Fast algorithms for biophysically-constrained inverse problems in medical imaging

We present algorithms and software for parameter estimation for forward and inverse tumor growth problems and diffeomorphic image registration. Our methods target the following scenarios: automatic image registration of healthy images to tumor bearing medical images and parameter estimation/calibration of tumor models. This thesis focuses on robust and scalable algorithms for these problems. Although the proposed framework applies to many problems in oncology, we focus on primary brain tumors and in particular low and high-grade gliomas. For the tumor model, the main quantity of interest is the extent of tumor infiltration into the brain, beyond what is visible in imaging. The inverse tumor problem assumes that we have patient images at two (or more) well-separated times so that we can observe the tumor growth. Also, the inverse problem requires that the two images are segmented. But in a clinical setting such information is usually not available. In a typical case, we just have multimodal magnetic resonance images with no segmentation. We address this lack of information by solving a coupled inverse registration and tumor problem. The role of image registration is to find a plausible mapping between the patient's tumor-bearing image and a normal brain (atlas), with known segmentation. Solving this coupled inverse problem has a prohibitive computational cost, especially in 3D. To address this challenge we have developed novel schemes, scaled up to 200K cores. Our main contributions is the design and implementation of fast solvers for these problems. We also study the performance for the tumor parameter estimation and registration solvers and their algorithmic scalability. In particular, we introduce the following novel algorithms: An adjoint formulation for tumor-growth problems with/without mass-effect; The first parallel 3D Newton-Krylov method for large diffeomorphic image registration; A novel parallel semi-Lagrangian algorithm for solving advection equations in image registration and its parallel implementation on shared and distributed memory architectures; and Accelerated FFT (AccFFT), an open-source parallel FFT library for CPU and GPUs scaled up to 131,000 cores with optimized kernels for computing spectral operators. The scientific outcomes of this thesis, has appeared in the proceedings of three ACM/IEEE SCxy conferences (two best student paper finalist, and one ACM SRC gold medal), two journal papers, two papers in review, four papers in preparation (coupling, mass effect, segmentation, and multi-species tumor model), and seven conference presentations.Computational Science, Engineering, and Mathematic

Rapid online reconstruction of non-Cartesian magnetic resonance images using commodity graphics cards

In Magnetic Resonance Imaging, energy of electromagnetic waves is used to excite protons placed in a static magnetic field. This generates a signal, which is further spatially encoded with linear magnetic field gradients. The signal exists in frequency domain called k-space. Traditionally, the signal is sampled in lines stored on a Cartesian grid. Next, Fast Fourier Transform is applied to generate images. However, the consecutive manner (line-by-line) of this strategy makes it very slow. Faster sampling strategies exist, but acquisitions with them require a more complex image reconstruction process. There is an obvious trade-off between acquisition time and complexity of image reconstruction. Real-time assessment protocols for day-to-day clinical work demand both data acquisition with rapid sampling trajectories and fast, robust image reconstructions. Computational solutions in form of parallel architectures can be used to aid image reconstruction, which has been proven to significantly speed-up reconstruction process. Regrettably, this is often done in off-line mode, where the data need to be downloaded from the scanner and reconstructed elsewhere. This process hinders the clinical workflow substantially. This work describes challenges entailed with translation of advanced imaging protocols into the clinical environment; (i) use of the advanced sequences is limited by their reconstruction time, and (ii) fast implementations exist but they still run in off-line mode. These were addressed and resolved with development of a novel online, heterogeneous image reconstruction system for Magnetic Resonance Imaging. The external platform was designed to support fast implementation of advanced reconstruction algorithms. An external computer equipped with a Graphic Processing Unit card was integrated into the scanner’s image reconstruction pipeline. This allowed direct access to high performance parallel hardware on which the rapid data reconstruction can be realised. Also, the automation of data transmission and reconstruction execution has preserved the non-interrupted assessment workflow

A new generation of user-friendly and machine learning-accelerated methods for protein pKa calculations

