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

Novel Numerical Models of Electrostatic Interactions and Their Application to S-Nitrosothiol Simulations

Atom-centered point charge model of the molecular electrostatics remains a major workhorse in the atomistic biomolecular simulations. However, this approximation fails to reproduce anisotropic features of the molecular electrostatic potential (MEP), and the existing methods of the charge derivation are often associated with the numerical instabilities. This work provides an in-depth analysis of these limitations and offers a novel approach to describe electrostatic interactions that paves the way toward efficient next-generation force fields. By analyzing the charge fitting problem from first principles, as an example of the mathematical inverse problem, we show that the numerical instabilities of the charge-fitting problem arise due to the decreasing contribution from the higher multipole moments to the overall MEP. This insight suggests that if the point charges are arranged over the sphere using Lebedev quadrature, the resulting point charge model is able to exactly reproduce multipoles up to a given rank. At the same time, point charge values can be derived without fitting to the MEP, avoiding numerically unstable method of the charge derivation. This approach provides a systematic way to reproduce multipole moments up to any rank within the point charge approximation, which makes this model a computationally efficient analog of the multipolar expansion. Moreover, the proposed charged sphere model can be also used in the multi-site expansions with the expansion centers located at each atom in a molecule. This provides a natural approach to expand the traditional atom-centered point charge approximation to include higher-rank atomic multipoles and to account for the anisotropy of the MEP. We applied the proposed charged sphere model to S-nitrosothiols (RSNOs)—a class of biomolecules that serves to store and transmit nitric oxide, a biologically important signaling molecule. We showed that when the atom-centered charged spheres are optimized together with the Lennard-Jones parameters, the resulting force field can accurately reproduce the anisotropic features of the intermolecular interactions that play a crucial role in the biological regulation of RSNO chemistry. Overall, the developed charge model is a promising approach that can be used in the biomolecular simulations and beyond, e.g. in the multipolar force fields for atomistic and coarse-grained simulations

1994 NASA-HU American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program

Since 1964, the National Aeronautics and Space Administration (NASA) has supported a program of summer faculty fellowships for engineering and science educators. In a series of collaborations between NASA research and development centers and nearby universities, engineering faculty members spend 10 weeks working with professional peers on research. The Summer Faculty Program Committee of the American Society for Engineering Education supervises the programs. Objectives: (1) To further the professional knowledge of qualified engineering and science faculty members; (2) To stimulate and exchange ideas between participants and NASA; (3) To enrich and refresh the research and teaching activities of participants' institutions; (4) To contribute to the research objectives of the NASA center

Efficient Acoustic Simulation for Immersive Media and Digital Fabrication

Sound is a crucial part of our life. Well-designed acoustic behaviors can lead to significant improvement in both physical and virtual interactions. In computer graphics, most existing methods focused primarily on improving the accuracy. It remained underexplored on how to develop efficient acoustic simulation algorithms for interactive practical applications. The challenges arise from the dilemma between expensive accurate simulations and fast feedback demanded by intuitive user interaction: traditional physics-based acoustic simulations are computationally expensive; yet, for end users to benefit from the simulations, it is crucial to give prompt feedback during interactions. In this thesis, I investigate how to develop efficient acoustic simulations for real-world applications such as immersive media and digital fabrication. To address the above-mentioned challenges, I leverage precomputation and optimization to significantly improve the speed while preserving the accuracy of complex acoustic phenomena. This work discusses three efforts along this research direction: First, to ease sound designer's workflow, we developed a fast keypoint-based precomputation algorithm to enable interactive acoustic transfer values in virtual sound simulations. Second, for realistic audio editing in 360° videos, we proposed an inverse material optimization based on fast sound simulation and a hybrid ambisonic audio synthesis that exploits the directional isotropy in spatial audios. Third, we devised a modular approach to efficiently simulate and optimize fabrication-ready acoustic filters, achieving orders of magnitudes speedup while maintaining the simulation accuracy. Through this series of projects, I demonstrate a wide range of applications made possible by efficient acoustic simulations

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

Parameter estimation with gravitational waves

The new era of gravitational wave astronomy truly began on September 14, 2015 with the detection of GW150914, the sensational first direct observation of gravitational waves from the inspiral and merger of two black holes by the two Advanced LIGO detectors. In the subsequent first three observing runs of the LIGO/Virgo network, gravitational waves from $\sim 50$ compact binary mergers have been announced, with more results to come. The events have mostly been produced by binary black holes, but two binary neutron star mergers have so far been observed, as well as the mergers of two neutron star - black hole systems. Furthermore, gravitational waves emitted by core-collapse supernovae, pulsars and the stochastic gravitational wave background are within the LIGO/Virgo/KAGRA sensitivity band and are likely to be observed in future observation runs. Beyond signal detection, a major challenge has been the development of statistical and computational methodology for estimating the physical waveform parameters and quantifying their uncertainties in order to accurately characterise the emitting system. These methods depend on the sources of the gravitational waves and the gravitational waveform model that is used. This article reviews the main waveform models and parameter estimation methods used to extract physical parameters from gravitational wave signals detected to date by LIGO and Virgo and from those expected to be observed in the future, which will include KAGRA, and how these methods interface with various aspects of LIGO/Virgo/KAGRA science. Also presented are the statistical methods used by LIGO and Virgo to estimate detector noise, test general relativity, and draw conclusions about the rates of compact binary mergers in the universe. Furthermore, a summary of major publicly available gravitational wave parameter estimation software packages is given

Computational ligand design and analysis in protein complexes using inverse methods, combinatorial search, and accurate solvation modeling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2006.Vita.Includes bibliographical references (p. 207-230).This thesis presents the development and application of several computational techniques to aid in the design and analysis of small molecules and peptides that bind to protein targets. First, an inverse small-molecule design algorithm is presented that can explore the space of ligands compatible with binding to a target protein using fast combinatorial search methods. The inverse design method was applied to design inhibitors of HIV-1 protease that should be less likely to induce resistance mutations because they fit inside a consensus substrate envelope. Fifteen designed inhibitors were chemically synthesized, and four of the tightest binding compounds to the wild-type protease exhibited broad specificity against a panel of drug resistance mutant proteases in experimental tests. Inverse protein design methods and charge optimization were also applied to improve the binding affinity of a substrate peptide for an inactivated mutant of HIV-1 protease, in an effort to learn more about the thermodynamics and mechanisms of peptide binding. A single mutant peptide calculated to have improved binding electrostatics exhibited greater than 10-fold improved affinity experimentally.(cont.) The second half of this thesis presents an accurate method for evaluating the electrostatic component of solvation and binding in molecular systems, based on curved boundary-element method solutions of the linearized Poisson-Boltzmann equation. Using the presented FFTSVD matrix compression algorithm and other techniques, a full linearized Poisson-Boltzmann equation solver is described that is capable of solving multi-region problems in molecular continuum electrostatics to high precision.Michael Darren Altman.Ph.D