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Table of contents
I Introduction
1 Preamble
1.1 Context: Safety pharmacology
1.2 Problematic and mathematical aspects
1.2.1 Classification problem
1.2.2 Challenges
1.3 Contributions
1.4 Organisation of the manuscript
2 Cardiac Safety Pharmacology
2.1 Introduction
2.2 Cardiac cell
2.2.1 Sarcolemma
2.2.2 Electrical activity
2.2.2.1 Electro-chemical equilibrium
2.2.2.2 Stimulation and cardiac action potential
2.2.2.3 Propagation
2.2.3 hIPSC-CM
2.3 In vitro electrophysiological devices
2.3.1 Patch-Clamp techniques
2.3.1.1 Overview of Patch-Clamp techniques
2.3.1.2 Automated Patch-Clamp
2.3.2 Microelectrode Arrays
2.3.2.1 Devices
2.3.2.2 Extensions
2.4 Conclusion
3 Mathematical modelling and simulations
3.1 Introduction
3.2 Action Potential simulation
3.2.1 Different AP models
3.2.2 Drug modelling
3.3 Field Potential simulation
3.3.1 Finite element mesh
3.3.2 Bidomain model
3.3.2.1 Boundary conditions
3.3.2.2 Source term: Iapp
3.3.3 Electrode model
3.3.4 Heterogeneity
3.3.5 Example of applications
3.3.5.1 Field Potential simulation at control case
3.3.5.2 Example of EAD simulation
3.4 Conclusion
4 Summary
II Methodology
5 Double Greedy Dimension Reduction method
5.1 Introduction
5.1.1 Notations and assumptions
5.2 Method
5.2.1 Classification score in the reduced space
5.2.1.1 Relation to the total variation
5.2.1.2 Relation to the Hellinger distance
5.2.1.3 Relation to the symmetrised Kullback-Leibler divergence
5.2.1.4 Some words on the semi-supervised classification
5.2.2 Optimisation of the classification success rate
5.2.2.1 Computation of (AS)
5.2.2.2 DGDR algorithm
5.2.3 Principle of analysis
5.3 Computational studies
5.3.1 Comparison with feature selection
5.3.2 Comparison with PCA
5.3.3 Comparison with metric learning techniques
5.3.4 A high-dimensional low sample size example
5.3.5 Application to classification problems
5.3.5.1 LSVT voice rehabilitation
5.3.5.2 Wisconsin breast cancer
5.4 Conclusion
5.5 Appendix
6 A method to enrich experimental datasets by means of numerical simulations in view of classification tasks
6.1 Introduction
6.2 Method
6.2.1 Context and notations
6.2.2 Augmented set enrichment based on the Hausdorff distance: ASE-HD
6.2.2.1 Analysis of the ASE-HD algorithm
6.2.3 Reducing noise oversensitivity and bias induced errors: pruning
6.2.4 On realistic scenarios
6.2.4.1 Biased database
6.2.4.2 The Validation set partially covers the set of possible outcomes
6.3 Discretisation of the method
6.3.1 Density estimation in high-dimension
6.3.2 Computing the Hausdorff distance of sets
6.3.3 Summary of the method
6.4 Numerical experiments
6.4.1 Two-dimensional cases
6.4.1.1 Influence of the KNN parameter
6.4.2 A model in electrophysiology of cells
6.4.2.1 Biased data
6.4.2.2 Dictionary entry computation
6.4.2.3 Datasets preprocessing
6.4.2.4 Computational results
6.5 Conclusion
6.6 Appendix
6.6.1 MV: scores in the incomplete validation set scenario
7 Conclusions
III Patch-clamp studies
8 Introduction
9 Channel activity estimation
9.1 Introduction
9.2 Methods
9.2.1 Stochastic AP Models at Baseline and under AS
9.2.1.1 Stochastic Human Ventricular ORd Model
9.2.1.2 Adrenergic Signaling model
