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Register a new userA stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced angiogenesis
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In this paper, a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced angiogenesis, using patient data, is presented. The dynamics of colon cancer is given by a stochastic process that captures the inherent randomness in the system. The stochastic framework is based on the Fokker-Planck equation that represents the evolution of the probability density function corresponding to the stochastic process. An optimization problem is formulated that takes input individual patient data with randomness present, and is solved to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, sensitivity analysis of the optimal parameter set is performed to determine the parameters that need to be controlled, thus, providing information of the type of drugs that can be used for treatment.
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Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. in 2015 for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we head back to the stochastic model and calculate the probability that the T cells all get exhausted during the treatment. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.
Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these low-fidelity and high-fidelity models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. We seek to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to Monte Carlo and multilevel Monte Carlo estimators based only on three-dimensional simulations. We demonstrate significant reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities and healthy models show larger reductions than local quantities and diseased model, as the latter rely more heavily on the highest fidelity model evaluations. In all cases, our workflow coupling Dakotas MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.
Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with relatively small amounts of noise, the relationship between observation noise and uncertainty in the learned differential equation models remains unexplored. We demonstrate that for noisy data sets there exists great variation in both the structure of the learned differential equation models as well as the parameter values. We explore how to combine data sets to quantify uncertainty in the learned models, and at the same time draw mechanistic conclusions about the target differential equations. We generate noisy data using a stochastic agent-based model and combine equation learning methods with approximate Bayesian computation (ABC) to show that the correct differential equation model can be successfully learned from data, while a quantification of uncertainty is given by a posterior distribution in parameter space.
Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.
Due to the computational complexity of micro-swimmer models with fully resolved hydrodynamics, parameter estimation has been prohibitively expensive. Here, we describe a Bayesian uncertainty quantification framework that is highly parallelizable, making parameter estimation for complex forward models tractable. Using noisy in-silico data for swimmers, we demonstrate the methodologys robustness in estimating the fluid and elastic swimmer parameters. Our proposed methodology allows for analysis of real data and demonstrates potential for parameter estimation for various types of micro-swimmers. Better understanding the movement of elastic micro-structures in a viscous fluid could aid in developing artificial micro-swimmers for bio-medical applications as well as gain a fundamental understanding of the range of parameters that allow for certain motility patterns.
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