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Zhang BS, Chemical Engineering and Biomedical Engineering, Carnegie Mellon University, 2012 MODEL-BASED DECISION SUPPORT FOR SEPSIS ENDOTYPES by Li Ang Zhang BS, Chemical Engineering and Biomedical Engineering, Carnegie Mellon University, 2012 Submitted to the Graduate Faculty of the Swanson School of Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2017 UNIVERSITY OF PITTSBURGH SWANSON SCHOOL OF ENGINEERING This dissertation was presented by Li Ang Zhang It was defended on August 25th 2017 and approved by Robert S. Parker Ph.D., Professor, Department of Chemical and Petroleum Engineering Ipsita Banerjee, Ph.D., Associate Professor, Department of Chemical and Petroleum Engineering Gilles Clermont, M.D., Professor, Department of Critical Care Medicine David Swigon, Ph.D., Associate Professor, Department of Mathematics Dissertation Director: Robert S. Parker Ph.D., Professor, Department of Chemical and Petroleum Engineering ii Copyright c by Li Ang Zhang 2017 iii MODEL-BASED DECISION SUPPORT FOR SEPSIS ENDOTYPES Li Ang Zhang, PhD University of Pittsburgh, 2017 Sepsis is a high mortality syndrome characterized by organ dysfunction due to a severe and dysregulated acute inflammatory response to infection. Research into therapies for this syn- drome has historically ended in failure, which has largely been attributed to the elevated levels of subject heterogeneity. What may have been previously attributed to variability in sepsis may be due to mechanistic differences between patients. Endotypes are distinct sub- types of disease, where underlying causes such as mechanistic or pathway related differences manifest into phenotypes of disease. The lack of mechanistic understanding of immune mediator dynamics and the responses they trigger necessitates a mathematical modeling approach to analyze its complexities. A transfer function model is proposed to describe and cluster the dynamics of key inflamma- tory mediators. Five sepsis endotypes were discovered and revealed motifs of overwhelming inflammation, various levels of immunosuppression, sustained inflammation, and immunod- eficiency. An accurate clinical tool was proposed to classify subjects into endotypes using six-hour trajectories of clinical data. A physiological ordinary differential equation model of sepsis is proposed that charac- terizes the interactions of inflammatory signaling molecules, neutrophils, and macrophages across the bone, blood, and tissue compartments of the body. This model used to gener- ate individual subject fits against human sepsis data. Population-level parameter analysis implicated macrophage cell death and cytokine half- dynamics in endotype-level differences. Several proof-of-concept statistical models were introduced to demonstrate that it is possible to estimate the pre-hospital time of sepsis subjects and to quantify their sepsis- iv induced systemic tissue damage. A nearest-neighbor-based method was verified against animal and human data and revealed that identifying infection time-zero of sepsis patients can be quickly estimated with high accuracy using commonly measured clinical features. A logistic regression ensemble model demonstrated revealed early organ dysfunction were significant contributors to systemic damage and mortality. Knowledge of time-zero and systemic damage levels, in combination with an endotype classifier, provides clinicians with a clear depiction of where a subject is located on their sepsis trajectory. Such a decision support system enables therapy timing, early organ support, and targeted therapies to guide personalized treatment and shift patients towards better outcomes in sepsis. Keywords: mathematical modeling, sepsis, cytokines, ordinary differential equations, ma- chine learning, statistical analysis. v TABLE OF CONTENTS PREFACE ......................................... xv 1.0 INTRODUCTION ................................. 1 1.1 Background and Significance .......................... 1 1.2 Problems with Current Approaches in Sepsis Therapy ............ 4 1.3 Decision Support Systems ............................ 6 1.4 Dissertation Overview .............................. 6 2.0 HIERARCHICAL CLUSTERING APPROACH TO IDENTIFY SEP- SIS ENDOPHENOTYPES ............................ 9 2.1 Methods ...................................... 11 2.1.1 Heatmap ................................. 14 2.1.2 Statistical Analysis ........................... 15 2.2 Results ...................................... 15 2.2.1 High-Risk Endophenotypes ....................... 20 2.2.2 Low-Risk Endophenotypes ....................... 21 2.2.3 Similarity between Endophenotype .................. 22 2.3 Discussion ..................................... 23 2.3.1 Study Limitations ............................ 26 2.3.2 Application into Temporal qSOFA Trajectories ............ 