Application of Eshelby's Solution to Elastography for Diagnosis of Breast Cancer

Non-Invasive Imaging of Mechanical Properties of Cancers In Vivo Based on Transformations of the Eshelby's Tensor Using Compression Elastography

Knowledge of the mechanical properties is of great clinical significance for diagnosis, prognosis and treatment of cancers. Recently, a new method based on Eshelby's theory to simultaneously assess Young's modulus (YM) and Poisson's ratio (PR) in tissues has been proposed. A significant limitation of this method is that accuracy of the reconstructed YM and PR is affected by the orientation/alignment of the tumor with the applied stress. In this paper, we propose a new method to reconstruct YM and PR in cancers that is invariant to the 3D orientation of the tumor with respect to the axis of applied stress. The novelty of the proposed method resides on the use of a tensor transformation to improve the robustness of Eshelby's theory and reconstruct YM and PR of tumors with high accuracy and in realistic experimental conditions. The method is validated using finite element simulations and controlled experiments using phantoms with known mechanical properties. The in vivo feasibility of the developed method is demonstrated in an orthotopic mouse model of breast cancer. Our results show that the proposed technique can estimate the YM and PR with overall accuracy of (97.06 ± 2.42) % under all tested tumor orientations. Animal experimental data demonstrate the potential of the proposed methodology in vivo. The proposed method can significantly expand the range of applicability of the Eshelby's theory to tumors and provide new means to accurately image and quantify mechanical parameters of cancers in clinical conditions.

Physics-informed UNets for discovering hidden elasticity in heterogeneous materials

Soft biological tissues often have complex mechanical properties due to variation in structural components. In this paper, we develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) to infer the spatial distributions of mechanical parameters from strain maps as input images, normal stress boundary conditions, and domain physics information. We show superior performance - both in terms of accuracy and computational cost - by El-UNet compared to fully-connected physics-informed neural networks in estimating unknown parameters and stress distributions for isotropic linear elasticity. We characterize different variations of El-UNet and propose a self-adaptive spatial loss weighting approach. To validate our inversion models, we performed various finite-element simulations of isotropic domains with heterogenous distributions of material parameters to generate synthetic data. El-UNet is faster and more accurate than the fully-connected physics-informed implementation in resolving the distribution of unknown fields. Among the tested models, the self-adaptive spatially weighted models had the most accurate reconstructions in equal computation times. The learned spatial weighting distribution visibly corresponded to regions that the unweighted models were resolving inaccurately. Our work demonstrates a computationally efficient inversion algorithm for elasticity imaging using convolutional neural networks and presents a potential fast framework for three-dimensional inverse elasticity problems that have proven unachievable through previously proposed methods.

Mechanics of Small-Scale Spherical Inclusions Using Nonlocal Poroelasticity Integrated with Light Gradient Boosting Machine

Detecting inclusions in materials at small scales is of high importance to ensure the quality, structural integrity and performance efficiency of microelectromechanical machines and products. Ultrasound waves are commonly used as a non-destructive method to find inclusions or structural flaws in a material. Mathematical continuum models can be used to enable ultrasound techniques to provide quantitative information about the change in the mechanical properties due to the presence of inclusions. In this paper, a nonlocal size-dependent poroelasticity model integrated with machine learning is developed for the description of the mechanical behaviour of spherical inclusions under uniform radial compression. The scale effects on fluid pressure and radial displacement are captured using Eringen's theory of nonlocality. The conservation of mass law is utilised for both the solid matrix and fluid content of the poroelastic material to derive the storage equation. The governing differential equations are derived by decoupling the equilibrium equation and effective stress-strain relations in the spherical coordinate system. An accurate numerical solution is obtained using the Galerkin discretisation technique and a precise integration method. A Dormand-Prince solution is also developed for comparison purposes. A light gradient boosting machine learning model in conjunction with the nonlocal model is used to extract the pattern of changes in the mechanical response of the poroelastic inclusion. The optimised hyperparameters are calculated by a grid search cross validation. The modelling estimation power is enhanced by considering nonlocal effects and applying machine learning processes, facilitating the detection of ultrasmall inclusions within a poroelastic medium at micro/nanoscales.

