Use of Machine Learning for Automated Convergence of Numerical Iterative Schemes

Convergence of a numerical solution scheme occurs when a sequence of increasingly refined iterative solutions approaches a value consistent with the modeled phenomenon. Approximations using iterative schemes need to satisfy convergence criteria, such as reaching a specific error tolerance or number of iterations. The schemes often bypass the criteria or prematurely converge because of oscillations that may be inherent to the solution. Using a Support Vector Machines (SVM) machine learning approach, an algorithm is designed to use the source data to train a model to predict convergence in the solution process and stop unnecessary iterations. The discretization of the Navier Stokes (NS) equations for a transient local hemodynamics case requires determining a pressure correction term from a Poisson-like equation at every time-step. The pressure correction solution must fully converge to avoid introducing a mass imbalance. Considering time, frequency, and time-frequency domain features of its residual’s behavior, the algorithm trains an SVM model to predict the convergence of the Poisson equation iterative solver so that the time-marching process can move forward efficiently and effectively. The fluid flow model integrates peripheral circulation using a lumped-parameter model (LPM) to capture the field pressures and flows across various circulatory compartments. Machine learning opens the doors to an intelligent approach for iterative solutions by replacing prescribed criteria with an algorithm that uses the data set itself to predict convergence

Nonlinear Stochastic Dynamic Systems Approach for Personalized Prognostics of Cardiorespiratory Disorders

This research investigates an approach rooted in nonlinear stochastic dynamic systems principles for personalized prognostics of cardiorespiratory disorders in the emerging point-of-care (POC) treatment contexts. Such an approach necessitates new methods for (a) quantitative and personalized modeling of underlying cardiovascular system dynamics to serve as a virtual instrument to derive surrogate (hemodynamic) signals, (b) high-specificity diagnostics to identify and localize disorders, (c) real-time prediction to provide forecasts of impending disorder episodes, and (d) personalized prognosis of the short-term variations of the risk, necessary for effective treatment decisions, based on estimating the distribution of the times remaining till the onset of an anomaly episode. The specific contributions of the dissertation work are as follows: 1. Quantitative modeling for real-time synthesis of hemodynamic signals. Features extracted from ECG signals were used to construct atrioventricular excitation inputs to a nonlinear deterministic lumped parameter model of cardiovascular system dynamics. The model-derived hemodynamic signals, personalized to an individual's physiological and anatomical conditions, would lead to cost-effective virtual medical instruments necessary for personalized POC prognostics. 2. Random graph representation of the complex cardiac dynamics for disorder diagnostics. The quantifiers of a random walk on a network reconstructed from vectorcardiogram (VCG) were investigated for the detection and localization of cardiovascular disorders. Extensive tests with signals from PTB database of PhysioNet databank suggest that locations of myocardial infarction can be determined accurately (sensitivity of ~88% and specificity of ~92%) from tracking certain consistently estimated invariants of this random walk representation. 3. Nonparametric prediction modeling of disorder episodes. A Dirichlet process based mixture Gaussian process was utilized to track and forecast the evolution of the complex nonlinear and nonstationary cardiorespiratory dynamics underlying of the measured signal features and health states. Extensive sleep tests suggest that the method can predict an impending sleep apnea episode to accuracies (R^2) of 83% and 77% for 1 step and 3 step-ahead predictions, respectively.4. Color-coded random graph representation of the state space for personalized prognostic modeling. The prognostic model used the stochastic evolution of the transition pathways from a normal state to an anomalous state in the color-coded state space network to estimate the distribution of the remaining useful life. The prognostic model was validated using the data from ECG Apnea Database (Physionet.org). The model can predict the estimated time till a disorder (apnea episode) onset to within 15% of the observed times 1-45 min ahead of their inception.Industrial Engineering & Managemen

Physiology-based Mathematical Models for the Intensive Care Unit: Application to Mechanical Ventilation

