Patent Publication Number: US-2022218310-A1

Title: Non-invasive estimation of material parameters

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application Ser. No. 62/846,191, filed by Raffaella Righetti, et al. on May 10, 2019, entitled “NON-INVASIVE IMAGING OF YOUNG&#39;S MODULUS AND POISSON&#39;S RATIO IN CANCERS,” U.S. Provisional Application Ser. No. 62/846,216, filed by Raffaella Righetti, et al. on May 10, 2019, entitled “ESTIMATION OF INTERSTITIAL PERMEABILITY AND VASCULAR PERMEABILITY IN CANCERS,” and U.S. Provisional Application Ser. No. 62/846,241, filed by Raffaella Righetti, et al. on May 10, 2019, entitled “POROELASTOGRAPHY METHOD TO ASSESS THE SOLID STRESS DISTRIBUTION IN CANCERS”, which are each commonly assigned with this application and incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     This application is directed, in general, to estimating material parameters and, more specifically, to the non-invasive assessment of mechanical and transport parameters inside materials, for example tissues such as tumors. 
     BACKGROUND 
     Understanding tissue parameters can be beneficial in treating patients. For example, various parameters can be used to describe the mechanical behavior of tumors and other tissues, and can also indicate changes as the mechanical properties of tissues are altered due to a disease, such as cancer, atherosclerosis, fibrosis of the liver, etc. Young&#39;s modulus (YM) and Poisson&#39;s ratio (PR) are examples of mechanical parameters that can be useful in the diagnosis, prognosis, and treatment of diseases. Young&#39;s modulus (YM) and Poisson&#39;s ratio (PR) can also be useful in understanding and predicting the behavior of non-biological materials. 
     Interstitial permeability and vascular permeability are also valuable material parameters that can be useful in understanding tumors. Both interstitial permeability and vascular permeability of a tumor can affect drug delivery to the tumor through modifying the convection and consolidation times of drug molecules inside the tumor. Solid stress (SSg) can also be a beneficial material parameter. 
     SSg inside a tumor can be divided in three main categories: stress exerted on the tumor by the surrounding host tissue also called “externally applied stress”, “swelling stress” and growth-induced or “residual stress.” The externally applied SSg is generated by the tissue surrounding the tumor as a consequence of cells within tumors growing and producing new solid material-cells and matrix fibers, which push against the surrounding host tissue to expand. The surrounding tissue, in turn, resists the expansion by exerting a stress on the tumor. Swelling SSg is related to a phenomenon called chemical expansion. The interstitial space of many tumors may have a high concentration of negatively charged hyaluronan chains. The repulsive electrostatic force among these negative charges may cause swelling in the tumor. In general terms, the residual SSg may be defined as the remaining stress inside a body, when all external loads on the body have been removed. 
    
    
     
