Mathematical problems in the intersection of operations research and healthcare operations have received increasing attention in recent years. This thesis is composed of four parts. In the first two parts, we study the surgical scheduling problem via discrete event patient flow simulation, optimization algorithm, and the optimal transport theory. In the last two parts, we briefly introduce atheoretical findings in optimal transport and a real-world application of data-driven decision-making in healthcare operations in response to the outbreak of COVID-19. In the first part, we report the development and deployment of BEDS (better elective day of surgery), a simple algorithm for smoothing across days the number of surgical patients requiring post-procedural beds. We introduce challenges faced by medical institutions for surgical schedule planning and a hospital-level patient flow simulation model, in which the impact of scheduling policies can be modeled without implementation. With the support of simulation results, BEDS was implemented in the Stanford Children's Hospital scheduling system in 2020.7. BEDS does not require significant reductions to surgeon autonomy or centralized scheduling, and is compatible with changes such as surgeon vacations, illness, or joining/leaving the hospital workforce; long-term changes in surgical volumes; and the opening or closing of new operating rooms and post-procedural beds. We present data from over the implementation of BEDS at an academic medical center and make the tool available as a dashboard in Tableau, a commercial software used by hundreds of hospitals in the United States. In the second part, we talk about supply-demand matching and scheduling via optimal transport. The optimal transport problem was formalized by the French mathematician Gaspard Monge in1781. We formulate the offline scheduling problem by a constrained optimization program with a demand density and a capacity bound in the format of optimal transport. We present the results for the optimal plan for the one-dimensionalL1cost function case. Next, we present the results of the optimal plan of the optimal scheduling problem via optimal transport in the presence of class-specific costs. In the third part, we present a result in empirical optimal transport projections with non-symmetric costs. Distributionally Robust Optimization (DRO) is a technique that generates estimators with enhanced generalization performance by introducing an adversary which quantifies the impact in out-of-sample variations in the training set. To provide an optimal approach for choosing the distributional uncertainty size in DRO, we contribute to the literature of DRO by considering more generally optimal transport costs, including the Bregman distance and the local Mahalanobis distance, and present an empirical experiment in portfolio optimization. Finally, we describe a personal protective equipment and hospital policy planning model we developed with Stanford Hospital in response to the outbreak of COVID-19. The model supports early decision-making and policy planning in the hospital to face the global shortage of personal protective equipment.

Vaccines remain one of the most effective medical treatments to prevent infectious diseases. In modern vaccine design, the co-delivery of a subunit vaccine's antigen and adjuvant is essential for inducing an optimal immune response and the subsequent adaptive immunity that is acquired. Small-molecule Toll-like receptor agonists (TLRa) have been increasingly recognized as promising adjuvants due to their targeted pathways, allowing for specific immune signatures and response. However, the pharmacokinetics/pharmacodynamics (PK/PD) profiles of small adjuvants are often mismatched from large protein antigens due to vast differences in molecular weight. Polymeric-based delivery platforms offer a highly tunable approach for antigen/ adjuvant co-delivery. By conjugating adjuvants to a polymeric nanoparticle, PK/PD can be favorably altered to improve retention and trafficking into lymphoid tissues, while also reducing systemic toxicity. Simultaneous release of vaccine components prolongs the cytokine response profile for higher antibody titers and isotype switching. Further, augmenting the co-delivery platform for sustained release elicits a more robust humoral immunity and improved antibody longevity and breadth. Sustained release, as compared to a traditional bolus delivery, more closely mimics a natural pathogen infection, and as a result of the extended antigen presentation and germinal center lifetime, enables an increased quality and magnitude of antibody response. In this work, we mixed biopolymers with nanoparticles to create dynamically cross-linked polymer nanoparticle (PNP) hydrogels. These PNP hydrogels are supramoleculary crosslinked networks that transiently form and break, simultaneously releasing protein antigens and small-molecule adjuvants in a slow-release manner. Although vaccines are commonly thought of as prophylactic in nature, they can also be utilized in a therapeutic setting. Cancer immunotherapy with vaccines is a promising strategy to overcome the immunosuppressive tumor microenviroment to stage a potent anti-tumor response. Potentiating the immune response with PNP hydrogel delivery increases the short-lived effector T cell populations compared to a bolus-delivered vaccine. Additionally, supplementing the vaccine with a novel immune checkpoint blockade therapy further enhances the increased T cell populations for a robust immune response. In this dissertation, I will discuss polymeric strategies for spatiotemporal control in vaccine design, enabling improved co-delivery of antigen and adjuvant. Extending the co-delivery into sustained delivery further improves humoral immunity for disease protection and cellular immunity for anti-cancer response.