Estimation of Mechanical and Transport Parameters in Cancers Using Short Time Poroelastography

Mechanical and transport properties of cancers such as Young's modulus (YM), Poisson's ratio (PR), and vascular permeability (VP) have great clinical importance in cancer diagnosis, prognosis, and treatment. However, non-invasive estimation of these parameters in vivo is challenged by many practical factors. Elasticity imaging methods, such as "poroelastography", require prolonged data acquisition, which can limit their clinical applicability. In this paper, we investigate a new method to perform poroelastography experiments, which results in shorter temporal acquisition windows. This method is referred to as "short-time poroelastography" (STPE). Finite element (FE) and ultrasound simulations demonstrate that, using STPE, it is possible to accurately estimate YM, PR (within 10% error) using windows of observation (WoOs) of length as short as 1 underlying strain Time Constant (TC). The error was found to be almost negligible (< 3%) when using WoOs longer than 2 strain TCs. In the case of VP estimation, WoOs of at least 2 strain TCs are required to obtain an error < 8% (in simulations). The stricter requirement for the estimation of VP with respect to YM and PR is due its reliance on the transient strain behavior while YM and PR depend on the steady state strain values only. In vivo experimental data are used as a proof-of-principle of the potential applicability of the proposed methodology in vivo. The use of STPE may provide a means to efficiently perform poroelastography experiments without compromising the accuracy of the estimated tissue properties.

Developing a biomechanical model-based elasticity imaging method for assessing hormone receptor positive breast cancer treatment-related myocardial stiffness changes

Purpose: Assessing cardiotoxicity as a result of breast cancer therapeutics is increasingly important as breast cancer diagnoses are trending younger and overall survival is increasing. With evidence showing that prevention of cardiotoxicity plays a significant role in increasing overall survival, there is an unmet need for accurate non-invasive methods to assess cardiac injury due to cancer therapies. Current clinical methods are too coarse and emerging research methods have not yet achieved clinical implementation. Approach: As a proof of concept, we examine myocardial elasticity imaging in the setting of premenopausal women diagnosed with hormone receptor positive (HR-positive) breast cancer undergoing severe estrogen depletion, as cardiovascular injury from early estrogen depletion is well-established. We evaluate the ability of our model-based cardiac elasticity imaging analysis method to indicate subclinical cancer therapy-related cardiac decline by examining differences in the change in cardiac elasticity over time in two cohorts of premenopausal women either undergoing severe estrogen depletion for HR-positive breast cancer or triple negative breast cancer patients as comparators. Results: Our method was capable of producing functional mechanical elasticity maps of the left ventricle (LV). Using these elasticity maps, we show significant differences in cardiac mechanical elasticity in the HR-positive breast cancer cohort compared to the comparator cohort. Conclusions: We present our methodology to assess the mechanical stiffness of the LV by interrogating cardiac magnetic resonance images within a computational biomechanical model. Our preliminary study suggests the potential of this method for examining cardiac tissue mechanical stiffness properties as an early indicator of cardiac decline.

