Computational modeling in bioengineering brings mathematical equations to life through code. By implementing physiological models and analyzing their dynamics, we can simulate complex biological systems and gain insights into their behavior.
Interpreting simulation results allows us to compare models with real-world data and generate new hypotheses. These models have practical applications in predicting outcomes, optimizing interventions, and guiding experimental design, bridging the gap between theory and practice.
Computational Modeling and Simulation
Implementation of physiological models
- Gain familiarity with programming languages and tools commonly used for physiological modeling such as MATLAB, Python, R, Simulink, and OpenModelica
- Learn to translate mathematical equations including ordinary differential equations (ODEs), partial differential equations (PDEs), and algebraic equations into code
- Understand numerical methods for solving equations like Euler's method, Runge-Kutta methods, and finite difference methods
- Implement model components and interactions including compartmental models, feedback loops, and time delays
- Verify and validate the implemented model by comparing with analytical solutions (if available), checking for mass balance and unit consistency, and testing with known input-output relationships
Analysis of model dynamics
- Understand the concepts of dynamic systems analysis such as stability, steady states, and transient response
- Perform sensitivity analysis using local sensitivity analysis (partial derivatives of outputs with respect to parameters, sensitivity coefficients) and global sensitivity analysis (Monte Carlo simulations, Sobol indices)
- Identify critical parameters and their impact on model behavior through parameter estimation and uncertainty quantification
- Explore the effects of initial conditions on model dynamics considering basin of attraction, bistability, and multistability
- Analyze the robustness and adaptability of the model in terms of homeostasis and allostasis
Interpretation and Application of Simulation Results
Interpretation of simulation results
- Compare simulation results with experimental observations in terms of qualitative agreement and quantitative fit
- Identify discrepancies and their potential sources such as model assumptions and simplifications, measurement errors and variability, and unmodeled factors and interactions
- Use physiological knowledge to explain the observed behavior considering mechanisms of regulation and control, adaptive responses to perturbations, and pathological conditions and their consequences
- Generate testable hypotheses based on simulation results by predicting the effects of interventions or perturbations, proposing new experiments to validate or refute the hypotheses, and identifying key variables or processes to be measured or manipulated
Applications of physiological modeling
- Use models for prediction and extrapolation to simulate scenarios beyond the range of available data, predict long-term outcomes or rare events, and estimate unmeasurable variables or parameters
- Optimize interventions using model-based approaches by defining objective functions and constraints, using optimization algorithms (gradient-based, evolutionary), and determining optimal timing, dosage, or combination of interventions
- Guide experimental design using model simulations to identify the most informative experiments, determine the required sample size and measurement frequency, and prioritize experiments based on their expected impact on model refinement
- Iterate between modeling and experimentation by using experimental data to calibrate and validate models, using model predictions to guide further experiments, and refining models based on new experimental insights