Some problems arising from mathematical model of ductal carcinoma in SITU.

Ductal carcinoma in situ (DCIS) is the earliest form of breast cancer. Three mathematical models in the one dimensional case arising from DCIS are proposed. The first two models are in the form of parabolic equation with initial and known moving boundaries. Direct and inverse problems are considered in model 1, existence and uniqueness are proved by using tool from heat potential theory and Volterra integral equations. Also, we discuss the direct problem and nonlocal problem of model 2, existence and uniqueness are proved. And approximation solution of these problems are implemented by Ritz-Galerkin method, which is the first attempt to deal with such problems. Based on the finding of the previous two models, the more general free boundary problem model - nonlinear parabolic partial differential equation with initial, boundary and free boundary condition is presented. Well-posedness theorems are proved by applying knowledge of semigroup solution operators. Illustrative examples are included to demonstrate the validity and applicability of the technique for all three models

Complexity Reduction in Image-Based Breast Cancer Care

The diversity of malignancies of the breast requires personalized diagnostic and therapeutic decision making in a complex situation. This thesis contributes in three clinical areas: (1) For clinical diagnostic image evaluation, computer-aided detection and diagnosis of mass and non-mass lesions in breast MRI is developed. 4D texture features characterize mass lesions. For non-mass lesions, a combined detection/characterisation method utilizes the bilateral symmetry of the breast s contrast agent uptake. (2) To improve clinical workflows, a breast MRI reading paradigm is proposed, exemplified by a breast MRI reading workstation prototype. Instead of mouse and keyboard, it is operated using multi-touch gestures. The concept is extended to mammography screening, introducing efficient navigation aids. (3) Contributions to finite element modeling of breast tissue deformations tackle two clinical problems: surgery planning and the prediction of the breast deformation in a MRI biopsy device

Computer-Aided, Multi-Modal, and Compression Diffuse Optical Studies of Breast Tissue

Diffuse Optical Tomography and Spectroscopy permit measurement of important physiological parameters non-invasively through ~10 cm of tissue. I have applied these techniques in measurements of human breast and breast cancer. My thesis integrates three loosely connected themes in this context: multi-modal breast cancer imaging, automated data analysis of breast cancer images, and microvascular hemodynamics of breast under compression. As per the first theme, I describe construction, testing, and the initial clinical usage of two generations of imaging systems for simultaneous diffuse optical and magnetic resonance imaging. The second project develops a statistical analysis of optical breast data from many spatial locations in a population of cancers to derive a novel optical signature of malignancy; I then apply this data-derived signature for localization of cancer in additional subjects. Finally, I construct and deploy diffuse optical instrumentation to measure blood content and blood flow during breast compression; besides optics, this research has implications for any method employing breast compression, e.g., mammography

Mammography

In this volume, the topics are constructed from a variety of contents: the bases of mammography systems, optimization of screening mammography with reference to evidence-based research, new technologies of image acquisition and its surrounding systems, and case reports with reference to up-to-date multimodality images of breast cancer. Mammography has been lagged in the transition to digital imaging systems because of the necessity of high resolution for diagnosis. However, in the past ten years, technical improvement has resolved the difficulties and boosted new diagnostic systems. We hope that the reader will learn the essentials of mammography and will be forward-looking for the new technologies. We want to express our sincere gratitude and appreciation?to all the co-authors who have contributed their work to this volume

Novel 3D Ultrasound Elastography Techniques for In Vivo Breast Tumor Imaging and Nonlinear Characterization

Breast cancer comprises about 29% of all types of cancer in women worldwide. This type of cancer caused what is equivalent to 14% of all female deaths due to cancer. Nowadays, tissue biopsy is routinely performed, although about 80% of the performed biopsies yield a benign result. Biopsy is considered the most costly part of breast cancer examination and invasive in nature. To reduce unnecessary biopsy procedures and achieve early diagnosis, ultrasound elastography was proposed.;In this research, tissue displacement fields were estimated using ultrasound waves, and used to infer the elastic properties of tissues. Ultrasound radiofrequency data acquired at consecutive increments of tissue compression were used to compute local tissue strains using a cross correlation method. In vitro and in vivo experiments were conducted on different tissue types to demonstrate the ability to construct 2D and 3D elastography that helps distinguish stiff from soft tissues. Based on the constructed strain volumes, a novel nonlinear classification method for human breast tumors is introduced. Multi-compression elastography imaging is elucidated in this study to differentiate malignant from benign tumors, based on their nonlinear mechanical behavior under compression. A pilot study on ten patients was performed in vivo, and classification results were compared with biopsy diagnosis - the gold standard. Various nonlinear parameters based on different models, were evaluated and compared with two commonly used parameters; relative stiffness and relative tumor size. Moreover, different types of strain components were constructed in 3D for strain imaging, including normal axial, first principal, maximum shear and Von Mises strains. Interactive segmentation algorithms were also evaluated and applied on the constructed volumes, to delineate the stiff tissue by showing its isolated 3D shape.;Elastography 3D imaging results were in good agreement with the biopsy outcomes, where the new classification method showed a degree of discrepancy between benign and malignant tumors better than the commonly used parameters. The results show that the nonlinear parameters were found to be statistically significant with p-value \u3c0.05. Moreover, one parameter; power-law exponent, was highly statistically significant having p-value \u3c 0.001. Additionally, volumetric strain images reconstructed using the maximum shear strains provided an enhanced tumor\u27s boundary from the surrounding soft tissues. This edge enhancement improved the overall segmentation performance, and diminished the boundary leakage effect. 3D segmentation provided an additional reliable means to determine the tumor\u27s size by estimating its volume.;In summary, the proposed elastographic techniques can help predetermine the tumor\u27s type, shape and size that are considered key features helping the physician to decide the sort and extent of the treatment. The methods can also be extended to diagnose other types of tumors, such as prostate and cervical tumors. This research is aimed toward the development of a novel \u27virtual biopsy\u27 method that may reduce the number of unnecessary painful biopsies, and diminish the increasingly risk of cancer