       BRIEF DESCRIPTION 
       Reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates a block diagram of an example of a system constructed according to the principles of the disclosure; 
         FIG. 2  illustrates a block diagram of an example of a material parameter estimator constructed according to the principles of the disclosure; 
         FIG. 3  illustrates a flow diagram of an example of a method that includes estimating parameters inside materials carried out according to the principles of the disclosure; 
         FIG. 4  illustrates a flow diagram of an example of another method that includes estimating parameters inside materials carried out according to the principles of the disclosure; and 
         FIG. 5  illustrates a flow diagram of an example of yet another method that includes estimating parameters inside materials carried out according to the principles of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Included herein are techniques or methods, an apparatus, and system to estimate material parameters using strain data from the material. The material parameters include mechanical and transport parameters of a material. Techniques disclosed herein use the strain data and analytical models to provide new, non-invasive tools to assess mechanical and transport parameters in materials, such as biological tissues including tumors. A tumor is a mass of tissue that can be benign or malignant. As such, the tumor can be cancer. The tumor can be from a sample that has been removed from a host or can still be with the host, i.e., unremoved. Accordingly, the strain data can be acquired employing ex vivo or in vivo measurements. The host can be a human or an animal. 
     A material is a biological or non-biological material. As noted above, a tissue, such as a tumor, is an example of a biological material. The techniques included herein can also be used to estimate tissue parameters in other materials or biological tissues that are not tumors such as musculoskeletal tissue, brain, kidney, liver and other tissues. The techniques included herein can also be used to estimate parameters of non-biological materials different than biological tissues such as man-made materials, minerals, soils, etc. 
     The strain data can be obtained from a material using an imaging method or can be obtained employing other methods used in the art. When using an imaging method, image data of a material is provided that corresponds to parameters of the material. From the acquired image data, the various parameters can be determined using the developed analytical models. The imaging method can be ultrasound, mammography, magnetic resonance imaging (MRI), computed tomography (CT), X-rays, optics, acoustics, photoacoustic imaging, etc. or a combination of imaging methods. In some embodiments disclosed herein, ultrasound is used as the imaging method. The imaging method can be part of a treatment or can be part of a testing process. For example, the image data can be obtained as part of a process to test the effect of drugs on a tissue. 
     The imaging method can be performed as part of an examination typically executed in clinical settings. Acquiring the image data can include compressing the tissue for a designated amount of time, while the imaging probe is in contact with the tissue. The compression time can vary depending on, for example, the imaging method and the tissue properties. Ultrasound elastography is an example of an imaging modality where compression is applied on a sample tissue and strain data is measured. Normal strain data of a tissue can be obtained from ultrasound elastography and employed in disclosed analytical models to estimate the various parameters. 
     The analytical models disclosed herein provide a relationship between the different material parameters and the strain data. The analytical models can be used with specific experimental set-ups, including but not limited to creep compression, stress relaxation, and sinusoidal excitations. For example, an analytical model can be used for tumors surrounded by background tissues wherein mechanopathological parameters are estimated using the strain data from the ultrasound experiment. 
     The disclosure provides a non-invasive technique that uses strain data and analytical models to determine mechanical and transport parameters in biological and non-biological materials. For example, the disclosure provides a non-invasive technique that uses strain data and analytical models to simultaneously reconstruct YM and PR of a tumor and of its surrounding tissues, irrespective of the shape and boundary conditions of the tumor. The disclosed methods can estimate the YM and PR of tumors in complex boundary conditions and for tumors of many different shapes such as sphere, ellipse, trigon, tetragon, pentagon, etc. The disclosed non-invasive method allows the generation of high spatial resolution YM and PR maps from strain data, such as axial and lateral strain data, obtained via, for example, an imaging method. Non-invasive techniques that use analytical models and strain data for estimating interstitial permeability, vascular permeability, and spatial distribution of the solid stress (SSg) are also disclosed. 
     Some of the advantages offered by the disclosed techniques include non-invasiveness, low cost, safety, non-radiation, portability, computational efficiency, etc. The disclosed techniques can also be used before or after different types of treatments such as vascular normalization, stress normalization, chemotherapy, immunotherapy, targeted drug delivery, etc. Additionally, the disclosed non-invasive technique can be integrated into multiple platforms such as computer program products, imaging systems, or dedicated devices, such as lab devices or lab equipment. Therefore, the technology can be made readily available for clinical applications in diagnostic systems, commercialized as a software package, and manufactured in a portable diagnostic and/or therapeutic device. The technology can also be made readily available for applications in non-medical systems, commercialized as a software package, and manufactured in a portable device. For example, a lab device can be configured, i.e., designed and constructed with the necessary logic, to employ the disclosed technology to quantify material properties or to test the efficacy of a drug or drugs on a tissue or a tumor. 
       FIG. 1  illustrates a block diagram of an example of a system  100  constructed according to the principles of the disclosure. The system  100  includes an imaging system  110  and a material parameter estimator  120 . The imaging system  110  and the material parameter estimator  120  can be in separate computing devices as illustrated that can be communicatively coupled via conventional connections. In some examples, the imaging system  110  and the material parameter estimator  120  are integrated in a single computing device. 
     The imaging system  110  is configured to acquire image data of a material. The data of the material is non-invasively acquired and can be acquired without the use of an imaging contrast agent. The imaging system  110  can be an ultrasound system. The ultrasound system can have a single element, linear or two-dimensional transducers for obtaining data. In one example, ultrasound poroelastography is used to obtain the image data. Other imaging systems, such as photoacoustic imaging, mammography, computed tomography (CT) and magnetic resonance imaging (MRI), can also be employed. 
     The material parameter estimator  120  is configured to calculate one or more parameters of the material employing strain data of the material and an analytical model or models  125 . The strain data can be determined from the image data provided by the imaging system  110 . The strain data can also be provided by other conventional methods or procedures. Various methods can be employed for obtaining the strain data, such as sample tracking, correlation, optical flow estimation, block matching, Doppler-based processing, etc. The strain data can be the axial, lateral, elevational, or volumetric strain data. The analytical models  125  relate the material parameters to the strain data. The material parameters can be YM, PR, interstitial permeability, vascular permeability, and SSg. The analytical models  125  can be represented as an algorithm or algorithms in software that are employed in a computing device or a processor thereof to determine the material parameters. Once the material parameters are determined, the parameters can be employed for various medical, industrial, or research processes and procedures, such as the diagnosis, prognosis and treatment of diseases, and the testing of drugs. As such, the material parameters can be employed for the benefit of the host, others, or both. An example of equations that can be used for the analytical models  125  are provided below. The analytical models  125  can be located in a data storage of the material parameter estimator  120 . 
     The material parameter estimator  120  can be configured to determine YM and PR of the material employing strain data and an analytical model, such as a cost function. The strain data can be or can include the axial strain and the lateral strain of the material. The cost function correlates the YM and the PR and the material parameter estimator  120  is configured to reconstruct the YM and the PR for the material by minimizing the cost function. The cost function and related equations can be represented as an algorithm in software wherein a computing device or a processor thereof is used to minimize the cost function to determine the YM and PR. 
     The cost function is represented by Equation 1. 
     