Engineering of 3D human liver tissue is important to model authentic human liver for drug testing, disease modeling, and transplantable construct development that can be an alternative solution for human liver transplantation which is the only reliable option for end-stage liver diseases but suffers from a human donor shortage. Recently, hydrogel inverted colloidal crystal (ICC) scaffold-based liver systems were introduced as mature functional liver constructs with human fetal liver cells and human induced pluripotent stem cells (iPS)-derived hepatocytes. However, primary human adult hepatocytes (hHeps), the gold standard cell type for human liver tissue engineering, has not yet been introduced to the ICC system, thus limiting multiple applications requiring highly preserved liver-specific functions and highly authentic liver modeling such as phase II metabolism, hepatitis B and D infection, fatty liver modeling and IL-6 release modeling for finding new drug targets, novel candidate drug screening and novel strategies for transplanting engineered human liver tissues. In this thesis, I developed hHep-based authentic human liver systems using several types of advanced ICC scaffolds and characterized authentic human liver functions that were not explored in other ICC systems before. Using the developed systems, human liver diseases were modeled, and we explored a new drug target for combatting hepatitis B infection and screened novel drug candidates for fatty liver disease, hepatitis D infection, and cytokine storms, which can be promising future therapeutics. Also, the system was applied to transplantation studies, and it showed proof-of-concept potential to be a bridge or an alternative to current human liver transplantation

The term 'prion' is loaded with fear and negative connotation. The reason for this is because the first prions to be described, those of PrP in various species, were agents of death and disease unlike any known to mankind up to that point. The PrP prions captured the attention and fear of the general public and shaped our understanding of what prions are or could be for decades after. But prions can be more than just agents of disease, they can drive paradigm-shifting biology. If we go back to the original definition as coined by Stanley Prusiner himself, the only requirements to be a prion is to be proteinaceous and infectious. There are no thresholds of Q/N enrichments that need to be met or β- amyloid fibers formed in order to be considered a prion. Prions are highly stable protein conformations that can drive new biological phenotypes endowed with certain characteristics unique to prions. These phenotypes are usually dominant, disobey Mendel's law on inheritance, rely on protein chaperones for the faithful propagation across generations, and are encoded not in nucleic acid, but in the protein conformation itself. In fluctuating environments, switching between different growth strategies, such as those affecting cell size and proliferation, can be advantageous to an organism. Trade-offs arise, however. Mechanisms that aberrantly increase cell size or proliferation— such as mutations or chemicals that interfere with growth regulatory pathways—can also shorten lifespan. We report a natural example of how the interplay between growth and lifespan can be epigenetically controlled. We find that a highly conserved RNA-modifying enzyme, the pseudouridine synthase Pus4/TruB, can act as a prion, endowing yeast with greater proliferation rates at the cost of a shortened lifespan. Cells harboring the prion grow larger and exhibit altered protein synthesis. This epigenetic state, [BIG+] (better in growth), allows cells to heritably yet reversibly alter their translational program, leading to the differential synthesis of dozens of proteins, including many that regulate proliferation and aging. Our data reveal a new role for prion-based control of an RNA-modifying enzyme in driving heritable epigenetic states that transform cell growth and survival

Magnetic resonance imaging (MRI) is a powerful diagnostic tool for visualizing soft tissue anatomy, but physical limits on data acquisition speed result in uncomfortably long MRI exams. This is problematic for many patient populations, but especially for pediatric patients, who often require general anesthesia (GA) to reduce anxiety and body motion. Many attempts at accelerating data acquisition have been made to reduce or eliminate use of GA for pediatric MRI. For example, compressed sensing (CS) methods have been used to iteratively reconstruct rapidly acquired measurements into high-quality images by leveraging sparse priors. More recently, deep learning (DL) methods have been used to train deep neural network models to map the rapidly acquired measurements into even higher-quality images. While DL reconstruction approaches may potentially accelerate data acquisition beyond CS, these approaches have several issues which impede their clinical adoption. First, DL reconstructions require large quantities of high-quality ground truth data for supervised training, which can be costly and time-consuming to acquire. Second, memory requirements during network training limit the applicability of DL reconstruction to low-dimensional MRI data, such as static or dynamic 2-D imaging with limited spatiotemporal resolution. In this thesis, a series of projects demonstrating robust DL reconstruction techniques for acceleration of high-dimensional pediatric MRI will be presented. First, physics-based models are incorporated into deep CNN architectures to enforce consistency between intermediate network outputs and the rapidly acquired measurements in a novel method called DL-ESPIRiT. Physics-based modeling allows DL-ESPIRiT to be trained end-to-end in a supervised fashion with relatively little training data compared to non-physics-driven DL reconstruction. DL-ESPIRiT is applied and validated on 12X prospectively accelerated dynamic 2-D MRI scans acquired at Lucile Packard Children's Hospital. Finally, DL-ESPIRiT is extended to leverage subspace methods within the network to address GPU memory limitations during training. This method, known as deep learning-based subspace reconstruction (DL-Subspace), reconstructs a compressed representation of the MRI data instead of the data directly, thereby reducing the memory footprint during training and accelerating DL inference times. DL-Subspace is demonstrated to reconstruct 2-D dynamic MRI data with 4X higher memory efficiency and inference speed

