A Force-Matched Approach to Large-Strain Nonlinearity in Elasticity Imaging for Breast Lesion Characterization.

OBJECTIVE: Ultrasound elasticity imaging is a class of ultrasound techniques with applications that include the detection of malignancy in breast lesions. Although elasticity imaging traditionally assumes linear elasticity, the large strain elastic response of soft tissue is known to be nonlinear. This study evaluates the nonlinear response of breast lesions for the characterization of malignancy using force measurement and force-controlled compression during ultrasound imaging. METHODS: 54 patients were recruited for this study. A custom force-instrumented compression device was used to apply a controlled force during ultrasound imaging. Motion tracking derived strain was averaged over lesion or background ROIs and matched with compression force. The resulting force-matched strain was used for subsequent analysis and curve fitting. RESULTS: Greater median differences between malignant and benign lesions were observed at higher compressional forces (p-value < 0.05 for compressional forces of 2-6N). Of three candidate functions, a power law function produced the best fit to the force-matched strain. A statistically significant difference in the scaling parameter of the power function between malignant and benign lesions was observed (p-value = 0.025). CONCLUSIONS: We observed a greater separation in average lesion strain between malignant and benign lesions at large compression forces and demonstrated the characterization of this nonlinear effect using a power law model. Using this model, we were able to differentiate between malignant and benign breast lesions. SIGNIFICANCE: With further development, the proposed method to utilize the nonlinear elastic response of breast tissue has the potential for improving non-invasive lesion characterization for potential malignancy.

Deep learning image segmentation approaches for malignant bone lesions: a systematic review and meta-analysis.

Introduction: Image segmentation is an important process for quantifying characteristics of malignant bone lesions, but this task is challenging and laborious for radiologists. Deep learning has shown promise in automating image segmentation in radiology, including for malignant bone lesions. The purpose of this review is to investigate deep learning-based image segmentation methods for malignant bone lesions on Computed Tomography (CT), Magnetic Resonance Imaging (MRI), and Positron-Emission Tomography/CT (PET/CT). Method: The literature search of deep learning-based image segmentation of malignant bony lesions on CT and MRI was conducted in PubMed, Embase, Web of Science, and Scopus electronic databases following the guidelines of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). A total of 41 original articles published between February 2017 and March 2023 were included in the review. Results: The majority of papers studied MRI, followed by CT, PET/CT, and PET/MRI. There was relatively even distribution of papers studying primary vs. secondary malignancies, as well as utilizing 3-dimensional vs. 2-dimensional data. Many papers utilize custom built models as a modification or variation of U-Net. The most common metric for evaluation was the dice similarity coefficient (DSC). Most models achieved a DSC above 0.6, with medians for all imaging modalities between 0.85-0.9. Discussion: Deep learning methods show promising ability to segment malignant osseous lesions on CT, MRI, and PET/CT. Some strategies which are commonly applied to help improve performance include data augmentation, utilization of large public datasets, preprocessing including denoising and cropping, and U-Net architecture modification. Future directions include overcoming dataset and annotation homogeneity and generalizing for clinical applicability.

A Radiomic-based Machine Learning Algorithm to Reliably Differentiate Benign Renal Masses from Renal Cell Carcinoma.

BACKGROUND: A substantial proportion of patients undergo treatment for renal masses where active surveillance or observation may be more appropriate. OBJECTIVE: To determine whether radiomic-based machine learning platforms can distinguish benign from malignant renal masses. DESIGN, SETTING, AND PARTICIPANTS: A prospectively maintained single-institutional renal mass registry was queried to identify patients with a computed tomography-proven clinically localized renal mass who underwent partial or radical nephrectomy. INTERVENTION: Radiomic analysis of preoperative scans was performed. Clinical and radiomic variables of importance were identified through decision tree analysis, which were incorporated into Random Forest and REAL Adaboost predictive models. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: The primary outcome was the degree of congruity between the virtual diagnosis and final pathology. Subanalyses were performed for small renal masses and patients who had percutaneous renal mass biopsies as part of their workup. Receiver operating characteristic curves were used to evaluate each model's discriminatory function. RESULTS AND LIMITATIONS: A total of 684 patients met the selection criteria. Of them, 76% had renal cell carcinoma; 57% had small renal masses, of which 73% were malignant. Predictive modeling differentiated benign pathology from malignant with an area under the curve (AUC) of 0.84 (95% confidence interval [CI] 0.79-0.9). In small renal masses, radiomic analysis yielded a discriminatory AUC of 0.77 (95% CI 0.69-0.85). When negative and nondiagnostic biopsies were supplemented with radiomic analysis, accuracy increased from 83.3% to 93.4%. CONCLUSIONS: Radiomic-based predictive modeling may distinguish benign from malignant renal masses. Clinical factors did not substantially improve the diagnostic accuracy of predictive models. Enhanced diagnostic predictability may improve patient selection before surgery and increase the utilization of active surveillance protocols. PATIENT SUMMARY: Not all kidney tumors are cancerous, and some can be watched. We evaluated a new method that uses radiographic features invisible to the naked eye to distinguish benign masses from true cancers and found that it can do so with acceptable accuracy.