       
         
           
             
               
                 
                   
                     J 
                     ⁡ 
                     
                       ( 
                       
                         
                           E 
                           i 
                         
                         , 
                         
                           ν 
                           i 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             J 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 E 
                                 i 
                               
                               , 
                               
                                 ν 
                                 i 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             J 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 E 
                                 i 
                               
                               , 
                               
                                 ν 
                                 i 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where 
     
       
         
           
             
               
                 
                   
                     
                       
                         J 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             E 
                             i 
                           
                           , 
                           
                             υ 
                             i 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           ϵ 
                           1 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                       - 
                       
                         
                           ϵ 
                           2 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           1 
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
                       
                         J 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             E 
                             i 
                           
                           , 
                           
                             υ 
                             i 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           ϵ 
                           1 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                       - 
                       
                         
                           ϵ 
                           2 
                           * 
                         
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Here, ∈ 1  is defined as 
     
       
         
           
             
               ϵ 
               = 
               
                 
                   ϵ 
                   0 
                 
                 + 
                 
                   S 
                   : 
                   
                     ϵ 
                     * 
                   
                 
               
             
             , 
           
         
       
     
     and ∈ 2  is defined as 
     
       
         
           
             
               
                 ϵ 
                 * 
               
               = 
               
                 
                   
                     ( 
                     
                       S 
                       + 
                       A 
                     
                     ) 
                   
                   
                     - 
                     1 
                   
                 
                 : 
                 
                   ( 
                   
                     - 
                     
                       ϵ 
                       0 
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     where A=[C−C 0 ] −1 ·C 0 . 
     Here, C and C 0  are the stiffness matrix of the inclusion and background, respectively; S is the Eshelby&#39; s tensor and depends on geometry of the inclusion and Poisson&#39;s ratio of the background; and ∈ 0 is the strain in the background. 
     By minimizing the cost function J of Equation 1, YM (E i ) and PR (v i ) of an inclusion can be obtained. The YM and PR of the background can be determined from Equation 3 
     
       
         
           
             
               
                 
                   
                     σ 
                     0 
                   
                   = 
                   
                     
                       C 
                       0 
                     
                     : 
                     
                       ϵ 
                       0 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The expressions of ∈ 1  and ∈ 2  for elliptic (prolate, oblate) and spherical inclusions are known in the art along with the expressions of the Eshelby&#39;s tensor S for cylindrical, flat elliptic, penny-shaped inclusions. Using these known expressions of S in the equations of ∈ 1  and ∈ 2  for elliptic inclusions, ∈ 1  and ∈ 2  for these shapes can be determined. Thus, YM and PR can also be determined. 
     The material parameter estimator  120  can also be configured to calculate interstitial permeability and vascular permeability of a material employing strain data and multiple analytical models. The strain data can be the axial strain and the lateral strain of the material. The analytical models relates the interstitial permeability and vascular permeability to the strain data. 
     First, a time constant τ of a strain inside an inclusion represented by the strain data is determined employing the strain data and Equation 4. 
     
       
         
           
             
               
                 
                   τ 
                   = 
                   
                     
                       
                         a 
                         2 
                       
                       
                         
                           H 
                           A 
                         
                         ⁢ 
                         k 
                         ⁢ 
                         
                           x 
                           1 
                         
                       
                     
                     + 
                     
                       1 
                       
                         
                           H 
                           A 
                         
                         ⁢ 
                         χ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In Equation 4, a is the radius of the inclusion, k is the interstitial permeability of the inclusion, H A  is the aggregate modulus of the inclusion, χ is the average microfiltration coefficient, and x 1  is the root of a Bessel equation depending on the Poisson&#39;s ratio of the inclusion. Values of x 1  for different Poisson&#39;s ratios are known in the art. The interstitial permeability can be determined employing the time constant τ in Equation 5. 
     
       
         
           
             
               
                 
                   k 
                   = 
                   
                     
                       a 
                       2 
                     
                     
                       
                         H 
                         A 
                       
                       ⁢ 
                       
                         τ 
                         ⁡ 
                         
                           ( 
                           
                             
                               α 
                               2 
                             
                             + 
                             
                               x 
                               1 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Equation 5 includes a spatial parameter of interstitial fluid pressure (IFP) α. In various examples, a spatial parameter of IFP α can be determined from the fluid pressure inside the material employing the strain data. The fluid pressure p can be determined by knowledge of the volumetric strain at two different times as 
     
       
         
           
             
               p 
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       ɛ 
                       
                         v 
                         ⁢ 
                         2 
                       
                     
                     - 
                     
                       ɛ 
                       
                         v 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                   
                   ) 
                 
               
             
             , 
           
         
       
     
     where 
     
       
         
           
             K 
             = 
             
               
                 E 
                 i 
               
               
                 3 
                 ⁢ 
                 
                   ( 
                   
                     1 
                     - 
                     
                       2 
                       ⁢ 
                       
                         υ 
                         i 
                       
                     
                   
                   ) 
                 
               
             
           
         
       
     
     is the compression modulus of the material and ε v2 , ε v1  are the volumetric strains at two different times, respectively. 
     The spatial parameter of IFP α can be determined employing the fluid pressure in Equation 6. A curve fitting algorithm can be used to solve for α. 
     