The ability to sense and react to external and internal pH changes is a survival requirement for any cell. pH homeostasis is tightly regulated, and even minor disruptions can severely impact cell metabolism, function, and survival. The pH dependence of proteins can be attributed to only 7 out of the 20 canonical amino acids, the titratable amino acids that can exchange protons with water in the usual 0-14 pH range. These amino acids make up for approximately 31% of all amino acids in the human proteome, meaning that, on average, roughly one-third of each protein is sensitive not only to the medium pH but also to alterations in the electrostatics of its surroundings. Unsurprisingly, protonation switches have been associated with a wide array of protein behaviors, including modulating the binding affinity in protein-protein, protein-ligand, or protein-lipid systems, modifying enzymatic activity and function, and even altering their stability and subcellular location. Despite its importance, our molecular understanding of pHdependent effects in proteins and other biomolecules is still very limited, particularly in big macromolecular complexes such as protein-protein or membrane protein systems. Over the years, several classes of methods have been developed to provide molecular insights into the protonation preference and dependence of biomolecules. Empirical methods offer cheap and competitive predictions for time- or resource-constrained situations. Albeit more computationally expensive, continuum electrostatics-based are a cost-effective solution for estimating microscopic equilibrium constants, pKhalf and macroscopic pKa. To study pH-dependent conformational transitions, constant-pH molecular dynamics (CpHMD) is the appropriate methodology. Unfortunately, given the computational cost and, in many cases, the difficulty associated with using CE-based and CpHMD, most researchers overuse empirical methods or neglect the effect of pH in their studies. Here, we address these issues by proposing multiple pKa predictor methods and tools with different levels of theory designed to be faster and accessible to more users. First, we introduced PypKa, a flexible tool to predict Poisson–Boltzmann/Monte Carlo-based (PB/MC) pKa values of titratable sites in proteins. It was validated with a large set of experimental values exhibiting a competitive performance. PypKa supports CPU parallel computing and can be used directly on proteins obtained from the Protein Data Bank (PDB) repository or molecular dynamics (MD) simulations. A simple, reusable, and extensible Python API is provided, allowing pKa calculations to be easily added to existing protocols with a few extra lines of code. This capability was exploited in the development of PypKa-MD, an easy-to-use implementation of the stochastic titration CpHMD method. PypKa-MD supports GROMOS and CHARMM force fields, as well as modern versions of GROMACS. Using PypKa’s API and consequent abstraction of PB/MC contributed to its greatly simplified modular architecture that will serve as the foundation for future developments. The new implementation was validated on alanine-based tetrapeptides with closely interacting titratable residues and four commonly used benchmark proteins, displaying highly similar and correlated pKa predictions compared to a previously validated implementation. Like most structural-based computational studies, the majority of pKa calculations are performed on experimental structures deposited in the PDB. Furthermore, there is an ever-growing imbalance between scarce experimental pKa values and the increasingly higher number of resolved structures. To save countless hours and resources that would be spent on repeated calculations, we have released pKPDB, a database of over 12M theoretical pKa values obtained by running PypKa over 120k protein structures from the PDB. The precomputed pKa estimations can be retrieved instantaneously via our web application, the PypKa Server. In case the protein of interest is not in the pKPDB, the user may easily run PypKa in the cloud either by uploading a custom structure or submitting an identifier code from the PBD or UniProtKB. It is also possible to use the server to get structures with representative pH-dependent protonation states to be used in other computational methods such as molecular dynamics. The advent of artificial intelligence in biological sciences presented an opportunity to drastically accelerate pKa predictors using our previously generated database of pKa values. With pKAI, we introduced the first deep learning-based predictor of pKa shifts in proteins trained on continuum electrostatics data. By combining a reasonable understanding of the underlying physics, an accuracy comparable to that of physics-based methods, and inference time speedups of more than 1000 ×, pKAI provided a game-changing solution for fast estimations of macroscopic pKa from ensembles of microscopic values. However, several limitations needed to be addressed before its integration within the CpHMD framework as a replacement for PypKa. Hence, we proposed a new graph neural network for protein pKa predictions suitable for CpHMD, pKAI-MD. This model estimates pH-independent energies to be used in a Monte Carlo routine to sample representative microscopic protonation states. While developing the new model, we explored different graph representations of proteins using multiple electrostatics-driven properties. While there are certainly many new features to be introduced and a multitude of development to be expanded, the selection of methods and tools presented in this work poses a significant improvement over the alternatives and effectively constitutes a new generation of user-friendly and machine learning-accelerated methods for pKa calculations

ANALYSIS OF BIOPATHWAY MODELS USING PARALLEL ARCHITECTURES

Ph.DDOCTOR OF PHILOSOPH

ANALYSIS OF BIOPATHWAY MODELS USING PARALLEL ARCHITECTURES

Ph.DDOCTOR OF PHILOSOPH

Computational Methods for Segmentation of Multi-Modal Multi-Dimensional Cardiac Images

Segmentation of the heart structures helps compute the cardiac contractile function quantified via the systolic and diastolic volumes, ejection fraction, and myocardial mass, representing a reliable diagnostic value. Similarly, quantification of the myocardial mechanics throughout the cardiac cycle, analysis of the activation patterns in the heart via electrocardiography (ECG) signals, serve as good cardiac diagnosis indicators. Furthermore, high quality anatomical models of the heart can be used in planning and guidance of minimally invasive interventions under the assistance of image guidance. The most crucial step for the above mentioned applications is to segment the ventricles and myocardium from the acquired cardiac image data. Although the manual delineation of the heart structures is deemed as the gold-standard approach, it requires significant time and effort, and is highly susceptible to inter- and intra-observer variability. These limitations suggest a need for fast, robust, and accurate semi- or fully-automatic segmentation algorithms. However, the complex motion and anatomy of the heart, indistinct borders due to blood flow, the presence of trabeculations, intensity inhomogeneity, and various other imaging artifacts, makes the segmentation task challenging. In this work, we present and evaluate segmentation algorithms for multi-modal, multi-dimensional cardiac image datasets. Firstly, we segment the left ventricle (LV) blood-pool from a tri-plane 2D+time trans-esophageal (TEE) ultrasound acquisition using local phase based filtering and graph-cut technique, propagate the segmentation throughout the cardiac cycle using non-rigid registration-based motion extraction, and reconstruct the 3D LV geometry. Secondly, we segment the LV blood-pool and myocardium from an open-source 4D cardiac cine Magnetic Resonance Imaging (MRI) dataset by incorporating average atlas based shape constraint into the graph-cut framework and iterative segmentation refinement. The developed fast and robust framework is further extended to perform right ventricle (RV) blood-pool segmentation from a different open-source 4D cardiac cine MRI dataset. Next, we employ convolutional neural network based multi-task learning framework to segment the myocardium and regress its area, simultaneously, and show that segmentation based computation of the myocardial area is significantly better than that regressed directly from the network, while also being more interpretable. Finally, we impose a weak shape constraint via multi-task learning framework in a fully convolutional network and show improved segmentation performance for LV, RV and myocardium across healthy and pathological cases, as well as, in the challenging apical and basal slices in two open-source 4D cardiac cine MRI datasets. We demonstrate the accuracy and robustness of the proposed segmentation methods by comparing the obtained results against the provided gold-standard manual segmentations, as well as with other competing segmentation methods