|Siemens Medical Solutions Usa, Inc.|Tissue viscoelastic estimation from shear velocity in ultrasound medical imaging|
    CN109077754B|2018-07-06|2020-04-14|深圳大学|Method and equipment for measuring tissue mechanical characteristic parameters|
    CN113536984A|2021-06-28|2021-10-22|北京沧沐科技有限公司|Image target identification and tracking system based on unmanned aerial vehicle|
    法律状态:
    2017-04-25| PLFP| Fee payment|Year of fee payment: 2 |
    2018-04-12| PLFP| Fee payment|Year of fee payment: 3 |
    2019-04-25| PLFP| Fee payment|Year of fee payment: 4 |
    2020-04-10| PLFP| Fee payment|Year of fee payment: 5 |
    2021-04-19| PLFP| Fee payment|Year of fee payment: 6 |
    优先权:
    申请号 | 申请日 | 专利标题
    US14/693,080|US9814446B2|2015-04-22|2015-04-22|Method and system for automatic estimation of shear modulus and viscosity from shear wave imaging|
    [返回顶部]