9.2.2 Synthetic Data
9.2.3 State-Space Formulation and Augmented States
9.2.3.1 State-Space Formulation
9.2.3.2 Augmented State-Space
9.2.4 Individual and Combined DGDR- and UKF-based Methods
9.2.4.1 DGDR and Dictionary entry computations
9.2.4.2 UKF
9.2.4.3 Combined UKF-DGDR
9.2.5 Performance Evaluation
9.2.5.1 AP estimation
9.2.5.2 State and parameter estimation
9.3 Results
9.3.1 Implementation of UKF method
9.3.2 Combined DGDR and UKF Methods: Initialisation Effects
9.3.3 Combined DGDR and UKF Methods: Updating Effects
9.3.4 Performance Comparison
9.3.5 Replication of AP traces and Biomarkers at Baseline
9.3.6 Estimation of Phosphorylation Factors, AP traces and Biomarkers under AS
9.4 Discussion
9.4.1 DGDR Method
9.4.2 UKF Method
9.4.3 Combined DGDR-UKF Method by Initialisation and Updating
9.4.4 Estimation of Ionic Current Conductances at Baseline
9.4.5 Estimation of Phosphorylation Levels of Cellular Substrates under AS Conditions
9.4.6 Characterisation of Spatio-temporal AP Variability from Parameter Estimates
9.4.7 Limitations and Future Studies
9.5 Conclusion
10 Automated Patch-Clamp signal classification
10.1 Introduction
10.2 Material & Method
10.2.1 Experimental protocol
10.2.1.1 Compounds
10.2.1.2 Signal traces
10.2.2 Pre-processing
10.2.2.1 Dictionary entry computations
10.2.2.2 Sets generation
10.2.2.3 Data Rescaling
10.2.3 Post-processing
10.3 Results
10.3.1 First study case: Validation of the method
10.3.1.1 Detailed results:
10.3.2 General Application
10.3.2.1 Computational Time
10.3.2.2 Second and Third study cases
10.3.2.3 Fourth study case
10.3.2.4 Comparisons
10.4 Discussion
10.5 Conclusion
10.6 Appendix
10.6.0.1 Second study case
10.6.0.2 Third study case
11 Conclusions
IV Microelectrode arrays studies
12 Introduction
13 Oriented dimension reduction method to assess ion channel blocking and arrhythmia risk in hIPSC-CMs
13.1 Introduction
13.2 Material & Method
13.2.1 Experimental setup
13.2.1.1 Cell culture
13.2.1.2 Test compounds
13.2.1.3 MEA recordings
13.2.2 MEA computational model
13.2.2.1 Heterogeneity
13.2.2.2 Drug modelling
13.2.3 Dictionary entry computations
13.2.3.1 Electrophysiological biomarkers
13.2.3.2 Wavelet coefficients
13.2.4 Classification
13.2.4.1 Classification optimisation
13.2.4.2 Cross-validation
13.3 Results
13.3.1 TdP classification
13.3.1.1 Tests setup
13.3.1.2 Results of TdP classification
13.3.2 Channel classification
13.3.2.1 Tests setup
13.3.2.2 Binary classification
13.3.2.3 Ternary classification
13.4 Conclusion
13.4.1 Algorithm
13.4.2 TdP risk assessment
13.4.3 Ion-channel blockade
13.5 Appendix
13.5.1 Field Potential Biomarkers computation
13.5.2 Calcium Signals Biomarkers computation
14 Application of ASE-HD/DGDR coupling on cardiac field potentials
14.1 Introduction
14.1.1 Applications
14.2 Method
14.2.1 Coupling
14.2.2 Post-processing
14.3 First application: Ncardia dataset
14.3.1 Experimental setup
14.3.2 Pre-processing
14.3.2.1 Datasets construction
14.3.3 Results
14.4 Second application: NMI dataset
14.4.1 Experimental setup
14.4.2 Pre-processing
14.4.2.1 Dictionary entry computations
14.4.2.2 Datasets construction and data rescaling
14.4.3 Results
14.4.3.1 Drug vs Control
15 Conclusions
V Conclusion
