Course in Modelling of Physiological Systems

To obtain the course certificate the student must be able:

Knowledge

• Characterize, analyze, and describe biological systems using fundamental laws of physics;
• Explain key mathematical and physical concepts — dynamical systems, stability analysis, oscillation theory, synchronization theory, control theory, statistics — to characterize the behavior of biological systems and argue when and where these concepts can be applied;
• Explain performance characteristics of fixed-step and adaptive numerical algorithms for solving differential equations (Runge–Kutta methods) and explain the principles and applications of techniques for time-frequency domain analysis (Fast Fourier Transform) of data;
• Explain the principles of data-driven and mechanism-based modeling, highlighting their core concepts, differences in application domains, and distinct purposes of use;
• Explain molecular principles and mechanisms of enzyme-catalysed chemical reactions and receptor–ligand binding in the context of pharmacokinetics, and explain their mathematical formulations;
• Explain biological principles of population dynamics, including population growth, immune responses, and  host-pathogen interactions. Explain different mathematical models, including the logistic model and its variants;
• Explain how physical principles are used to develop mathematical models of excitable cells and describe classical examples of such models. Explain mathematical concepts of phase portraits and bifurcations, and discuss how they can be used to characterize the neurocomputational properties of excitable cells.
• Explain biological and physical principles of cellular calcium signalling, including mechanisms of calcium homeostasis and calcium oscillations related to gap-junction regulated synchronization and vasomotion;
• Explain the central dogma of molecular biology including the processes of DNA replication, transcription, and translation. Explain mathematical models thereof using rate equations and extend the central dogma to modelling of the circadian rhythms;
• Explain the biological principles of insulin-glucose regulation, and explain mathematical models using differential equations to describe homeostasis, insulin secretion, hepatic glucose release, glucose utilization, and delay effects.
• Explain the physiological mechanisms of kidney autoregulation of blood flow, including myogenic response and tubuloglomerular feedback. Explain mathematical models, in the form of differential equations, and their use to simulate renal blood flow and glomerular filtration rate regulation.

Skills

• Integrate mathematical and physical concepts into biomedical problem-solving;
• Design an appropriate mathematical model (e.g., continuous/discrete, linear/nonlinear) based on system characteristics and biological hypothesis. Identify modeling assumptions and their implications;
• Implement the model in a computational environment. Validate the results by comparing to independent experiments and other models;
• Calibrate model parameters using experimental data and physiological assumptions. Perform sensitivity and stability analysis to assess how parameter and initial condition variations affect the model output, and evaluate the effects of uncertainties on the model's predictions;
• Assess different numerical algorithms and select the most suitable method for solving a given mathematical model, considering accuracy, stability, and computational efficiency;
• Optimize the model performance by refining assumptions, improving the algorithm, and addressing identified uncertainties;
• Validate the  model through its capacity to reproduce the characteristics of the considered dynamical phenomenon: the observed amplitudes, frequencies, and waveforms as well as the phase relationships between the different variables;
• Interpret simulation results in the framework of hypothesis testing, generating new insights, and deepening understanding of biological systems. 

Competences

• Critical Analysis & Problem-Solving: Assess biological problems critically, selecting and developing appropriate modeling and computational tools for their resolution;
• Interdisciplinary Integration: Apply knowledge from physics, mathematics, and biology to deepen the understanding of regulatory mechanisms in biological systems;
• Problem Definition & Study Design: Clearly define the problem, establish objectives for the modeling study, and formulate hypothesis to be tested;
• Data Collection & Preliminary Analysis: Collect relevant experimental, clinical, or literature data and perform preliminary analyses to define assumptions, parameters, and model structure;
• Model Simplification & Abstraction: Transform complex physiological systems into idealized models by focusing on essential features while eliminating extraneous details, ensuring a mathematically tractable representation;
• Mathematical Model Development: Construct appropriate mathematical models  ensuring they accurately reflect the biological system and can be effectively implemented computationally;
• Simulation Design & Optimization: Plan and conduct simulation studies which optimize resource efficiency while minimizing computational redundancy;
• Validation & Interpretation: Compare simulation results with experimental or real-world data, interpret findings objectively, and present them in a clear and meaningful context;
• Documentation & Communication: Thoroughly document the modeling process, including assumptions, methods, and results, and effectively communicate findings to both technical and non-technical audiences, emphasizing implications and limitations;
• Biological Inspiration for Innovation: Recognize how biological principles can inspire engineering solutions and drive technological advancements and how mathematics, physics and engineering can enhance the understanding of biological systems.