       
         
           
             
               
                 
                   
                     
                       p 
                       ⁡ 
                       
                         ( 
                         R 
                         ) 
                       
                     
                     = 
                     
                       Ω 
                       ⁡ 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               sinh 
                               ⁡ 
                               
                                 ( 
                                 
                                   α 
                                   ⁢ 
                                   R 
                                 
                                 ) 
                               
                             
                             
                               R 
                               ⁢ 
                               sinh 
                               ⁢ 
                               α 
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
                       where 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       α 
                     
                     = 
                     
                       a 
                       ⁢ 
                       
                         
                           
                             
                               L 
                               p 
                             
                             k 
                           
                           ⁢ 
                           
                             S 
                             V 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Here, Ω is related to the peak fluid pressure p 0 , i.e., p 0 =Ω(1−α cosec (α)), a is the radius of the inclusion, L p  is the vascular permeability, k is the interstitial permeability and 
     
       
         
           
             S 
             V 
           
         
       
     
     is the surface area to volume ratio, which can be determined using methods available in the art. By knowledge of α, the ratio between vascular permeability and interstitial permeability 
     
       
         
           
             
               L 
               p 
             
             k 
           
         
       
     
     can also be determined using Equation 6, if desired. 
     From Equation 5, the vascular permeability of the material can be determined employing Equation 7. 
     
       
         
           
             
               
                 
                   
                     L 
                     p 
                   
                   = 
                   
                     
                       χ 
                       ⁢ 
                       
                         V 
                         S 
                       
                     
                     = 
                     
                       
                         
                           
                             α 
                             2 
                           
                           
                             a 
                             2 
                           
                         
                         ⁢ 
                         k 
                         ⁢ 
                         
                           V 
                           S 
                         
                       
                       = 
                       
                         
                           
                             α 
                             2 
                           
                           
                             
                               H 
                               A 
                             
                             ⁢ 
                             
                               τ 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     α 
                                     2 
                                   
                                   + 
                                   
                                     x 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                           V 
                           S 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     In addition to the interstitial permeability and vascular permeability, the SSg of a material can be determined from SSc (compression induced stress inside the material) and the relationships between various mechanical and transport parameters. For example, SSg is theoretically linked to IFP, IFP is theoretically linked to FPc, and FPc is theoretically linked to SSc. The SSc can be determined employing strain data and at least one analytical model, and therefore the SSg with the understanding that the spatial distribution of SSc corresponds to the spatial distribution of SSg, differing, for example, only in peak and boundary values. The radial and circumferential SSc inside the sample (in cylindrical coordinates) may, in some embodiments, be assumed to be equal in axisymmetric conditions. Therefore, the radial and circumferential SSc components and fluid pressure (FPc) in spherical coordinates may be determined from Equations 8 and 9 below. 
     
       
         
           
             
               
                 
                   
                     
                       σ 
                       
                         R 
                         ⁢ 
                         R 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         R 
                         , 
                         t 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           
                             σ 
                             rr 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   
                                     r 
                                     2 
                                   
                                   + 
                                   
                                     z 
                                     2 
                                   
                                 
                               
                               , 
                               t 
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           σ 
                           zz 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   2 
                                 
                                 + 
                                 
                                   z 
                                   2 
                                 
                               
                             
                             , 
                             t 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       σ 
                       
                         θ 
                         ⁢ 
                         θ 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         R 
                         , 
                         t 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       σ 
                       rr 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               r 
                               2 
                             
                             + 
                             
                               z 
                               2 
                             
                           
                         
                         , 
                         t 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Here, σ RR  and σ zz  can be computed by knowledge of the applied compression and YM and PR of the inclusion and background. 
     FPc can be determined employing Equation 10. 
     
