2018 Capstone Conference
Keynote: Healthcare Transformation Innovation Laboratory: Evaluation of Federally Qualified Health Centers Advanced Primary Care Practice DemonstrationNancy McMillan
There is broad support for transforming Payment and Service Delivery Models away from Fee For Service (FFS) and to Value-based Payments (VBP). Centers for Medicare and Medicaid Services Innovation (CMMI) Center has a primary role in testing various payment and service delivery models (PSDMs) that aim to achieve better care for patients, smarter spending and healthier communities. To date, the pilot tests run have been costly, risky, and inconclusive. In this work, we propose a simulation tool developed to improve decision-making before pilot implementation (decrease costs, reduce risk), support evaluation design by identifying key sources of uncertainty (yield more conclusive evaluations), and support program integrity studies (long term monitoring). Our simulation tool is in the early stages of development; we demonstrate itâ€™s value by comparing simulation results with a PSDM previously tested by CMMI, the Federally Qualified Health Centers (FQHC) Advanced Primary Care Practice (APCP) Demonstration.
Homeostasis of blood glucose is the central tenet of metabolic disease and its treatment. This nonlinear dynamics problem is an obvious application of mathematical modeling. In particular, the practical questions of pharmaceutical research and development has offered several opportunities to bring modeling to an enterprise that is only recently accepting quantitative approaches on an equal footing with empirical approaches. Mathematical modeling of metabolic disease will be discussed in the context of pharmaceutical development from target discovery to translation of animal models informing clinical design to drug registration PK/PD.
Maike Morrison, Emily Strong
The tail of the dispersal kernel of individual movement plays a critical role in the spatial spread of infectious disease, invasive species, and other spreading phenomena. However, most studies where the dispersal kernel has been estimated from observed natural systems have assumed homogeneous dispersal in space, even though non-uniform use of space (i.e., resource selection) has long been recognized as important in many systems. In our project, we explore the consequences of ignoring terrain heterogeneity when estimating parameters governing the tail of a dispersal kernel. We show that ignoring resource selection in general leads to estimates of dispersal kernels with heavier tails than the true kernels used for simulation. In addition, this often leads to predictions of the rate of spatial infectious disease spread that are much faster than the true spread through a population that is moving across patchy terrain.
Amy Carpenter, Allison Torsey
Sepsis is a serious health condition that is not well understood. It is defined as an overactive immune response that causes severe damage to healthy tissue, often resulting in death. Mathematical modeling has emerged as a useful tool to investigate key elements of the immune response and thus offers a useful method for studying sepsis. Here, a system of four ordinary differential equations is developed to simulate the dynamics of bacteria, the pro-inflammatory immune response, anti-inflammatory immune response, and tissue damage. The pro-inflammatory response is triggered by the presence of bacteria and leads to destruction of bacteria as well as damage to the tissue once the level of inflammation exceeds a certain threshold. The anti-inflammatory response works to temper the pro-inflammatory response, although it is not always capable of preventing sustained tissue damage. The model is used to assess the conditions under which health, aseptic (inflammation-driven) death, or septic (bacteria-driven) death is predicted in both the presence and absence of an induced E. Coli bacterial infection in rats. Model parameters are fit to experimental data from rat sepsis studies. The model is used to predict the survivability range for an infection while varying the initial amount, growth rate, or virulence of the bacteria in the system.
Modeling Physarum polycephalum Decision-Making: Examining the Current Reinforcement and Reaction-Diffusion-Advection ModelsYassine Dribki, Alanna Haslam
Physarum polycephalum, commonly known as slime mold, is a large single-celled, multi-nucleated protist. As it searches for and exploits food sources, slime moldâ€™s amoeboid movement and network-like structure exhibit intelligent behavior such as maze-solving and network optimization. To explore the mechanisms behind this brainless intelligence we explore two models. The Reaction-Diffusion-Advection model attempts to describe the rhythmic contractions, chemical oscillations, and pattern formation observed in the plasmodium of slime mold. The Current Reinforcement model attempts to replicate the network formation and optimization of slime mold. Together these micro- and macro-level models can describe the known behavior of slime mold and suggest the possible mechanisms and methods that propel its surprising intelligence.
In contrast to in vitro particle tracking experiments, wherein there are great controls on particle and environmental homogeneity, live cell (in vivo) tracking features tremendous diversity in particle movement. In this work, we have developed a suite of â€œfirst-passâ€? statistical tools to categorize disparate types of particle trajectories. The data we used for this project was generated in the the lab of Prof. Christine Payne, using fluorescence microscopy in HeLa (model human) cells. Some particle paths were easily distinguishable as free diffusion, stuck diffusion, or directed transport, while other trajectories were difficult to categorize. Several of the more complex paths indicated the potential for tracking error. The tools we developed for the categorization process include the correlation between consecutive increments and effective diffusivity from a maximum likelihood estimation. The standard deviation for the major and minor axis and the creation of a parameterized path to represent a fictional moving anchor employed principal components analysis. This anchor estimation allowed the computation of effective velocity and the average distance the particle deviated from the anchor. Based on these data measures, K-means clustering was utilized to distinguish between free diffusion, stuck diffusion, directed transport, and tracker error. This automated categorization process proved to be successful on data simulated using stochastic differential equations and provided interesting results on the live cell data.