Repeatability of Linear and Nonlinear Elastic Modulus Maps From Repeat Scans in the Breast.

Compression elastography allows the precise measurement of large deformations of soft tissue in vivo. From an image sequence showing tissue undergoing large deformation, an inverse problem for both the linear and nonlinear elastic moduli distributions can be solved. As part of a larger clinical study to evaluate nonlinear elastic modulus maps (NEMs) in breast cancer, we evaluate the repeatability of linear and nonlinear modulus maps from repeat measurements. Within the cohort of subjects scanned to date, 20 had repeat scans. These repeated scans were processed to evaluate NEM repeatability. In vivo data were acquired by a custom-built, digitally controlled, uniaxial compression device with force feedback from the pressure-plate. RF-data were acquired using plane-wave imaging, at a frame-rate of 200 Hz, with a ramp-and-hold compressive force of 8N, applied at 8N/sec. A 2D block-matching algorithm was used to obtain sample-level displacement fields which were then tracked at subsample resolution using 2D cross correlation. Linear and nonlinear elasticity parameters in a modified Veronda-Westmann model of tissue elasticity were estimated using an iterative optimization method. For the repeated scans, B-mode images, strain images, and linear and nonlinear elastic modulus maps are measured and compared. Results indicate that when images are acquired in the same region of tissue and sufficiently high strain is used to recover nonlinearity parameters, then the reconstructed modulus maps are consistent.

Shape and texture-based radiomics signature on CT effectively discriminates benign from malignant renal masses.

OBJECTIVES: Using a radiomics framework to quantitatively analyze tumor shape and texture features in three dimensions, we tested its ability to objectively and robustly distinguish between benign and malignant renal masses. We assessed the relative contributions of shape and texture metrics separately and together in the prediction model. MATERIALS AND METHODS: Computed tomography (CT) images of 735 patients with 539 malignant and 196 benign masses were segmented in this retrospective study. Thirty-three shape and 760 texture metrics were calculated per tumor. Tumor classification models using shape, texture, and both metrics were built using random forest and AdaBoost with tenfold cross-validation. Sensitivity analyses on five sub-cohorts with respect to the acquisition phase were conducted. Additional sensitivity analyses after multiple imputation were also conducted. Model performance was assessed using AUC. RESULTS: Random forest classifier showed shape metrics featuring within the top 10% performing metrics regardless of phase, attaining the highest variable importance in the corticomedullary phase. Convex hull perimeter ratio is a consistently high-performing shape feature. Shape metrics alone achieved an AUC ranging 0.64-0.68 across multiple classifiers, compared with 0.67-0.75 and 0.68-0.75 achieved by texture-only and combined models, respectively. CONCLUSION: Shape metrics alone attain high prediction performance and high variable importance in the combined model, while being independent of the acquisition phase (unlike texture). Shape analysis therefore should not be overlooked in its potential to distinguish benign from malignant tumors, and future radiomics platforms powered by machine learning should harness both shape and texture metrics. KEY POINTS: • Current radiomics research is heavily weighted towards texture analysis, but quantitative shape metrics should not be ignored in their potential to distinguish benign from malignant renal tumors. • Shape metrics alone can attain high prediction performance and demonstrate high variable importance in the combined shape and texture radiomics model. • Any future radiomics platform powered by machine learning should harness both shape and texture metrics, especially since tumor shape (unlike texture) is independent of the acquisition phase and more robust from the imaging variations.

Recovery of Tractions Exerted by Single Cells in Three-Dimensional Nonlinear Matrices.

Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell-matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.

Volumetric quantitative optical coherence elastography with an iterative inversion method.