26 2.3.3 Summary ................................ 28 3.0 MIXTURE MODELING APPROACH TO IDENTIFY SEPSIS EN- DOTYPES ...................................... 29 3.1 Methods ...................................... 32 vi 3.1.1 Systems Analysis and Mixture Modeling ............... 34 3.2 Results ...................................... 38 3.2.1 Statistical Analysis of Endotypes ................... 42 3.3 Discussion ..................................... 43 3.3.1 Study Limitations and Potential Improvements ........... 47 3.3.2 Bedside Endotype Classification Tool ................. 50 3.3.3 Clinical Implications .......................... 51 3.3.4 Summary ................................ 52 4.0 MECHANISTIC DIFFERENCES BETWEEN ENDOTYPES ..... 54 4.1 Methods ...................................... 55 4.1.1 Model Formulation and Simulation .................. 56 4.1.1.1 Initiation of Inflammation and the Cytokine Storm ..... 58 4.1.1.2 Cytokine Diffusion and their Roles .............. 59 4.1.1.3 Neutrophil Dynamics ..................... 61 4.1.1.4 Pathogen Dynamics ...................... 65 4.1.1.5 Macrophage Dynamics ..................... 65 4.1.2 Model Post-hoc Analysis ........................ 67 4.2 Results ...................................... 69 4.3 Discussion ..................................... 75 4.3.1 Study Limitations ............................ 80 4.4 Summary ..................................... 80 5.0 IDENTIFICATION OF TRUE SEPSIS TIME-ZERO AND QUANTI- FYING SEPSIS-INDUCED DAMAGE .................... 82 5.1 Pre-hospital Time Identification ......................... 82 5.1.1 Methods ................................. 83 5.1.1.1 One-Nearest-Neighbor ..................... 84 5.1.1.2 In Silico Experiments and Validations ............ 88 5.1.2 Results .................................. 89 5.1.2.1 Feasibility Experiments .................... 91 5.1.2.2 Validation on Porcine Data .................. 92 vii 5.1.3 Discussion ................................ 95 5.1.3.1 Study Limitations ....................... 96 5.1.4 Translation into GLUE Grant Human Trauma Subjects ....... 97 5.1.5 Summary ................................ 99 5.2 Systemic Damage Models ............................ 99 5.2.1 Methods ................................. 100 5.2.2 Results .................................. 103 5.2.2.1 Damage Trajectories ...................... 103 5.2.3 Discussion ................................ 108 5.2.4 Summary ................................ 110 6.0 RELEVANT MODELING TOOLS ....................... 111 6.1 Boolean-LP, a Network Pathway Optimizer .................. 111 6.1.1 MILP Formulation of Network Optimizer Problem .......... 113 6.1.2 Detailed Formulation Example ..................... 115 6.1.3 Applications in Age-related Immune Pathways ............ 116 6.2 APT-MCMC, a C++/Python implementation of Markov Chain Monte Carlo for Parameter Identification ........................... 116 6.2.1 Methods ................................. 123 6.2.1.1 APT-MCMC Package ..................... 123 6.2.1.2 APT-MCMC Performance Evaluation ............ 127 6.2.2 Results .................................. 133 6.2.2.1 Benchmarks ........................... 133 6.2.2.2 Hyperparameters ........................ 134 6.2.2.3 Van de Vusse Reaction Scheme ................ 139 6.2.2.4 Bioreactor ............................ 142 6.2.2.5 Limitations ........................... 142 6.2.3 Summary ................................ 143 7.0 SUMMARY AND FUTURE WORK ..................... 144 7.1 Contributions ................................... 145 7.1.1 Endotype Identification and Prediction in the Clinic ......... 145 viii 7.1.2 Mechanistic Ordinary Differential Equation Model of Sepsis ..... 146 7.1.3 Quantifying Pre-hospital Time and Systemic Damage ........ 146 7.1.4 Efficient MCMC Sampling Software for Parameter-Fitting ..... 147 7.2 Future Work ................................... 148 7.2.1 Predicting Organ Failure ........................ 148 7.2.2 Early Endotype Classifier ....................... 148 7.2.3 Improving Neutrophil Dynamics with Damage ............ 149 7.2.4 Estimator of Pre-hospital Time .................... 150 7.2.5 Optimization of Therapy and Damage ................ 151 7.2.6 Updates to APT-MCMC ........................ 152 7.3 Improving Sepsis Clinical Outcomes with Mathematical Models ....... 152 APPENDIX A. DETAILED RESULTS FOR NEAREST-NEIGHBOR PRE- HOSPITAL TIME ESTIMATION TOOL .................. 154 APPENDIX B. DETAILED BENCHMARK FUNCTIONS USED TO VAL- IDATE APT-MCMC ............................... 158 B.0.1 Ackley .................................. 158 B.0.2 Adjiman ................................. 160 B.0.3 Alpine .................................. 161 B.0.4 Bard ................................... 162 B.0.5 Beale ..................................
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