Measurement of the Hyperelastic Properties of Ex Vivo Breast Tissue Slices

The elastic and hyperelastic properties of biological soft tissues have been of interest to the medical community as there are several applications where parameters characterizing these properties are critical for a reliable clinical outcome. This includes applications such as surgery planning, needle biopsy, and cancer diagnosis using medical imaging. While there has been considerable research on the measurement of the linear elastic modulus of small tissue samples, little research has been conducted for measuring parameters that characterize non-linear elasticity of tissues included in slice specimens. In this work a method for measuring the hyperelastic parameters of tissue slice samples with tumours is presented. In this method, to measure the hyperelastic properties of a tumour within a slice sample, the tumour was indented to acquire its force-displacement response while the slice remained intact. To calculate the hyperelastic parameters from the acquired data, two inversion techniques were developed that use the slice nonlinear finite element model as their forward problem solver. One of these techniques was based on nonlinear optimization while the other is a novel iterative technique that processes the variable slopes ofthe force-displacement response to calculate the hyperelastic parameters. The latter was developed specifically for the Yeoh and the second order Polynomial hyperelastic model, since it was found that the other optimization based inversion technique did not perform well with these models. To validate the proposed techniques, numerical and phantom experiments were performed. Convergence with wide ranges of parameters of initial guesses was achieved, to within 1% error with the numerical simulation experiments, and also with errors of around 5-10% with the tissue mimicking phantoms. Moreover, these techniques were successfully applied to data that was acquired from 44 pathological breast tissue slice specimens where the goal was to determine the hyperelastic properties of the tumour within the breast tissue slices. A statistical analysis was performed in an attempt to correlate specific hyperelastic propertiestotissuepathology. Itwasconcludedthatfurtherresearchisrequiredto ascertain the reliability of using a hyperelastic parameter for cancer classification. It was also concluded that, based on the available data, it may be difficult to identify specific pathologies based solely on individual hyperelastic parameters and that a consideration of the entire parameter set may be necessary and that factors other than tissue pathology may be involved in tissue stifftιess, such as age

Personalized Decision Modeling for Intervention and Prevention of Cancers

Personalized medicine has been utilized in all stages of cancer care in recent years, including the prevention, diagnosis, treatment and follow-up. Since prevention and early intervention are particularly crucial in reducing cancer mortalities, personalizing the corresponding strategies and decisions so as to provide the most appropriate or optimal medical services for different patients can greatly improve the current cancer control practices. This dissertation research performs an in-depth exploration of personalized decision modeling of cancer intervention and prevention problems. We investigate the patient-specific screening and vaccination strategies for breast cancer and the cancers related to human papillomavirus (HPV), representatively. Three popular healthcare analytics techniques, Markov models, regression-based predictive models, and discrete-event simulation, are developed in the context of personalized cancer medicine. We discuss multiple possibilities of incorporating patient-specific risk into personalized cancer prevention strategies and showcase three practical examples. The first study builds a Markov decision process model to optimize biopsy referral decisions for women who receives abnormal breast cancer screening results. The second study directly optimizes the annual breast cancer screening using a regression-based adaptive decision model. The study also proposes a novel model selection method for logistic regression with a large number of candidate variables. The third study addresses the personalized HPV vaccination strategies and develops a hybrid model combining discrete-event simulation with regression-based risk estimation. Our findings suggest that personalized screening and vaccination benefit patients by maximizing life expectancies and minimizing the possibilities of dying from cancer. Preventive screening and vaccination programs for other cancers or diseases, which have clearly identified risk factors and measurable risk, may all benefit from patient-specific policies

Imaging of the Breast

Early detection of breast cancer combined with targeted therapy offers the best outcome for breast cancer patients. This volume deal with a wide range of new technical innovations for improving breast cancer detection, diagnosis and therapy. There is a special focus on improvements in mammographic image quality, image analysis, magnetic resonance imaging of the breast and molecular imaging. A chapter on targeted therapy explores the option of less radical postoperative therapy for women with early, screen-detected breast cancers