It is widely accepted that accurate mechanical properties of three-dimensional soft tissues and cellular samples are not available on the microscale. Current methods based on optical coherence elastography can measure displacements at the necessary resolution, and over the volumes required for this task. However, in converting this data to maps of elastic properties, they often impose assumptions regarding homogeneity in stress or elastic properties that are violated in most realistic scenarios. Here, we introduce novel, rigorous, and computationally efficient inverse problem techniques that do not make these assumptions, to realize quantitative volumetric elasticity imaging on the microscale. Specifically, we iteratively solve the three-dimensional elasticity inverse problem using displacement maps obtained from compression optical coherence elastography. This is made computationally feasible with adaptive mesh refinement and domain decomposition methods. By employing a transparent, compliant surface layer with known shear modulus as a reference for the measurement, absolute shear modulus values are produced within a millimeter-scale sample volume. We demonstrate the method on phantoms, on a breast cancer sample ex vivo, and on human skin in vivo. Quantitative elastography on this length scale will find wide application in cell biology, tissue engineering and medicine.

Three-Dimensional Traction Microscopy with a Fiber-Based Constitutive Model.

Tractions exerted by cells on their surroundings play an important role in many biological processes including stem cell differentiation, tumorigenesis, cell migration, cancer metastasis, and angiogenesis. The ability to quantify these tractions is important in understanding and manipulating these processes. Three-dimensional traction force microscopy (3DTFM) provides reliable means of evaluating cellular tractions by first measuring the displacement of fluorescent beads in response to these tractions in the surrounding matrix, and then using this measurement to compute the tractions. However, most applications of 3DTFM assume that the surrounding extra-cellular matrix (ECM) is non-fibrous, despite the fact that in many natural and synthetic environments the ECM contains a significant proportion of fibrous components. Motivated by this, we develop a computational approach for determining tractions, while accounting for the fibrous nature of the ECM. In particular, we make use of a fiber-based constitutive model in which the stress contains contributions from a distribution of nonlinear elastic fibers and a hyperelastic matrix. We solve an inverse problem with the nodal values of the traction vector as unknowns, and minimize the difference between a predicted displacement field, obtained by solving the equations of equilibrium in conjunction with the fiber-based constitutive model, and the measured displacement field at the bead locations. We employ a gradient-based minimization method to solve this problem and determine the gradient efficiently by solving for the appropriate adjoint field. We apply this algorithm to problems with experimentally observed cell geometries and synthetic, albeit realistic, traction fields to gauge its sensitivity to noise, and quantify the impact of using an incorrect constitutive model: the so-called model error. We conclude that the approach is robust to noise, yielding about 10% error in tractions for 5% displacement noise. We also conclude that the impact of model error is significant, where using a nonlinear exponential hyperelastic model instead of the fiber-based model, can lead to more than 100% error in the traction field. These results underline the importance of using appropriate constitutive models in 3DTFM, especially in fibrous ECM constructs.

Direct Error in Constitutive Equation Formulation for Plane stress Inverse Elasticity Problem.

We present a new computational formulation for inverse problems in elasticity with full field data. The formulation is a variant of an error in the constitutive equation formulation, but allows direct solution for the modulus field and accommodates discontinuous strain fields. The development of the formulation is motivated by the relatively poor performance of current direct formulations, reported so far in literature, in dealing with discontinuities in the strain and material property distribution. The formulation relies on minimizing the error in the constitutive equation, and a momentum equation constraint. Numerical results on model problems show that the formulation is capable handling discontinuous, and noisy strain fields, and also converging with mesh refinement for continuous and discontinuous material property distributions. The application to reconstruct the elastic modulus distribution in solid breast tumors is shown.

Improving three-dimensional mechanical imaging of breast lesions with principal component analysis.

PURPOSE: Elastography has emerged as a new tool for detecting and diagnosing many types of diseases including breast cancer. To date, most clinical applications of elastography have utilized two-dimensional strain images. The goal of this paper is to present a new quasi-static elastography technique that yields shear modulus images in three dimensions. METHODS: An automated breast volume scanner was used to acquire ultrasound images of the breast as it was gently compressed. Cross-correlation between successive images was used to determine the displacement within the tissue. The resulting displacement field was filtered of all but compressive motion through principal component analysis. This displacement field was used to infer spatial distribution of shear modulus by solving a 3D elastic inverse problem. RESULTS: Three dimensional shear modulus images of benign breast lesions for two subjects were generated using the techniques described above. It was found that the lesions were visualized more clearly in images generated using the displacement data de-noised through the use of principal components. CONCLUSIONS: We have presented experimental and algorithmic techniques that lead to three-dimensional imaging of shear modulus using quasi-static elastography. This work demonstrates feasibility of this approach, and lays the foundation for images of other, more informative, mechanical parameters.