       
         
           
             
               
                 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         R 
                         , 
                         t 
                       
                       ) 
                     
                   
                   = 
                   
                     p 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               r 
                               2 
                             
                             + 
                             
                               z 
                               2 
                             
                           
                         
                         , 
                         t 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The radial and circumferential SSc and FPc may be normalized by dividing them by an applied pressure used when taking the data. 
     The normalized SSg (SSn) can be determined using Equation 11. 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                       
                         S 
                         n 
                       
                       ⁡ 
                       
                         ( 
                         R 
                         ) 
                       
                     
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         sinh 
                         ⁡ 
                         
                           ( 
                           
                             α 
                             ⁢ 
                             
                               R 
                               a 
                             
                           
                           ) 
                         
                       
                       
                         
                           R 
                           a 
                         
                         ⁢ 
                         sinh 
                         ⁢ 
                         α 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where R is the spherical coordinate. 
     Equation 12 can be used to compute the surface area to volume ratio of the capillary walls inside the inclusion, for example a tumor. 
     
       
         
           
             
               
                 
                   
                     S 
                     V 
                   
                   = 
                   
                     10 
                     ⁢ 
                     
                       fV 
                       t 
                       g 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In Equation 12, V t  is the volume of the inclusion. In spherical inclusions, V t  can be computed as V t =4/3πa 3 , f= 54 . 68 , and g=−0.2021. For Equation 12, a is in units of mm and S/V is in units of cm −1 . 
       FIG. 2  illustrates a block diagram of an example of a material parameter estimator  200  constructed according to the principles of the disclosure. The material parameter estimator  200  is configured to calculate material parameters of material, such as a cancer material, employing strain data and analytical models. The material parameter estimator  200  can be integrated on one or more computing devices or systems. Thus, functions performed by the material parameter estimator  200  can be distributed to different computing devices or systems. For example, some of the functions performed by the material parameter estimator  200  can be performed by a computing device located at a clinic or lab, and other functions can be performed at a data processing center, a computing facility, or another suitable location. As such, the material parameter estimator  200  can be implemented on a server, a cloud service, a tablet, a laptop, a smartphone, other types of computing systems, or a combination thereof. 
     The material parameter estimator  200  includes an interface  210 , a memory  220 , and a processor  230 . The interface  210  is a component or device interface configured to receive strain data of a material and provide parameters of the material determined by the material parameter estimator  200 . The strain data can be obtained from an imaging system or obtained from image data from the imaging system. In some applications, the material parameter estimator  200  can receive the strain data from an imaging system. The strain data can also be obtained via other non-imaging methods. 
     The material parameters can be sent to a storage device, such as a digital memory storage, provided to a user, such as a clinician, researcher or a lab technician, by sending the material parameters to a user interface, such as a display, or sent to another computing device. The computing device can be remote from the material parameter estimator  200 , such as a cloud server connected via a communications network, or proximate the material parameter estimator  200 . The interface  210  can be a conventional interface that communicates data according to standard protocols. As such, the interface  210  is configured to communicate data, i.e., transmit and receive data. Accordingly, the interface  210  includes the necessary logic, ports, terminals, connectors, etc., to communicate data. The ports, terminals, connectors, may be conventional receptacles for communicating data via a communications network. 
     The memory  220  is configured to store the analytical models employed to determine the material parameters from the strain data. Additionally, the memory  220  is configured to store a series of operating instructions that direct the operation of the processor  230  when initiated. At least a portion of the operating instructions can correspond to the analytical models disclosed herein. The memory  220  is a non-transitory computer readable medium. 
     As such, the memory  220  is a data storage configured to store computer executable instructions to direct the operation of the processor  230  when initiated thereby. The memory can be a non-volatile memory. The memory  220  can also store data, such as the strain data. The operating instructions may correspond to the analytical models or corresponding algorithms that provide the functionality of the techniques or schemes disclosed herein. For example, the operating instructions may correspond to the algorithm or algorithms that, when executed, determine material parameters from strain data. 
     The processor  230  is configured to direct the operation of the material parameter estimator  200 . As such, the processor  230  includes the necessary logic to communicate with the interface  210  and the memory  220  and perform the functions described herein to determine parameters of a material from strain data obtained from the material. For example, the processor  230  is can be configured, e.g., designed and constructed, to perform at least some of the methods represented by  FIGS. 3-5 . 