This work takes us a step closer to realizing personalized medicine, complementing empirical and heuristic way in which clinicians typically work. This thesis presents mechanistic models of physiology. These models, given continuous signals from a patient, can be fine-tuned via parameter estimation methods so that the model's outputs match the patient's. We thus obtain a virtual patient mimicking the patient at hand. Therapeutic scenarios can then be applied and optimal diagnosis and therapy can thus be attained. As such, personalized medicine can then be achieved without resorting to costly genetics. In particular we have developed a novel comprehensive mathematical model of the cardiopulmonary system that includes cardiovascular circulation, respiratory mechanics, tissue and alveolar gas exchange, as well as short-term neural control. Validity of the model was proven by the excellent agreement with real patient data, under normo-physiological as well as hypercapnic and hypoxic conditions, taken from literature. As a concrete example, a submodel of the lung mechanics was fine-tuned using real patient data and personalized respiratory parameters (resistance, R_rs, and compliance, C_rs) were estimated continually. This allows us to compute the patient's effort (Work of Breathing), continuously and more importantly noninvasively. Finally, the use of Bayesian estimation techniques, which allow incorporation of population studies and prior information about model's parameters, was proposed in the contest of patient-specific physiological models. A Bayesian Maximum a Posteriori Probability (MAP) estimator was implemented and applied to a case-study of respiratory mechanics. Its superiority against the classical Least Squares method was proven in data-poor conditions using both simulated and real animal data. This thesis can serve as a platform for a plethora of applications for cardiopulmonary personalized medicine

Modulation of the oscillatory mechanics of lung tissue and the oxidative stress response induced by arginase inhibition in a chronic allergic inflammation model

Abstract\ud \ud \ud \ud Background\ud The importance of the lung parenchyma in the pathophysiology of asthma has previously been demonstrated. Considering that nitric oxide synthases (NOS) and arginases compete for the same substrate, it is worthwhile to elucidate the effects of complex NOS-arginase dysfunction in the pathophysiology of asthma, particularly, related to distal lung tissue. We evaluated the effects of arginase and iNOS inhibition on distal lung mechanics and oxidative stress pathway activation in a model of chronic pulmonary allergic inflammation in guinea pigs.\ud \ud \ud \ud Methods\ud Guinea pigs were exposed to repeated ovalbumin inhalations (twice a week for 4 weeks). The animals received 1400 W (an iNOS-specific inhibitor) for 4 days beginning at the last inhalation. Afterwards, the animals were anesthetized and exsanguinated; then, a slice of the distal lung was evaluated by oscillatory mechanics, and an arginase inhibitor (nor-NOHA) or vehicle was infused in a Krebs solution bath. Tissue resistance (Rt) and elastance (Et) were assessed before and after ovalbumin challenge (0.1%), and lung strips were submitted to histopathological studies.\ud \ud \ud \ud Results\ud Ovalbumin-exposed animals presented an increase in the maximal Rt and Et responses after antigen challenge (p<0.001), in the number of iNOS positive cells (p<0.001) and in the expression of arginase 2, 8-isoprostane and NF-kB (p<0.001) in distal lung tissue. The 1400 W administration reduced all these responses (p<0.001) in alveolar septa. Ovalbumin-exposed animals that received nor-NOHA had a reduction of Rt, Et after antigen challenge, iNOS positive cells and 8-isoprostane and NF-kB (p<0.001) in lung tissue. The activity of arginase 2 was reduced only in the groups treated with nor-NOHA (p <0.05). There was a reduction of 8-isoprostane expression in OVA-NOR-W compared to OVA-NOR (p<0.001).\ud \ud \ud \ud Conclusions\ud In this experimental model, increased arginase content and iNOS-positive cells were associated with the constriction of distal lung parenchyma. This functional alteration may be due to a high expression of 8-isoprostane, which had a procontractile effect. The mechanism involved in this response is likely related to the modulation of NF-kB expression, which contributed to the activation of the arginase and iNOS pathways. The association of both inhibitors potentiated the reduction of 8-isoprostane expression in this animal model.FAPESP and LIM20HCFMUSP.FAPESP and LIM-20-HC-FMUSP