Noninvasive In-Vivo Quantification of Mechanical Heterogeneity of Invasive Breast Carcinomas.

Heterogeneity is a hallmark of cancer whether one considers the genotype of cancerous cells, the composition of their microenvironment, the distribution of blood and lymphatic microvasculature, or the spatial distribution of the desmoplastic reaction. It is logical to expect that this heterogeneity in tumor microenvironment will lead to spatial heterogeneity in its mechanical properties. In this study we seek to quantify the mechanical heterogeneity within malignant and benign tumors using ultrasound based elasticity imaging. By creating in-vivo elastic modulus images for ten human subjects with breast tumors, we show that Young's modulus distribution in cancerous breast tumors is more heterogeneous when compared with tumors that are not malignant, and that this signature may be used to distinguish malignant breast tumors. Our results complement the view of cancer as a heterogeneous disease on multiple length scales by demonstrating that mechanical properties within cancerous tumors are also spatially heterogeneous.

Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis.

We reconstruct the in vivo spatial distribution of linear and nonlinear elastic parameters in ten patients with benign (five) and malignant (five) tumors. The mechanical behavior of breast tissue is represented by a modified Veronda-Westmann model with one linear and one nonlinear elastic parameter. The spatial distribution of these elastic parameters is determined by solving an inverse problem within the region of interest (ROI). This inverse problem solution requires the knowledge of the displacement fields at small and large strains. The displacement fields are measured using a free-hand ultrasound strain imaging technique wherein, a linear array ultrasound transducer is positioned on the breast and radio frequency echo signals are recorded within the ROI while the tissue is slowly deformed with the transducer. Incremental displacement fields are determined from successive radio-frequency frames by employing cross-correlation techniques. The rectangular regions of interest were subjectively selected to obtain low noise displacement estimates and therefore were variables that ranged from 346 to 849.6 mm2 . It is observed that malignant tumors stiffen at a faster rate than benign tumors and based on this criterion nine out of ten tumors were correctly classified as being either benign or malignant.

Recent results in nonlinear strain and modulus imaging.

We report a summary of recent developments and current status of our team's efforts to image and quantify in vivo nonlinear strain and tissue mechanical properties. Our work is guided by a focus on applications to cancer diagnosis and treatment using clinical ultrasound imaging and quasi-static tissue deformations. We review our recent developments in displacement estimation from ultrasound image sequences. We discuss cross correlation approaches, regularized optimization approaches, guided search methods, multiscale methods, and hybrid methods. Current implementations can return results of high accuracy in both axial and lateral directions at several frames per second.We compare several strain estimators. Again we see a benefit from a regularized optimization approach. We then discuss both direct and iterative methods to reconstruct tissue mechanical property distributions from measured strain and displacement fields. We review the formulation, discretization, and algorithmic considerations that come into play when attempting to infer linear and nonlinear elastic properties from strain and displacement measurements. Finally we illustrate our progress with example applications in breast disease diagnosis and tumor ablation monitoring. Our current status shows that we have demonstrated quantitative determination of nonlinear parameters in phantoms and in vivo, in the context of 2D models and data. We look forward to incorporating 3D data from 2D transducer arrays to noninvasively create calibrated 3D quantitative maps of nonlinear elastic properties of breast tissues in vivo.

Quantitative ultrasonic elastography for gel dosimetry.

