Conditional generative learning for medical image imputation.

Image imputation refers to the task of generating a type of medical image given images of another type. This task becomes challenging when the difference between the available images, and the image to be imputed is large. In this manuscript, one such application is considered. It is derived from the dynamic contrast enhanced computed tomography (CECT) imaging of the kidneys: given an incomplete sequence of three CECT images, we are required to impute the missing image. This task is posed as one of probabilistic inference and a generative algorithm to generate samples of the imputed image, conditioned on the available images, is developed, trained, and tested. The output of this algorithm is the "best guess" of the imputed image, and a pixel-wise image of variance in the imputation. It is demonstrated that this best guess is more accurate than those generated by other, deterministic deep-learning based algorithms, including ones which utilize additional information and more complex loss terms. It is also shown that the pixel-wise variance image, which quantifies the confidence in the reconstruction, can be used to determine whether the result of the imputation meets a specified accuracy threshold and is therefore appropriate for a downstream task.

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.

Probabilistic Brain Extraction in MR Images via Conditional Generative Adversarial Networks.

Brain extraction, or the task of segmenting the brain in MR images, forms an essential step for many neuroimaging applications. These include quantifying brain tissue volumes, monitoring neurological diseases, and estimating brain atrophy. Several algorithms have been proposed for brain extraction, including image-to-image deep learning methods that have demonstrated significant gains in accuracy. However, none of them account for the inherent uncertainty in brain extraction. Motivated by this, we propose a novel, probabilistic deep learning algorithm for brain extraction that recasts this task as a Bayesian inference problem and utilizes a conditional generative adversarial network (cGAN) to solve it. The input to the cGAN's generator is an MR image of the head, and the output is a collection of likely brain images drawn from a probability density conditioned on the input. These images are used to generate a pixel-wise mean image, serving as the estimate for the extracted brain, and a standard deviation image, which quantifies the uncertainty in the prediction. We test our algorithm on head MR images from five datasets: NFBS, CC359, LPBA, IBSR, and their combination. Our datasets are heterogeneous regarding multiple factors, including subjects (with and without symptoms), magnetic field strengths, and manufacturers. Our experiments demonstrate that the proposed approach is more accurate and robust than a widely used brain extraction tool and at least as accurate as the other deep learning methods. They also highlight the utility of quantifying uncertainty in downstream applications. Additional information and codes for our method are available at: https://github.com/bmri/bmri.

Graph Laplacian-based spectral multi-fidelity modeling.

Low-fidelity data is typically inexpensive to generate but inaccurate, whereas high-fidelity data is accurate but expensive. To address this, multi-fidelity methods use a small set of high-fidelity data to enhance the accuracy of a large set of low-fidelity data. In the approach described in this paper, this is accomplished by constructing a graph Laplacian from the low-fidelity data and computing its low-lying spectrum. This is used to cluster the data and identify points closest to the cluster centroids, where high-fidelity data is acquired. Thereafter, a transformation that maps every low-fidelity data point to a multi-fidelity counterpart is determined by minimizing the discrepancy between the multi- and high-fidelity data while preserving the underlying structure of the low-fidelity data distribution. The method is tested with problems in solid and fluid mechanics. By utilizing only a small fraction of high-fidelity data, the accuracy of a large set of low-fidelity data is significantly improved.

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 Mechanistic Model of Aqueous Humor Flow to Study Effects of Angle Closure on Intraocular Pressure.

Purpose: To study the relationship between the circumferential extent of angle closure and elevation in intraocular pressure (IOP) using a novel mechanistic model of aqueous humor (AH) flow. Methods: AH flow through conventional and unconventional outflow pathways was modeled using the unified Stokes and Darcy equations, which were solved using the finite element method. The severity and circumferential extent of angle closure were modeled by lowering the permeability of the outflow pathways. The IOP predicted by the model was compared with biometric and IOP data from the Chinese American Eye Study, wherein the circumferential extent of angle closure was determined using anterior segment OCT measurements of angle opening distance. Results: The mechanistic model predicted an initial linear rise in IOP with increasing extent of angle closure which became nonlinear when the extent of closure exceeded around one-half of the circumference. The nonlinear rise in IOP was associated with a nonlinear increase in AH outflow velocity in the open regions of the angle. These predictions were consistent with the nonlinear relationship between angle closure and IOP observed in the clinical data. Conclusions: IOP increases rapidly when the circumferential extent of angle closure exceeds 180°. Residual AH outflow may explain why not all angle closure eyes develop elevated IOP when angle closure is extensive. Translational Relevance: This study provides insight into the extent of angle closure that is clinically relevant and confers increased risk of elevated IOP. The proposed model can be utilized to study other mechanisms of impaired aqueous outflow.

Hyperelastic continuum models for isotropic athermal fibrous networks.

Many biological materials contain fibrous protein networks as their main structural components. Understanding the mechanical properties of such networks is important for creating biomimicking materials for cell and tissue engineering, and for developing novel tools for detecting and diagnosing disease. In this work, we develop continuum models for isotropic, athermal fibrous networks by combining a single-fibre model that describes the axial response of individual fibres, with network models that assemble individual fibre properties into overall network behaviour. In particular, we consider four different network models, including the affine, three-chain, eight-chain, and micro-sphere models, which employ different assumptions about network structure and kinematics. We systematically investigate the ability of these models to describe the mechanical response of athermal collagen and fibrin networks by comparing model predictions with experimental data. We test how each model captures network behaviour under three different loading conditions: uniaxial tension, simple shear, and combined tension and shear. We find that the affine and three-chain models can accurately describe both the axial and shear behaviour, whereas the eight-chain and micro-sphere models fail to capture the shear response, leading to unphysical zero shear moduli at infinitesimal strains. Our study is the first to systematically investigate the applicability of popular network models for describing the macroscopic behaviour of athermal fibrous networks, offering insights for selecting efficient models that can be used for large-scale, finite-element simulations of athermal networks.

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.

A comprehensive spatial-temporal infection model.

Motivated by analogies between the spread of infections and of chemical processes, we develop a model that accounts for infection and transport where infected populations correspond to chemical species. Areal densities emerge as the key variables, thus capturing the effect of spatial density. We derive expressions for the kinetics of the infection rates, and for the important parameter R 0 , that include areal density and its spatial distribution. We present results for a batch reactor, the chemical process equivalent of the SIR model, where we examine how the dependence of R 0 on process extent, the initial density of infected individuals, and fluctuations in population densities effect the progression of the disease. We then consider spatially distributed systems. Diffusion generates traveling waves that propagate at a constant speed, proportional to the square root of the diffusivity and R 0 . Preliminary analysis shows a similar behavior for the effect of stochastic advection.

Machine learning based predictors for COVID-19 disease severity.

Predictors of the need for intensive care and mechanical ventilation can help healthcare systems in planning for surge capacity for COVID-19. We used socio-demographic data, clinical data, and blood panel profile data at the time of initial presentation to develop machine learning algorithms for predicting the need for intensive care and mechanical ventilation. Among the algorithms considered, the Random Forest classifier performed the best with [Formula: see text] for predicting ICU need and [Formula: see text] for predicting the need for mechanical ventilation. We also determined the most influential features in making this prediction, and concluded that all three categories of data are important. We determined the relative importance of blood panel profile data and noted that the AUC dropped by 0.12 units when this data was not included, thus indicating that it provided valuable information in predicting disease severity. Finally, we generated RF predictors with a reduced set of five features that retained the performance of the predictors trained on all features. These predictors, which rely only on quantitative data, are less prone to errors and subjectivity.

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.

Characterization of Spatially Graded Biomechanical Scaffolds.

Advances in fabrication have allowed tissue engineers to better mimic complex structures and tissue interfaces by designing nanofibrous scaffolds with spatially graded material properties. However, the nonuniform properties that grant the desired biomechanical function also make these constructs difficult to characterize. In light of this, we developed a novel procedure to create graded nanofibrous scaffolds and determine the spatial distribution of their material properties. Multilayered nanofiber constructs were synthesized, controlling spatial gradation of the stiffness to mimic the soft tissue gradients found in tendon or ligament tissue. Constructs were characterized using uniaxial tension testing with digital image correlation (DIC) to measure the displacements throughout the sample, in a noncontacting fashion, as it deformed. Noise was removed from the displacement data using principal component analysis (PCA), and the final denoised field served as the input to an inverse elasticity problem whose solution determines the spatial distribution of the Young's modulus throughout the material, up to a multiplicative factor. Our approach was able to construct, characterize, and determine the spatially varying moduli, in four electrospun scaffolds, highlighting its great promise for analyzing tissues and engineered constructs with spatial gradations in modulus, such as those at the interfaces between two disparate tissues (e.g., myotendinous junction, tendon- and ligament-to-bone entheses).

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.

Stochasticity in materials structure, properties, and processing-A review.

We review the concept of stochasticity-i.e., unpredictable or uncontrolled fluctuations in structure, chemistry, or kinetic processes-in materials. We first define six broad classes of stochasticity: equilibrium (thermodynamic) fluctuations; structural/compositional fluctuations; kinetic fluctuations; frustration and degeneracy; imprecision in measurements; and stochasticity in modeling and simulation. In this review, we focus on the first four classes that are inherent to materials phenomena. We next develop a mathematical framework for describing materials stochasticity and then show how it can be broadly applied to these four materials-related stochastic classes. In subsequent sections, we describe structural and compositional fluctuations at small length scales that modify material properties and behavior at larger length scales; systems with engineered fluctuations, concentrating primarily on composite materials; systems in which stochasticity is developed through nucleation and kinetic phenomena; and configurations in which constraints in a given system prevent it from attaining its ground state and cause it to attain several, equally likely (degenerate) states. We next describe how stochasticity in these processes results in variations in physical properties and how these variations are then accentuated by-or amplify-stochasticity in processing and manufacturing procedures. In summary, the origins of materials stochasticity, the degree to which it can be predicted and/or controlled, and the possibility of using stochastic descriptions of materials structure, properties, and processing as a new degree of freedom in materials design are described.

Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation.

We consider the problem of estimating the 2D vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the 2D vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimates decreased from about 50% to about 2%, and strain error decreased from more than 250% to below 2%.

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.