Non-invasive imaging of Young's modulus and Poisson's ratio in cancers in vivo

Alterations of Young's modulus (YM) and Poisson's ratio (PR) in biological tissues are often early indicators of the onset of pathological conditions. Knowledge of these parameters has been proven to be of great clinical significance for the diagnosis, prognosis and treatment of cancers. Currently, however, there are no non-invasive modalities that can be used to image and quantify these parameters in vivo without assuming incompressibility of the tissue, an assumption that is rarely justified in human tissues. In this paper, we developed a new method to simultaneously reconstruct YM and PR of a tumor and of its surrounding tissues based on the assumptions of axisymmetry and ellipsoidal-shape inclusion. This new, non-invasive method allows the generation of high spatial resolution YM and PR maps from axial and lateral strain data obtained via ultrasound elastography. The method was validated using finite element (FE) simulations and controlled experiments performed on phantoms with known mechanical properties. The clinical feasibility of the developed method was demonstrated in an orthotopic mouse model of breast cancer. Our results demonstrate that the proposed technique can estimate the YM and PR of spherical inclusions with accuracy higher than 99% and with accuracy higher than 90% in inclusions of different geometries and under various clinically relevant boundary conditions.

Estimation of Vascular Permeability in Irregularly Shaped Cancers Using Ultrasound Poroelastography

OBJECTIVE

Vascular permeability (VP) is a mechanical parameter which plays an important role in cancer initiation, metastasis, and progression. To date, there are only a few non-invasive methods that can be used to image VP in solid tumors. Most of these methods require the use of contrast agents and are expensive, limiting widespread use.

METHODS

In this paper, we propose a new method to image VP in tumors, which is based on the use of ultrasound poroelastography. Estimation of VP by poroelastography requires knowledge of the Young's modulus (YM), Poisson's ratio (PR), and strain time constant (TC) in the tumors. In our method, we find the ellipse which best fits the tumor (regardless of its shape) using an eigen-system-based fitting technique and estimate the YM and PR using Eshelby's elliptic inclusion formulation. A Fourier method is used to estimate the axial strain TC, which does not require any initial guess and is highly robust to noise.

RESULTS

It is demonstrated that the proposed method can estimate VP in irregularly shaped tumors with an accuracy of above [Formula: see text] using ultrasound simulation data with signal-to-noise ratio of 20 dB or higher. In vivo feasibility of the proposed technique is demonstrated in an orthotopic mouse model of breast cancer.

CONCLUSION

The proposed imaging method can provide accurate and localized estimation of VP in cancers non-invasively and cost-effectively.

SIGNIFICANCE

Accurate and non-invasive assessment of VP can have a significant impact on diagnosis, prognosis, and treatment of cancers.

Elastography for portable ultrasound

Portable wireless ultrasound has been emerging as a new ultrasound device due to its unique advantages including small size, lightweight, wireless connectivity and affordability. Modern portable ultrasound devices can offer high quality sonogram images and even multiple ultrasound modes such as color Doppler, echocardiography, and endovaginal examination. However, none of them can provide elastography function yet due to the limitations in computational performance and data transfer speed of wireless communication. Also phase-based strain estimator (PSE) that is commonly used for conventional elastography cannot be adopted for portable ultrasound, because ultrasound parameters such as data dumping interval are varied significantly in the practice of portable ultrasound. Therefore, this research aims to propose a new elastography method suitable for portable ultrasound, called the robust phase-based strain estimator (RPSE), which is not only robust to the variation of ultrasound parameters but also computationally effective. Performance and suitability of RPSE were compared with other strain estimators including time-delay, displacement-gradient and phase-based strain estimators (TSE, DSE and PSE, respectively). Three types of raw RF data sets were used for validation tests: two numerical phantom data sets modeled by an open ultrasonic simulation code (Field II) and a commercial FEA (Abaqus), and the one experimentally acquired with a portable ultrasound device from a gelatin phantom. To assess image quality of elastograms, signal-to-noise (SNRe) and contrast-to-noise (CNRe) ratios were measured on the elastograms produced by each strain estimator. The computational efficiency was also estimated and compared. Results from the numerical phantom experiment showed that RPSE could achieve highest values of SNRe and CNRe (around 5.22 and 47.62 dB) among all strain estimators tested, and almost 10 times higher computational efficiency than TSE and DSE (around 0.06 vs. 5.76 s per frame for RPSE and TSE, respectively).

