Emerging Techniques in Breast MRI

As indicated throughout this chapter, there is a constant effort to move to more sensitive, specific, and quantitative methods for characterizing breast tissue via magnetic resonance imaging (MRI). In the present chapter, we focus on six emerging techniques that seek to quantitatively interrogate the physiological and biochemical properties of the breast. At the physiological scale, we present an overview of ultrafast dynamic contrast-enhanced MRI and magnetic resonance elastography which provide remarkable insights into the vascular and mechanical properties of tissue, respectively. Moving to the biochemical scale, magnetization transfer, chemical exchange saturation transfer, and spectroscopy (both “conventional” and hyperpolarized) methods all provide unique, noninvasive, insights into tumor metabolism. Given the breadth and depth of information that can be obtained in a single MRI session, methods of data synthesis and interpretation must also be developed. Thus, we conclude the chapter with an introduction to two very different, though complementary, methods of data analysis: (1) radiomics and habitat imaging, and (2) mechanism-based mathematical modeling

From tumour perfusion to drug delivery and clinical translation of in silico cancer models

In silico cancer models have demonstrated great potential as a tool to improve drug design, optimise the delivery of drugs to target sites in the host tissue and, hence, improve therapeutic efficacy and patient outcome. However, there are significant barriers to the successful translation of in silico technology from bench to bedside. More precisely, the specification of unknown model parameters, the necessity for models to adequately reflect in vivo conditions, and the limited amount of pertinent validation data to evaluate models' accuracy and assess their reliability, pose major obstacles in the path towards their clinical translation. This review aims to capture the state-of-the-art in in silico cancer modelling of vascularised solid tumour growth, and identify the important advances and barriers to success of these models in clinical oncology. Particular emphasis has been put on continuum-based models of cancer since they - amongst the class of mechanistic spatio-temporal modelling approaches - are well-established in simulating transport phenomena and the biomechanics of tissues, and have demonstrated potential for clinical translation. Three important avenues in in silico modelling are considered in this contribution: first, since systemic therapy is a major cancer treatment approach, we start with an overview of the tumour perfusion and angiogenesis in silico models. Next, we present the state-of-the-art in silico work encompassing the delivery of chemotherapeutic agents to cancer nanomedicines through the bloodstream, and then review continuum-based modelling approaches that demonstrate great promise for successful clinical translation. We conclude with a discussion of what we view to be the key challenges and opportunities for in silico modelling in personalised and precision medicine

Advanced diffusion MRI for microstructure imaging: theoretical developments

An accurate characterization of tissue features at microscopic level is essential for understanding the brain structure or staging a large variety of diseases, such as Alzheimer’s, multiple sclerosis or cancer. The aim of microstructure imaging is to provide information related to cellular structure from non-invasive imaging modali¬ties, such as Magnetic Resonance Imaging (MRI). This can be achieved by developing accurate tissue models and relating them to imaging data. Diffusion weighted MRI (DW-MRI) measures the displacement of the water molecules inside the tissue which is sensitive to the configuration of cellular membranes, therefore it provides relevant information for characterizing tissue microstructure. This PhD thesis presents my work on developing novel DW-MRI sequences and tissue models which provide improved sensitivity to cellular features such as pore size and shape. To model the DW-MRI signal, the tissue is regarded as a porous medium with cells described as fluid-filled pores separated by impermeable membranes. The first part of this thesis is concentrated on improving the estimation of intrinsic diffu¬sivity and pore size. Specifically, it analyses a promising class of diffusion sequences, namely oscillating gradients, which measure diffusion on a short time scale and give access to small structures, such as cell nuclei. Additionally, it emphasises the benefits of low-frequency oscillating waveforms over the standard acquisition for estimating axon diameter. The second part of my project focuses on estimating complex tissue features such as pore elongation and size distribution, and it demonstrates that these features are in¬trinsically linked and need to be explicitly modelled for accurate results. Moreover, it shows that pulse sequences with varying gradient orientation, such as double diffusion encoding, are able to separate these effects more effectively than standard sequences. The most recent study combines the benefits of both sequences in an innovative acqui¬sition with double oscillating gradients. This supports estimates of cell size distribution and eccentricity for a wider range of substrates

Coupling schemes and inexact Newton for multi-physics and coupled optimization problems

This work targets mathematical solutions and software for complex numerical simulation and optimization problems. Characteristics are the combination of different models and software modules and the need for massively parallel execution on supercomputers. We consider two different types of multi-component problems in Part I and Part II of the thesis: (i) Surface coupled fluid- structure interactions and (ii) analysis of medical MR imaging data of brain tumor patients. In (i), we establish highly accurate simulations by combining different aspects such as fluid flow and arterial wall deformation in hemodynamics simulations or fluid flow, heat transfer and mechanical stresses in cooling systems. For (ii), we focus on (a) facilitating the transfer of information such as functional brain regions from a statistical healthy atlas brain to the individual patient brain (which is topologically different due to the tumor), and (b) to allow for patient specific tumor progression simulations based on the estimation of biophysical parameters via inverse tumor growth simulation (given a single snapshot in time, only). Applications and specific characteristics of both problems are very distinct, yet both are hallmarked by strong inter-component relations and result in formidable, very large, coupled systems of partial differential equations. Part I targets robust and efficient quasi-Newton methods for black-box surface-coupling of parti- tioned fluid-structure interaction simulations. The partitioned approach allows for great flexibility and exchangeable of sub-components. However, breaking up multi-physics into single components requires advanced coupling strategies to ensure correct inter-component relations and effectively tackle instabilities. Due to the black-box paradigm, solver internals are hidden and information exchange is reduced to input/output relations. We develop advanced quasi-Newton methods that effectively establish the equation coupling of two (or more) solvers based on solving a non-linear fixed-point equation at the interface. Established state of the art methods fall short by either requiring costly tuning of problem dependent parameters, or becoming infeasible for large scale problems. In developing parameter-free, linear-complexity alternatives, we lift the robustness and parallel scalability of quasi-Newton methods for partitioned surface-coupled multi-physics simulations to a new level. The developed methods are implemented in the parallel, general purpose coupling tool preCICE. Part II targets MR image analysis of glioblastoma multiforme pathologies and patient specific simulation of brain tumor progression. We apply a joint medical image registration and biophysical inversion strategy, targeting at facilitating diagnosis, aiding and supporting surgical planning, and improving the efficacy of brain tumor therapy. We propose two problem formulations and decompose the resulting large-scale, highly non-linear and non-convex PDE-constrained optimization problem into two tightly coupled problems: inverse tumor simulation and medical image registration. We deduce a novel, modular Picard iteration-type solution strategy. We are the first to successfully solve the inverse tumor-growth problem based on a single patient snapshot with a gradient-based approach. We present the joint inversion framework SIBIA, which scales to very high image resolutions and parallel execution on tens of thousands of cores. We apply our methodology to synthetic and actual clinical data sets and achieve excellent normal-to-abnormal registration quality and present a proof of concept for a very promising strategy to obtain clinically relevant biophysical information. Advanced inexact-Newton methods are an essential tool for both parts. We connect the two parts by pointing out commonalities and differences of variants used in the two communities in unified notation