To obtain the grade 12, the student must be able to

Knowledge

• Characterize, analyze, and describe biological systems using fundamental laws of physics;
• Explain key mathematical and physical concepts — dynamical systems, stability analysis, oscillation theory, synchronization theory, control theory, statistics — to characterize the behavior of biological systems and argue when and where these concepts can be applied;
• Explain performance characteristics of fixed-step and adaptive numerical algorithms for solving differential equations (Runge–Kutta methods) and explain the principles and applications of techniques for time-frequency domain analysis (Fast Fourier Transform) of data;
• Explain the principles of data-driven and mechanism-based modeling, highlighting their core concepts, differences in application domains, and distinct purposes of use;
• Explain molecular principles and mechanisms of enzyme-catalysed chemical reactions and receptor–ligand binding in the context of pharmacokinetics, and explain their mathematical formulations;
• Explain biological principles of population dynamics, including population growth, immune responses, and  host-pathogen interactions. Explain different mathematical models, including the logistic model and its variants;
• Explain how physical principles are used to develop mathematical models of excitable cells and describe classical examples of such models. Explain mathematical concepts of phase portraits and bifurcations, and discuss how they can be used to characterize the neurocomputational properties of excitable cells.
• Explain biological and physical principles of cellular calcium signalling, including mechanisms of calcium homeostasis and calcium oscillations related to gap-junction regulated synchronization and vasomotion;
• Explain the central dogma of molecular biology including the processes of DNA replication, transcription, and translation. Explain mathematical models thereof using rate equations and extend the central dogma to modelling of the circadian rhythms;
• Explain the biological principles of insulin-glucose regulation, and explain mathematical models using differential equations to describe homeostasis, insulin secretion, hepatic glucose release, glucose utilization, and delay effects.
• Explain the physiological mechanisms of kidney autoregulation of blood flow, including myogenic response and tubuloglomerular feedback. Explain mathematical models, in the form of differential equations, and their use to simulate renal blood flow and glomerular filtration rate regulation.

Skills

• Integrate mathematical and physical concepts into biomedical problem-solving;
• Design an appropriate mathematical model (e.g., continuous/discrete, linear/nonlinear) based on system characteristics and biological hypothesis. Identify modeling assumptions and their implications;
• Implement the model in a computational environment. Validate the results by comparing to independent experiments and other models;
• Calibrate model parameters using experimental data and physiological assumptions. Perform sensitivity and stability analysis to assess how parameter and initial condition variations affect the model output, and evaluate the effects of uncertainties on the model's predictions;
• Assess different numerical algorithms and select the most suitable method for solving a given mathematical model, considering accuracy, stability, and computational efficiency;
• Optimize the model performance by refining assumptions, improving the algorithm, and addressing identified uncertainties;
• Validate the  model through its capacity to reproduce the characteristics of the considered dynamical phenomenon: the observed amplitudes, frequencies, and waveforms as well as the phase relationships between the different variables;
• Interpret simulation results in the framework of hypothesis testing, generating new insights, and deepening understanding of biological systems. 

Competences

• Critical Analysis & Problem-Solving: Assess biological problems critically, selecting and developing appropriate modeling and computational tools for their resolution;
• Interdisciplinary Integration: Apply knowledge from physics, mathematics, and biology to deepen the understanding of regulatory mechanisms in biological systems;
• Problem Definition & Study Design: Clearly define the problem, establish objectives for the modeling study, and formulate hypothesis to be tested;
• Data Collection & Preliminary Analysis: Collect relevant experimental, clinical, or literature data and perform preliminary analyses to define assumptions, parameters, and model structure;
• Model Simplification & Abstraction: Transform complex physiological systems into idealized models by focusing on essential features while eliminating extraneous details, ensuring a mathematically tractable representation;
• Mathematical Model Development: Construct appropriate mathematical models  ensuring they accurately reflect the biological system and can be effectively implemented computationally;
• Simulation Design & Optimization: Plan and conduct simulation studies which optimize resource efficiency while minimizing computational redundancy;
• Validation & Interpretation: Compare simulation results with experimental or real-world data, interpret findings objectively, and present them in a clear and meaningful context;
• Documentation & Communication: Thoroughly document the modeling process, including assumptions, methods, and results, and effectively communicate findings to both technical and non-technical audiences, emphasizing implications and limitations;
• Biological Inspiration for Innovation: Recognize how biological principles can inspire engineering solutions and drive technological advancements and how mathematics, physics and engineering can enhance the understanding of biological systems.