       FIGS. 3-5  illustrate flow diagrams of examples of methods for determining parameters of materials using strain data and analytical models, such as represented by the Equations provide herein.  FIGS. 3-5  include getting the strain data from image data. As disclosed herein, the strain data can alternatively be obtained via other methods and used with the analytical models. 
       FIG. 3  illustrates a flow diagram of an example of a method  300  for reconstructing YM and PR parameters inside materials carried out according to the principles of the disclosure. The method  300  is a non-invasive method. In some examples, the method  300  does not use imaging contrast agents. At least some of the steps of the method  300  are performed by a processor, such as the processor  230 . The processor can be directed to perform the steps by a computer program product. The method  300  can be carried out by a material parameter estimator such as disclosed herein; for example, the material parameter estimator  200 . The method  300  begins in a step  305 . 
     In a step  310 , image data is received from a material, such as from tissue sample or a tumor sample or a tissue sample of a human or animal having a tumor. In other examples, the material can be a non-biological tissue. The image data can be obtained from an ultrasound scan. In other examples, image data can be obtained from another type of imaging method, such as mammography, MRI, CT, acoustics or photoacoustic imaging or a combination of imaging methods. An ultrasound poroelastography procedure can be used to obtain the image data. 
     In a step  320  strain data of the material is obtained from the imaging data. The strain data can be estimated from the image data via conventional methods such as sample tracking, correlation, optical flow estimation, block matching, Doppler-based processing, etc. In some examples, the strain data can be obtained from multiple images at different times. The strain data can be axial and lateral strain data. 
     In a step  330  a first analytical model is employed that includes the strain data, YM, and PR of the material. Equation 1 provided above is an example of a cost function that can be employed as the first analytical model. 
     In a step  340 , the YM and the PR of the material are reconstructed employing the first analytical model. A second analytical model can be employed with the first analytical model for the reconstructing. Continuing the example of Equation 1, YM and PR can be reconstructed by minimizing the cost function employing Equation 2. The reconstructing can be performed without imposing assumptions on boundary conditions of the material. In some examples, the reconstructing is only based on the strain data, known values of applied stress on the material, and geometry of the material. The YM and the PR can be reconstructed or determined at each pixel inside the material, both simultaneously and independently. At least some of the pixels can be determined in parallel, or at least partially in parallel, employing a parallel processor. 
     At least one of the material parameters is employed in a process, such as a medical or research or industrial process, in a step  350 . The material parameter can be provided to a user for application in various medical, non-medical, industrial, or research processes. The user can be a clinician, doctor, researcher, technician, imaging expert, nurse, or other medical or non-medical or research personnel. The parameter can be provided to a user or users by various user interfaces. For example, a visual display can be used. The different processes include the diagnosis, prognosis and treatment of cancers. Knowledge of the values of YM in cancers can be used by a doctor to determine the cancer stage and sometimes cancer metastasis. PR can be beneficial for monitoring cancer-related diseases such as lymphedema. Both YM and PR can be employed to estimate other important properties, such as interstitial fluid pressure, interstitial permeability and vascular permeability, of a material, such as a tumor. The method  300  continues to step  360  and ends. 
       FIG. 4  illustrates a flow diagram of an example of a method  400  for estimating interstitial permeability and vascular permeability inside materials carried out according to the principles of the disclosure. The method  400  is a non-invasive method that does not, for example, use imaging contrast agents. At least some of the steps of the method  400  are performed by a processor, such as the processor  230  of  FIG. 2 . The processor can be directed to perform the steps by a computer program product. The method  400  can be carried out by a material parameter estimator such as disclosed herein. The method  400  begins in a step  405 . 
     In a step  410 , image data is received from a material, such as from a tissue sample of a human or animal having a tumor. The image data can be obtained from an ultrasound scan. In other examples, image data can be obtained from another type of imaging method, such as mammongraphy, MRI, CT, acoustics, photoacoustic imaging or a combination of imaging methods. An ultrasound poroelastography procedure can be used to obtain the image data. 
     In a step  420 , strain data of the material is obtained from the imaging data. The strain data can be estimated from the image data via conventional methods such as sample tracking, correlation, optical flow estimation, block matching, Doppler-based processing, etc. In some examples, the strain data can be obtained from multiple images at different times. The strain data can be axial and lateral strain data of the material. 
     In a step  430  a time constant of a strain inside the material represented by the strain data is determined employing the strain data and a first analytical model. The first analytical model for method  400  can be Equation 4 provided above. 
     An interstitial permeability is determined in a step  440  employing the time constant in a second analytical model. The second analytical model can be Equation 5 provided above. Equation 5 includes a spatial parameter of IFP α. The interstitial permeability can be determined via Equation 5 with a known spatial parameter of IFP α. In various examples, a spatial parameter of IFP α can be determined from the fluid pressure inside the material employing the strain data. For determining the fluid pressure, the volumetric strain can be calculated at two different times. For example, the volumetric strain can be calculated at 10 seconds and at 60 seconds. 