Our work examines the effect of molecular motor binding reactions on intracellular transportation. Motor proteins (namely kinesin and dynein) carry cargo along microtubule at rates faster than diffusion would allow. However, molecular motors are known to have low processivity, thus spending a significant amount of time freely diffusing with their cargo. We therefore seek to model this system to connect aspects of this complex dynamic to its efficiency. This model is examined as a Partial Differential Equation, a probability density function, and a Monte Carlo simulation. Emphasis is placed on binding reactions needed to create active crosslinks between cargo and the microtubule. We have shown that when cargo have multiple motor binding sites, motors with low processivity optimize microtubule flux by increasing cargo binding while maintaining at least one active crosslink. Our work highlights the benefit of current molecular motor transport and presents an alternative process for engineering motors that could augment processes such as protein synthesis and modification, cell signaling, and cell repairing.
Estimating Gap Junction Properties of Electrically Coupled Neurons From Measurements Made in the SomaSusan Cheng
The stomatogastric ganglion (STG) is a neuronal circuit found in lobsters and crabs that generates simple rhythmic behaviors such as walking and breathing. While the circuit as a whole can be observed, the smaller scale structure is mostly unknown and unstudied. In particular, the location of gap junctions electrically coupling one neuron to another is difficult to determine. This location affects errors made in studying coupled versus uncoupled neurons and can affect nearby chemical synapses. We aim to use computational modeling to better understand how different properties of electrically coupled neurons affect voltage measurements made in the soma (cell body). We then determine rudimentary fits to biological data that give a rough first estimate of the location of the gap junction.
ChIP-exo is a laboratory protocol used to identify the location of protein binding sites on DNA, with applications to the study of cancer and immune function. However, few methods exist for assessing the reproducibility of ChIP-exo data between different replicates in the same experiment. We used Euclidean distance to produce a reproducibility score for each potential binding event, determining a relationship between reproducibility and the presence of sequence motifs, as well as exploring ways to classify replicated events according to their reproducibility.
Topology optimization is a numerical method to find the optimal distribution of a given amount of material that maximizes the performance of the resulting structure, which is subjected to boundary conditions that include external forces and heat loads. An effective approach to solve a topology optimization problem is the use of the level set method. In this method, the boundary of an n-dimensional structure is defined as the zero level set map of a (n+1)-dimensional surface. Benefits of the level set method include an easily adaptive topology, the ability to set parameters that change complexity of the resulting object, and speed of the code. Drawbacks include intermittent re-initialization of the level set function and ill-posed, steady state solutions. This work studies various implementations of the level set method and compare them to traditional density-based methods, which are widely used in topology optimization.
Due to the evolution of resistance, drug therapies often fail to treat ailments such as bacterial infections, cancer, and viral diseases, despite initial successes. Improvements in next generation sequencing technologies already allow us to pinpoint resistance conferring mutations. Since evolution is a stochastic process, however, each evolutionary trajectory, or sequence of advantageous mutations, occurs with a certain, currently unknown, probability. By predicting the likelihoods of each trajectory, we can design treatment plans to genetically steer populations away from a resistant phenotype. To this end, we have constructed a morbidostat, an automated continuous culture device, to monitor the evolution of resistance. Using fitness data gathered from the morbidostat, we will parameterize our numerical Agent Based Model (ABM) model and Fokker-Plank mathematic model to predict under what conditions certain trajectories occur. In light of these results, we will update treatment plans for morbidostat experiments and monitor the resulting evolutionary dynamics to verify our predictions.
Quantifying tumor growth and therapeutic response from bioluminescence imaging in patient-derived xenograftsJavier Urcuyo
Glioblastoma is an aggressive primary brain cancer that is notoriously difficult to treat, in part due to its diffuse infiltration of brain tissue and the limitations of the blood-brain barrier (BBB), which often prevents drugs from reaching the entire tumor. Specifically, rapid tumor proliferation leads to accelerated angiogenesis resulting in a â€˜leakyâ€™ BBB, which affects drug distribution. To address the differential impact of this BBB heterogeneity across patients, time series bioluminescence imaging (BLI) data was compiled from experiments treating murine orthotopic glioblastoma patient-derived xenografts (PDXs). The extent of BBB breakdown has been previously quantified for multiple PDX lines, allowing us to examine the heterogeneity in this feature among human patients. BLI data directly quantifies total tumor cell abundance, allowing us to observe how therapy affects tumor cell populations. After adjusting for lead time bias via a nonlinear mixed effects approach, we used the serial BLI data to obtain an overall growth rate for each PDX line across multiple subjects. These different growth kinetics were used to parametrize corresponding therapeutic models of the individual PDX lines. While further work is needed to verify our results across more PDX lines, they suggest that our existing characterization of tumor invasiveness may be able to aid in matching patients to the best therapy for their individual tumors.
Developing Mathematical Models to Investigate Pathways Responsible for Protein Aggregation in Alzheimer's DiseaseLindsay Duvernoy
Every 65 seconds someone is diagnosed with Alzheimerâ€™s Disease (AD). AD is the 6th leading cause of death in the United States, and it has become a national healthcare crisis. AD is a neurodegenerative disorder, which atrophies the cerebral cortex and subcortical regions of the brain. The Amyloid Hypothesis of AD focuses on extracellular amyloid beta 42 ( ) protein plaques. Based on the model by Puri et al. (2010), different rates of input signaling received by neurons can be quantified by their unique synaptic weights. In this work, we have recreated the Puri model, a 7th order state variable system, which illustrates inputs of crosstalk between neuronal components including the neuron, astrocytes, and microglia. Our hypothesis states through quantifying increased rates of input signals of , we illustrate through mathematical modeling how negatively impacts neuronal survival and highlight the synergistic effect of from neurons and astrocytes on neuronal death ( ). This research demonstrates that produced by astrocytes plays a larger role in than previously reported. Our results will lead to a greater awareness of the biological origins of AD.