Title: Recover All Coefficients in Second-order Hyperbolic Equations from Finite Sets of Boundary Measurements
Abstract: In this talk we consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on an open bounded domain with smooth enough boundary. We show that by appropriately selecting finite pairs of initial conditions as well as a boundary condition we can uniquely and stably recover all those coefficients from the corresponding boundary measurements of their solutions. The proofs are based on sharp Carleman estimate, continuous observability inequality and regularity theory for general second-order hyperbolic equations.

Title: Tracing and Forecasting Metabolic Indices of Cancer Patients Using Patient-Specific Deep Learning Models
Abstract: With the advancements in medical research ad practice, more and more cancer patients can live a long time after their cancer treatments, making the quality of life and toxicity management during and post-treatments the primary focus of healthcare providers and cancer patients. How to detect early health anomalies and predict potential adverse effects from some measurable biomarkers or signals for an individual cancer patient is of great importance in cancer patient care. Developing the ability to track a patient’s health status and to monitor the evolution of the specific disease intelligently would provide an enormous benefit to both the patient and the healthcare provider, enabling faster responses to deal with adverse effects and more precise and effective treatments and interventions. With the longitudinally collected time-series data of the patient at multiple time points before, during and after cancer treatments, it is becoming increasingly plausible to have an intelligent tools or device for continuous monitoring, tracking, and forecasting of cancer patients’ health status based on statistical, causal, and mechanistic modeling of patient phenotypes and various biomarkers in the time series data. We develop a patient-specific dynamical system model from the time series data of the cancer patient’s metabolic panel taken during the period of cancer treatment and recovery. The model consists of a pair of stacked long short-term memory (LSTM) recurrent neural networks and a fully connected neural network in each unit. It is intended to be used by physicians to trace back and look forward at the patient’s metabolic indices, to identify potential adverse events, and to make short-term predictions. Once a master model is built, the patient-specific models can be calibrated through transfer learning.

Title: Evaluating impacts of physiological variability on human equivalent doses using PBPK models
Abstract: Evaluating impacts of physiological variability on human equivalent doses using PBPK models CM Schacht1, AE Meade2,3, AS Bernstein3,4, B Prasad4, PM Schlosser4, HT Tran1, DF Kapraun4 1 Center for Research in Scientific Computation, North Carolina State University, Raleigh, N.C. 2 Center for Computational Toxicology and Exposure, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, N.C. 3 Oak Ridge Institute for Science and Education, Oak Ridge, T.N. 4 Center for Public Health and Environmental Assessment, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, N.C. Physiologically based pharmacokinetic (PBPK) models, which are typically expressed as systems of ordinary differential equations, are regularly used to inform human health risk assessments of chemicals. By performing simulations with a PBPK model, one can estimate human exposure levels that result in internal doses equal to those predicted for laboratory animals exposed to substances according to specific experimental dosing regimens. For chemical risk assessment, doses associated with adverse health outcomes are typically considered. Using scalar parameter values representing an “average” adult human, one can apply a PBPK model to estimate a scalar “human equivalent dose” (HED), which refers to the human concentration (for inhalation exposure) or dose (for oral exposure) of a substance that is expected to induce the same magnitude of toxic effect for a human as that observed for laboratory animals exposed to a known concentration or dose. However, such scalar values do not address variability among humans or uncertainty in parameter values. The World Health Organization International Programme on Chemical Safety (IPCS) has proposed a chemical hazard characterization approach, APROBA, that seeks to incorporate these and other elements of uncertainty to generate probabilistic reference values for chemicals. A key assumption in the APROBA approach is that various underlying distributions, including distributions of HEDs, are lognormal. We sought to evaluate this assumption by performing simulations using published PBPK models for dichloromethane and chloroform. We investigated how the shapes of HED distributions were impacted when we made different assumptions about the distributions of PBPK model parameters. To account for pharmacokinetic (PK) variability in humans, we used Monte Carlo methods to randomly draw sets of values for the PBPK model parameters based on distributions that describe uncertainty and human variability. We then used reverse dosimetry to obtain samples of HEDs. Using the Royston normality test, we found that while some HED distributions were lognormal, this depended on the distributions chosen to represent parameter variability as well as the applied doses. For higher doses (which generally coincide with higher internal dose metrics), HED distributions were less likely to be lognormal. Also, while lognormal parameter distributions produced mainly lognormal HED distributions, uniform parameter distributions produced dramatically less lognormal results. In the future, our conclusions about HED distributions and the impact of parameter distributions may be generalized by investigating other PBPK models to better characterize uncertainty in reverse dosimetry calculations.