     Employing a third analytical model, the spatial parameter of IFP α can be determined employing the fluid pressure. The third analytical model for method  400  can be Equation 6. A curve fitting algorithm can be used to solve for α. In some examples, α and a peak fluid pressure can be made floating when using the curve fitting algorithm. 
     In a step  450 , vascular permeability of the material is determined. A fourth analytical model of method  400  can be used to determine the vascular permeability. The fourth analytical model can be Equation 7 provided above. 
     At least one of the interstitial permeability or vascular permeability is employed in a process, such as a medical or industrial or research process, in a step  460 . The permeabilities can be provided to a user for application in various medical or non-medical or industrial or research processes. The user can be a clinician, doctor, researcher, technician, imaging expert, nurse, or other medical or non-medical or research personnel. The permeability can be provided to a user or users by various user interfaces. For example, a visual display can be used. The different processes include the diagnosis, prognosis and treatment of cancers. The method  400  continues to step  470  and ends. 
       FIG. 5  illustrates a flow diagram of an example of a method  500  for estimating SSg inside material carried out according to the principles of the disclosure. The method  500  can be a non-invasive method that does not use imaging contrast agents. At least some of the steps of the method  500  are performed by a processor, such as the processor  230  of  FIG. 2 . The processor can be directed to perform the steps by a computer program product. The method  500  can be carried out by a material parameter estimator such as disclosed herein. The method  500  begins in a step  505 . 
     In a step  510 , image data is received from a material, such as from a tissue sample, tumor sample or a tissue sample of a human or animal having a tumor. The image data can be obtained from an ultrasound scan. In other examples, image data can be obtained from another type of imaging method, such as mammography, CT, MRI, acoustics, photoacoustic imaging or a combination of imaging methods. An ultrasound poroelastography procedure can be used to obtain the image data. 
     In a step  520 , strain data of the material is obtained from the imaging data. The strain data can be estimated from the image data via conventional methods such as sample tracking, correlation, optical flow estimation, block matching, Doppler-based processing, etc. In some examples, the strain data can be obtained from multiple images at different times. The strain data can be axial and lateral strain data of the material. 
     In a step  530 , SSc and FPc values are calculated using the strain data and at least one analytical model. Analytical models represented by Equations 8, 9, 10 and 11 can be employed to determine SSc and FPc values. The radial and circumferential SSc inside a material (in cylindrical coordinates) may, in some embodiments, be assumed to be equal in axisymmetric conditions. Therefore, the radial and circumferential SSc components and the FPc in spherical coordinates may be determined from the SSc components and FPc in cylindrical coordinates. In some embodiments, estimation of YM and PR of the inclusion and background, such as via the method  300 , can be employed for determining SSc and FPc. Other methods for estimating YM and PR can also be used. In some examples, the radial and circumferential SSc and FPc may be normalized by dividing them by an applied pressure used when taking the data such that the values correspond, in some embodiments, to 1 kPa of applied pressure. 
     In a step  550 , the solid stress distribution SSg is determined. The SSg can be determined based on the spatial distribution of SSc inside the material and the calculations and determinations made in step  530 . 
     At least one of the parameters is employed in a process in a step  560 . For example, the SSg can be employed in a medical or industrial or research process in step  560 . The SSg can be provided to a user for application in various medical or industrial or research processes. The user can be a clinician, doctor, researcher, technician, imaging expert, nurse, or other medical or non-medical or research personnel. The SSg can be provided to a user or users by various user interfaces. For example, a visual display can be used. The different processes include the diagnosis, prognosis and treatment of diseases such as cancers. The method  500  continues to step  570  and ends. 
     A portion of the above-described apparatus, systems or methods may be embodied in or performed by various analog or digital data processors or computers, wherein the computers are programmed or store executable programs of sequences of software instructions to perform one or more of the steps of the methods. The software instructions of such programs may represent algorithms and be encoded in machine-executable form on non-transitory digital data storage media, e.g., magnetic or optical disks, random-access memory (RAM), magnetic hard disks, flash memories, and/or read-only memory (ROM), to enable various types of digital data processors or computers to perform one, multiple or all of the steps of one or more of the above-described methods, or functions, systems or apparatuses described herein. Portions of disclosed embodiments may relate to computer storage products with a non-transitory computer-readable medium that have program code thereon for performing various computer-implemented operations that embody a part of an apparatus, device or carry out the steps of a method set forth herein. Non-transitory used herein refers to all computer-readable media except for transitory, propagating signals. Examples of non-transitory computer-readable media include, but are not limited to: magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM disks; magneto-optical media such as floptical disks; and hardware devices that are specially configured to store and execute program code, such as ROM and RAM devices. Examples of program code include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. 
     Those skilled in the art to which this application relates will appreciate that other and further additions, deletions, substitutions and modifications may be made to the described embodiments. 
     Various aspects of the disclosure can be claimed including the apparatuses, systems, computer program products, and methods as disclosed herein including: 
     A. A non-invasive method for simultaneously estimating Young&#39;s modulus (YM) and Poisson&#39;s ratio (PR) of materials, including: (1) receiving image data from the material, (2) obtaining strain data from the image data, and (3) reconstructing the YM and the PR of the material based on the strain data at a steady state. 
     B. A material parameter estimator, including: (1) an interface configured to receive data of a material, and (2) a processor configured to determine YM and PR of the material employing strain data determined from the data and a cost function corresponding to the YM and the PR. 
     C. A non-invasive method for estimating the interstitial permeability and vascular permeability of materials, including: (1) obtaining strain data of a material, (2) calculating a time constant of the strain data employing a first analytical model, and (3) determining interstitial permeability of the material employing the time constant in a second analytical model. 
     D. A material parameter estimator, including: (1) an interface configured to receive strain data of a material, and (2) a processor configured to calculate a time constant of the strain data employing a first analytical model and calculate interstitial permeability of the material employing the time constant in a second analytical model. 
     E. A non-invasive method for estimating parameters of materials, including: (1) obtaining strain data of a material, (2) calculating a compression induced solid stress distribution (SSc) and a fluid pressure (FPc) inside the material employing the strain data in a first analytical model, (3) determining spatial parameter of interstitial fluid pressure (IFP) α using a second analytical model employing the fluid pressure, (4) determining a ratio of vascular permeability (VP) to interstitial pressure (IP) employing the fluid pressure in a third analytical model, and (5) determining a solid stress (SSg) distribution inside the material based on the calculated α. 
     F. A material parameter estimator, including: (1) an interface configured to receive strain data of a material and (2) a processor configured to calculate material parameters of the material employing strain data determined from the data and multiple analytical models and determine SSg based on the calculated material parameters. 
     Each of aspects A to F can have one or more of the following additional elements in combination. 
     Element 1: wherein the material is a biological tissue. Element 2: wherein the material is a tumor. Element 3: wherein the reconstructing is based on minimizing a cost function representing the YM and the PR. Element 4: further comprising developing the cost function. Element 5: wherein the reconstructing is performed without imposing assumptions on boundary conditions of the material. Element 6: wherein the reconstructing is based on the strain data, known values of applied stress on the material, and geometry of the material. Element 7: wherein the reconstructing includes reconstructing the YM and the PR at each pixel inside the material simultaneously and independently. Element 8: wherein the image data is obtained from an ultrasound scan. Element 9: wherein the ultrasound scan is an ultrasound poroelastography experiment. Element 10: wherein the processor is configured to determine the YM and the PR simultaneously employing the cost function. Element 11: wherein the processor is configured to simultaneously determine the YM and the PR by minimizing the cost function. Element 12: wherein the processor is configured to determine the YM and the PR of the material based on the strain data at a steady state. Element 13: wherein the cost function can be based on eigen strain formulations. Element 14: wherein the processor is further configured to determine the YM and the PR without imposing assumptions on boundary conditions of the material. Element 15: wherein the processor is configured to determine the YM and the PR by reconstructing the YM and the PR at each pixel inside the material simultaneously and independently. Element 16: wherein the strain data includes axial and lateral strain data. Element 17: further comprising determining vascular permeability employing a third analytical model. Element 18: wherein the strain data includes normal strain data inside the material. Element 19: wherein the strain data is from image data of the material. Element 20: wherein the image data is obtained from an ultrasound scan. Element 21: wherein the ultrasound scan is an ultrasound poroelastography experiment. Element 22: wherein the determining includes using a curve fitting technique on a temporal profile of the strain data. Element 23: wherein the determining the vascular permeability includes using a curve fitting technique on a temporal profile of the strain data. Element 24: wherein the strain data is obtained from an ultrasound poroelastography procedure. Element 25: wherein the processor is configured to calculate vascular permeability of the material employing a third analytical model. Element 26: wherein the processor is configured to determine interstitial permeability employing a curve fitting algorithm. Element 27: wherein the processor is configured to determine the vascular permeability employing a curve fitting algorithm. Element 28: wherein the strain data includes axial strain inside the material. Element 29: wherein the strain data is obtained without employing a contrast agent. Element 30: wherein the strain data includes normal strain data. Element 31: wherein the determining spatial parameter of interstitial fluid pressure (IFP) α includes employing a curve fitting algorithm. Element 32: wherein the curve fitting algorithm includes varying a peak value, a boundary value. Element  33 : wherein the determining the VP to IP ratio includes employing a curve fitting algorithm. Element  34 : wherein the curve fitting algorithm includes varying a peak value, a boundary value, and α. Element  35 : wherein the strain data is obtained from image data. Element  36 : wherein the image data is obtained from an ultrasound scan via an ultrasound poroelastography experiment. Element  37 : wherein the strain data is obtained from an image via an ultrasound scan of the material. Element  38 : wherein the ultrasound scan is an ultrasound poroelastography experiment. Element  39 : wherein the processor is configured to calculate a compression induced solid stress distribution (SSc) and a fluid pressure (FPc) inside the material employing the volumetric strain data in a first analytical model. Element  40 : wherein the processor is further configured to determine a spatial parameter of interstitial fluid pressure (IFP) α using a second analytical model employing the fluid pressure. Element  41 : wherein the processor is further configured to determine a ratio of vascular permeability (VP) to interstitial permeability (IP) employing the fluid pressure in a third analytical model andetermine a solid stress (SSg) distribution inside the material based on the calculated SSc, FPc, α, and the VP to IP ratio. Element  42 : wherein the processor is configured to determine α employing a curve fitting algorithm. Element  43 : wherein the curve fitting algorithm includes varying a peak value, a boundary value.