Resource limitations and socioeconomic challenges pose obstacles to equitable healthcare access worldwide. Accurate diagnosis is an important early step in which technical innovation can help to bridge some gaps. Towards this goal, I worked on developing anomalous cell detection tools to enable broader access to health information for resource-constrained clinical settings. In this thesis, I explore portable tools for detecting malaria in blood samples and screening forensic swab samples. Quantifying the malaria-causing parasite Plasmodium falciparum relies on isolating the ring-stage infected red blood cells, which are challenging to differentiate from the majority of uninfected cells. I used magnetic levitation to perform label-free biophysical separation and detection of malaria-infected cells, by cumulatively leveraging density and magnetic susceptibility differences in the cells. Next, I built an accessible platform to process, image, and analyse whole blood patient samples in field settings, in a malaria-endemic region of Uganda. I combined cell lysis, suspension, and machine learning on cellphone images to develop an automated morphology-based classifier for blood samples. I also explored a different application for portable image-based screening, to address a sample processing backlog in sequencing forensic samples in the sexual assault justice workflow. I developed an automated algorithm for differentiating sperm from epithelial cells in sexual assault swab samples, using morphology features captured in cellphone imaging of microchips. Overall, this work demonstrates examples of anomalous cell detection technology built specifically for under-resourced settings. Such interdisciplinary techniques could help to overcome existing gaps in access to biological data, with the aims of supporting accurate diagnosis and surveillance of malaria, or screening of backlogged sexual assault samples

Mutations are the fundamental source of variation among organisms, and they can have deleterious, neutral, or beneficial effects on the overall fitness of an organism. Whether a mutation affects the organism it arises in, the offspring of that organism, or both depends on what type of cell it arises in. In many animals, mutations in germ cells are inherited by the offspring, whereas somatic cells are generally thought not to be inherited. Somatic mutations can cause cancer, aging, and general genome instability. However, plants and many basal animal taxa may lack embryonic germ-soma distinction. Colonial reef-building corals can grow to be meters across, live for hundreds to thousands of years while maintaining fertility, and almost never develop recognizable tumors. Whether they have embryonic germline segregation is controversial. All of this makes them a pivotal group in which to understand genome maintenance. Corals also create critical ecosystems that are threatened by many stressors, including ocean warming. Mutation research in corals thus has far-reaching implications for the study of genome integrity and cell lineage development, as well as for the capacity of these animals to adapt when faced with selective pressures. In this dissertation I characterize the rates and patterns of somatic, germ, and stem cell mutations in corals. I show that 26% of the post-embryonic mutations found in the parent soma are inherited by their sperm. I also compare the rates of different types of mutations in corals living under normal conditions to those living in former nuclear test sites. The results yield insight into genome maintenance dynamics and somatic mutation inheritance in a colonial organism with a position in the tree of life that suits it to be key in understanding the evolution of germline-soma distinction. It also points to how population diversity arises in these animals, key information when considering how they may adapt in the coming years

Thin-film lithium niobate has opened the doors to new opportunities in integrated acousto-optics. Low-loss, wavelength-scale waveguides enable devices of an unprecedented size and efficiency. In this thesis, I develop a general framework for treating acousto-optic waveguides and design tools for the piezoelectric transducers that drive them. This work culminates in two demonstrations: a collinear acousto-optic modulator in suspended lithium niobate with a record figure-of-merit, and an integrated acousto-optic deflector for on-chip beam-steering in lithium niobate-on-sapphire