Compressed Sensing for Elastography in Portable Ultrasound

Portable ultrasound is recently emerging as a new medical imaging modality featuring high portability, easy connectivity, and real-time on-site diagnostic ability. However, it does not yet provide ultrasound elastography function that enables the diagnosis of malignant lesions using elastic properties. This is mainly due to the limitations of hardware performance and wireless data transfer speed for processing the large amount of data for elastography. Therefore, data transfer reduction is one of the feasible solutions to overcome these limitations. Recently, compressive sensing (CS) theory has been rigorously studied as a means to break the conventional Nyquist sampling rate and thus can significantly decrease the amount of measurement signals without sacrificing signal quality. In this research, we implemented various CS reconstruction frameworks and comparatively evaluated their reconstruction performance for realizing ultrasound elastography function on portable ultrasound. Combinations of three most common model bases (Fourier transform [FT], discrete cosine transform [DCT], and wave atom [WA]) and two reconstruction algorithms (L1 minimization and block sparse Bayesian learning [BSBL]) were considered for CS frameworks. Echoic and elastography phantoms, were developed to evaluate the performance of CS on B-mode images and elastograms. To assess the reconstruction quality, mean absolute error (MAE), signal-to-noise ratio (SNRe), and contrast-to-noise ratio (CNRe) were measured on the B-mode images and elastograms from CS reconstructions. Results suggest that CS reconstruction adopting BSBL algorithm with DCT model basis can yield the best results for all the measures tested, and the maximum data reduction rate for producing readily discernable elastograms is around 60%.

Application of compressive sensing to portable ultrasound elastography

Feasibility of applying compressive sensing (CS) to ultrasound radio-frequency (RF) data to produce elastography is investigated. The research also compares the performance of various CS frameworks associated with three common model bases (Fourier transform, discrete cosine transform (DCT), and wave atom (WA)) and two reconstruction algorithms (ℓ₁ minimization and block sparse Bayesian learning (BSBL)) using the quality of B-mode images and elastograms from the RF data subsampled and reconstructed by each framework. Results suggest that CS reconstruction adopting BSBL algorithm with DCT model basis can yield the best results for all the measures tested, and the maximum data reduction rate for producing readily discernable elastograms is around 60%.

Electromechanical Coupling Factor of Breast Tissue as a Biomarker for Breast Cancer

GOAL

This research aims to validate a new biomarker of breast cancer by introducing electromechanical coupling factor of breast tissue samples as a possible additional indicator of breast cancer. Since collagen fibril exhibits a structural organization that gives rise to a piezoelectric effect, the difference in collagen density between normal and cancerous tissue can be captured by identifying the corresponding electromechanical coupling factor.

METHODS

The design of a portable diagnostic tool and a microelectromechanical systems (MEMS)-based biochip, which is integrated with a piezoresistive sensing layer for measuring the reaction force as well as a microheater for temperature control, is introduced. To verify that electromechanical coupling factor can be used as a biomarker for breast cancer, the piezoelectric model for breast tissue is described with preliminary experimental results on five sets of normal and invasive ductal carcinoma (IDC) samples in the 25-45 temperature range.

CONCLUSION

While the stiffness of breast tissues can be captured as a representative mechanical signature which allows one to discriminate among tissue types especially in the higher strain region, the electromechanical coupling factor shows more distinct differences between the normal and IDC groups over the entire strain region than the mechanical signature. From the two-sample -test, the electromechanical coupling factor under compression shows statistically significant differences ( 0.0039) between the two groups.

SIGNIFICANCE

The increase in collagen density in breast tissue is an objective and reproducible characteristic of breast cancer. Although characterization of mechanical tissue property has been shown to be useful for differentiating cancerous tissue from normal tissue, using a single parameter may not be sufficient for practical usage due to inherent variation among biological samples. The portable breast cancer diagnostic tool reported in this manuscript shows the feasibility of measuring multiple parameters of breast tissue allowing for practical application.