Advanced radiation techniques such as intensity-modulated radiotherapy (IMRT) for complex geometries in which targets are close to organs at risk have been introduced in radiation therapy, creating a need for procedures that allow easy three-dimensional (3-D) measurement of dose for verification purposes. Polymer gels that change their material properties when irradiated have been suggested for such use. For example, the change in their magnetic properties has been thoroughly investigated with magnetic resonance imaging (MRI). Also, we have previously shown that the mechanical stiffness, i.e., Young's modulus, of these gels changes with dose. This finding prompted us to assess whether we can image a radiation-induced stiffness distribution with quantitative ultrasound elastography and whether the stiffness distribution is correlated with the dose distribution. A methacrylic-acid-based gel was loaded with scatterers to create an ultrasound echoic signal. It was irradiated to create a rod-like region of increased stiffness with a 10 x 10 mm(2) cross-section. The gel block was compressed in a frame that restricted the movement of the gel to planes orthogonal to the long axis of the irradiated region and ultrasonic echo data were acquired in the central plane during compression. This simplified irradiation pattern and experimental set-up were designed to approximate plane-strain conditions and was chosen for proof of concept. The movement of the gel was tracked from ultrasound images of a different compressional state using cross-correlation, enabling a displacement map to be created. The shear modulus was reconstructed using an inverse algorithm. The role of the magnitude of the regularization parameter in the inverse problem and the boundary conditions in influencing the spatial distribution of stiffness and, thus, final dose contrast was investigated through parametric studies. These parameters were adjusted using prior knowledge about the stiffness in parts of the material, e.g., the background was not irradiated and therefore its stiffness was homogeneous. It was observed that a suitable choice for these reconstruction parameters was essential for a quantitative application of stiffness measurement such as dosimetry. The dose contrast and distribution found with the optimal parameters were close to those obtained with MRI. Initial results reported in this article are encouraging and indicate that with ongoing refinement of ultrasound elastography techniques and accompanying inverse algorithms, this approach could play an important role in gel dosimetry.

Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility.

We establish the feasibility of imaging the linear and nonlinear elastic properties of soft tissue using ultrasound. We report results for breast tissue where it is conjectured that these properties may be used to discern malignant tumors from benign tumors. We consider and compare three different quantities that describe nonlinear behavior, including the variation of strain distribution with overall strain, the variation of the secant modulus with overall applied strain and finally the distribution of the nonlinear parameter in a fully nonlinear hyperelastic model of the breast tissue.

Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study.

We present a methodology to image and quantify the shear elastic modulus of three-dimensional (3D) breast tissue volumes held in compression under conditions similar to those of a clinical mammography system. Tissue phantoms are made to mimic the ultrasonic and mechanical properties of breast tissue. Stiff lesions are created in these phantoms with size and modulus contrast values, relative to the background, that are within the range of values of clinical interest. A two-dimensional ultrasound system, scanned elevationally, is used to acquire 3D images of these phantoms as they are held in compression. From two 3D ultrasound images, acquired at different compressed states, a three-dimensional displacement vector field is measured. The measured displacement field is then used to solve an inverse problem, assuming the phantom material to be an incompressible, linear elastic solid, to recover the shear modulus distribution within the imaged volume. The reconstructed values are then compared to values measured independently by direct mechanical testing.

Coupling between elastic strain and interstitial fluid flow: ramifications for poroelastic imaging.

We study the effects of interstitial fluid flow and interstitial fluid drainage on the spatio-temporal response of soft tissue strain. The motivation stems from the ability to measure in vivo strain distributions in soft tissue via elastography, and the desire to explore the possibility of using such techniques to investigate soft tissue fluid flow. Our study is based upon a mathematical model for soft tissue mechanics from the literature. It is a simple generalization of biphasic theory that includes coupling between the fluid and solid phases of the soft tissue, and crucially, fluid exchange between the interstitium and the local microvasculature. We solve the mathematical equations in two dimensions by the finite element method (FEM). The finite element implementation is validated against an exact analytical solution that is derived in the appendix. Realistic input tissue properties from the literature are used in conjunction with FEM modelling to conduct several computational experiments. The results of these lead to the following conclusions: (i) different hypothetical flow mechanisms lead to different patterns of strain relaxation with time; (ii) representative tissue properties show fluid drainage into the local microvasculature to be the dominant flow-related stress/strain relaxation mechanism; (iii) the relaxation time of strain in solid tumours due to drainage into the microvasculature is on the order of 5-10 s; (iv) under realistic applied pressure magnitudes, the magnitude of the strain relaxation can be as high as approximately 0.4% strain (4000 microstrains), which is well within the range of strains measurable by elastography.

Evaluation of the adjoint equation based algorithm for elasticity imaging.

Recently a new adjoint equation based iterative method was proposed for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation. In this method the original problem was reformulated as a minimization problem, and a gradient-based optimization algorithm was used to solve it. Significant computational savings were realized by utilizing the solution of the adjoint elasticity equations in calculating the gradient. In this paper, we examine the performance of this method with regard to measures which we believe will impact its eventual clinical use. In particular, we evaluate its abilities to (1) resolve geometrically the complex regions of elevated stiffness; (2) to handle noise levels inherent in typical instrumentation; and (3) to generate three-dimensional elasticity images. For our tests we utilize both synthetic and experimental displacement data, and consider both qualitative and quantitative measures of performance. We conclude that the method is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency.