Analytical derivation of elasticity in breast phantoms for deformation tracking

Patient-specific biomedical modeling of the breast is of interest for medical applications such as image registration, image guided procedures and the alignment for biopsy or surgery purposes. The computation of elastic properties is essential to simulate deformations in a realistic way. This study presents an innovative analytical method to compute the elastic modulus and evaluate the elasticity of a breast using magnetic resonance (MRI) images of breast phantoms.An analytical method for elasticity computation was developed and subsequently validated on a series of geometric shapes, and on four physical breast phantoms that are supported by a planar frame. This method can compute the elasticity of a shape directly from a set of MRI scans. For comparison, elasticity values were also computed numerically using two different simulation software packages.Application of the different methods on the geometric shapes shows that the analytically derived elongation differs from simulated elongation by less than 9% for cylindrical shapes, and up to 18% for other shapes that are also substantially vertically supported by a planar base. For the four physical breast phantoms, the analytically derived elasticity differs from numeric elasticity by 18% on average, which is in accordance with the difference in elongation estimation for the geometric shapes. The analytic method has shown to be multiple orders of magnitude faster than the numerical methods.It can be concluded that the analytical elasticity computation method has good potential to supplement or replace numerical elasticity simulations in gravity-induced deformations, for shapes that are substantially supported by a planar base perpendicular to the gravitational field. The error is manageable, while the calculation procedure takes less than one second as opposed to multiple minutes with numerical methods. The results will be used in the MRI and Ultrasound Robotic Assisted Biopsy (MURAB) project

COMPUTATIONAL ULTRASOUND ELASTOGRAPHY: A FEASIBILITY STUDY

Ultrasound Elastography (UE) is an emerging set of imaging modalities used to assess the biomechanical properties of soft tissues. UE has been applied to numerous clinical applications. Particularly, results from clinical trials of UE in breast lesion differentiation and staging liver fibrosis indicated that there was a lack of confidence in UE measurements or image interpretation. Confidence on UE measurements interpretation is critically important for improving the clinical utility of UE. The primary objective of my thesis is to develop a computational simulation platform based on open-source software packages including Field II, VTK, FEBio and Tetgen. The proposed virtual simulation platform can be used to simulate SE and acoustic radiation force based SWE simulations, including pSWE, SSI and ARFI. To demonstrate its usefulness, in this thesis, examples for breast cancer detections were provided. The simulated results can reproduce what has been reported in the literature. To statistically analyze the intrinsic variations of shear wave speed (SWS) in the fibrotic liver tissues, a probability density function (PDF) of the SWS distribution in conjunction with a lossless stochastic tissue model was derived using the principle of Maximum Entropy (ME). The performance of the proposed PDF was evaluated using Monte-Carlo (MC) simulated shear wave data and against three other commonly used PDFs. We theoretically demonstrated that SWS measurements follow a non-Gaussian distribution for the first time. One advantage of the proposed PDF is its physically meaningful parameters. Also, we conducted a case study of the relationship between shear wave measurements and the microstructure of fibrotic liver tissues. Three different virtual tissue models were used to represent underlying microstructures of fibrotic liver tissues. Furthermore, another innovation of this thesis is the inclusion of “biologically-relevant” fibrotic liver tissue models for simulation of shear wave elastography. To link tissue structure, composition and architecture to the ultrasound measurements directly, a “biologically relevant” tissue model was established using Systems Biology. Our initial results demonstrated that the simulated virtual liver tissues qualitatively could reproduce histological results and wave speed measurements. In conclusions, these computational tools and theoretical analysis can improve the confidence on UE image/measurements interpretation

Dual modality optical coherence tomography : Technology development and biomedical applications

Optical coherence tomography (OCT) is a cross-sectional imaging modality that is widely used in clinical ophthalmology and interventional cardiology. It is highly promising for in situ characterization of tumor tissues. OCT has high spatial resolution and high imaging speed to assist clinical decision making in real-time. OCT can be used in both structural imaging and mechanical characterization. Malignant tumor tissue alters morphology. Additionally, structural OCT imaging has limited tissue differentiation capability because of the complex and noisy nature of the OCT signal. Moreover, the contrast of structural OCT signal derived from tissue’s light scattering properties has little chemical specificity. Hence, interrogating additional tissue properties using OCT would improve the outcome of OCT’s clinical applications. In addition to morphological difference, pathological tissue such as cancer breast tissue usually possesses higher stiffness compared to the normal healthy tissue, which indicates a compelling reason for the specific combination of structural OCT imaging with stiffness assessment in the development of dual-modality OCT system for the characterization of the breast cancer diagnosis. This dissertation seeks to integrate the structural OCT imaging and the optical coherence elastography (OCE) for breast cancer tissue characterization. OCE is a functional extension of OCT. OCE measures the mechanical response (deformation, resonant frequency, elastic wave propagation) of biological tissues under external or internal mechanical stimulation and extracts the mechanical properties of tissue related to its pathological and physiological processes. Conventional OCE techniques (i.e., compression, surface acoustic wave, magnetomotive OCE) measure the strain field and the results of OCE measurement are different under different loading conditions. Inconsistency is observed between OCE characterization results from different measurement sessions. Therefore, a robust mechanical characterization is required for force/stress quantification. A quantitative optical coherence elastography (qOCE) that tracks both force and displacement is proposed and developed at NJIT. qOCE instrument is based on a fiber optic probe integrated with a Fabry-Perot force sensor and the miniature probe can be delivered to arbitrary locations within animal or human body. In this dissertation, the principle of qOCE technology is described. Experimental results are acquired to demonstrate the capability of qOCE in characterizing the elasticity of biological tissue. Moreover, a handheld optical instrument is developed to allow in vivo real-time OCE characterization based on an adaptive Doppler analysis algorithm to accurately track the motion of sample under compression. For the development of the dual modality OCT system, the structural OCT images exhibit additive and multiplicative noises that degrade the image quality. To suppress noise in OCT imaging, a noise adaptive wavelet thresholding (NAWT) algorithm is developed to remove the speckle noise in OCT images. NAWT algorithm characterizes the speckle noise in the wavelet domain adaptively and removes the speckle noise while preserving the sample structure. Furthermore, a novel denoising algorithm is also developed that adaptively eliminates the additive noise from the complex OCT using Doppler variation analysis

Image guided constitutive modeling of the brain tissue

Issued as final reportUnited States. Department of Health and Human Service

Mechanical characterization of tissue-like materials using information based machine learning

Changes in the mechanical properties of soft tissues may be indicative of disease processes. Medical elastography techniques are an attempt to create images of the mechanical behavior to increase the sensitivity and specificity of existing imaging modalities. Current quantitative elasticity imaging methods rely on a priori assumptions of the tissue biomechanics in order to simply the forward problem, from which an inverse problem is developed. Erroneous assumptions and noisy image data result in incorrect estimates of the mechanical parameters. This thesis presents a new method of characterizing the mechanical response of soft tissues. Machine-learning techniques and measured force-displacement data are used to create empirical models of the constitutive behavior. Informational models are developed without enforcing simplyfing assumptions of the true underlying mechanics, allowing the mechanical properties of the tissue to be investigated after the model is developed. Knowledge of the true behavior allows the appropriate consitutive model to be chosen to create a parametric summary of the tissue suitable for imaging. The informational modeling process is demonstrated on gelatin phantoms comprised of a soft background material with one or three stiffer inclusions. An ultrasound probe was used to uniaxially compress the phantoms while acquiring surface force and displacement data, as well as ultrasound images. A speckle-tracking algorithm estimated motion of the phantoms within the imaged region. Force-displacement data and the Autoprogressive training algorithm was then used to build informational models describing the constitutive behavior of the gelatin materials. It will be shown that estimates of the full stress and strain vectors throughout an entire model can be computed with the use of informational models, a feat not previously possible in ultrasound elastography. These vectors can then be used to create a parametric summary of mechanical properties of the gelatin materials - in this case, estimates of the Young's modulus. The resuling images of the Young's modulus distribution clearly differentiate the stiff inclusion(s) from the soft background. Results from this investigation are just the starting point for developing informational models of soft tissues. Sampling requirements and training methods to improve the ability of the models to characterize the linear-elastic properties of the gelatin are discussed. Future work will involve extending this method to 3D and characterizing more complex mechanical behaviors, including nonlinear, time-dependent, path-dependent properties

Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities

We consider the design of finite element methods for inverse problems with full-field data governed by elliptic forward operators. Such problems arise in applications in inverse heat conduction, in mechanical property characterization, and in medical imaging. For this class of problems, novel finite element methods have been proposed (Barbone et al., 2010) that give good performance, provided the solutions are in the H^1(Ω) function space. The material property distributions being estimated can be discontinuous, however, and therefore it is desirable to have formulations that can accommodate discontinuities in both data and solution. Toward this end, we present a mixed variational formulation for this class of problems that handles discontinuities well. We motivate the mixed formulation by examining the possibility of discretizing using a discontinuous discretization in an irreducible finite element method, and discuss the limitations of that approach. We then derive a new mixed formulation based on a least-square error in the constitutive equation. We prove that the continuous variational formulations are well-posed for applications in both inverse heat conduction and plane stress elasticity. We derive a priori error bounds for discretization error, valid in the limit of mesh refinement. We demonstrate convergence of the method with mesh refinement in cases with both continuous and discontinuous solutions. Finally we apply the formulation to measured data to estimate the elastic shear modulus distributions in both tissue mimicking phantoms and in breast masses from data collected in vivo