Bioengineering approach to physiological control systems: general topics of control system theory are recalled and applied to physiological systems. General topics - Analysis and simulation of dynamic systems and control systems. Open and closed loop system identification. Elements of monitoring and regulation of vital parameters. Physiological systems - General structure of the autonomic nervous systems, sympathetic and parasympathetic. Cardiovascular function and control, baroreceptive regulation, peripheral circulation, regulation of blood volumes, chemoceptive mechanism, metabolic regulation.

(IT – Approccio bioingegneristico ai sistemi fisiologici di controllo: vengono richiamati temi generali di teoria dei sistemi di controllo e applicati a sistemi fisiologici. Temi generali - Analisi e simulazione dei sistemi dinamici e dei sistemi di controllo. Identificazione di sistemi in anello aperto e chiuso. Cenni a monitoraggio e regolazione di parametri vitali. Sistemi fisiologici - Struttura generale del sistema nervoso autonomo, simpatico e parasimpatico. Funzione e controllo cardiovascolare, regolazione barocettiva, circolazione periferica, regolazione dei volumi ematici, meccanismi chemocettivi, regolazione metabolica). 

Students will gain knowledge and understanding of:

• the potentials and limits of modeling in physiological and biological systems;
• the relevance of automatic control in the physiological and clinical fields;
• some major examples of physiological control mechanisms and their modeling.

Students will acquire the capability to:

• understand a physiological control model;
• apply the main mathematical tools in the evaluation of physiological control systems.

Students will also develop skills relevant to:

• the evaluation of the appropriateness of applied mathematical tools and validation of models;
• the interdisciplinary interaction needed in the modeling and validation process.

(ref. to pp. of M.C. Khoo’s textbook; or other source)

Introduction: course aims, prerequisites, methods and physiological applications

Introduction to closed loop (CL) control systems (1-11)

The Autonomic nervous system (ANS): overview of physiology and anatomy (slides)

Mathematical Models: physical models and analogs, black-box or data models

Basic linear elements: analogs of resistance, capacitance, and inductance (13-19)

Concept of system state. Ordinary Differential Equations (ODE)

State space (SS) models. The core role of integration (28-30)

Linear time invariant (LTI) models: impulse response and transfer function (23-28)

PC-Lab - Numerical Simulation of Models through Matlab Simulink

Lumped elements in CV models - Windkessel models of arterial and peripheral response to the beating heart (Westerhof's review par.1, 2, 3, 6, 7, 8; outline par. 4, 5)

Peripheral circulation, time constants - Mean systemic pressure and CO-VR WP in more detail (Mark's text p 3-5 + 12-22)

Heart contractility and P-V loops; heart-lung pumping unit (Mark's text p 29-36 + 38-42). - Global description of the intact CV system (Mark's 49-53 + 55-63)

Seminar on modeling and monitoring of CV regulation mechanisms

Equilibrium - Static analysis and working point (WP) of closed loop systems (39-42)

WP Example 1 - Cardiac output and venous return WP by Guyton's model (49-55)

WP Example 2 - Plasmatic glucose and insulin WP (55-58)

Time domain analysis and transients in open and closed loop (lucidi, 69-80)

Disturbance compensation and damping vs. closed loop gain (lucidi, 86-87)

Baroreflex, physiological and anatomical outline. Evaluation of the baroreflex sensitivity (BRS): response to phenilephrine, ectopic beat turbulence, Valsalva (slides)

Frequency domain analyses, Bode plots (slides e 108-111)

Vagal and sympathetic frequency response of the sinus node (Berger et al., Saul et al.)

Sinus respiratory arrhythmia physiology overview (slides).

Saul's model of sinus respiratory arrhythmia and baroreflex (slides e 119-123)

Overview of stability and linearization - Stability analysis of CL LTI systems (131-133)

Root locus (134-137) - Nyquist criterion (139-143 e slides)

Gain and phase margins - Effect of delays in a CL

Example 1: Stability of pupil dilation control (146-150)

Example 2; Stability of the chemoreflex and Cheyne-Stokes periodic respiration (151-156)

Stability: Example 3: Brief recall about HR and AP variabilities: HF respiration-related waves and LF Mayer waves - Kitney's baroreflex regulation model of LF waves (slides)

Overview of model identification general concepts (171-174)

Introduction of the closed loop identification problem - Examples of experimental setups opening the loop (182-187)

PC Lab - Matlab Control System Toolbox

Identification of dynamic systems: prediction error minimization

Parametric sensitivity and parameter identification variance (176-178)

Need of minimizing the number of parameters

Example: the glucose/insulin minimal model (190-193)

Linear prediction error models (PEMs) for open-loop system identification (slides)

Identifying closed-loop systems by PEMs: the direct approach virtually opening the loop (slides) - Example 1: Chemoreflex identification (193-200)

- Example 2: Identification of RR-SAP-respiration interactions (slides, paper MBEC, 1994)

Overview of CV regulation identification models

PC Lab - Matlab System Identification Toolbox

Prerequisites concern basic principle of dynamic system theory and automatic control, with the relevant background of ordinary differential equations, Fourier transform, and Laplace transform. However, all the basic theory will be recalled while introducing physiological examples.

Written Test     - 15 open questions - 2 points each - laude upon quality.

                       - The written test is valid 1 year. It can be improved in a subsequent call, but a new delivered test will substitute the former one.

                       - Questions in English; answers either in English or in Italian.

Oral Discussion - After passing the written test; in the same call or in a further one.

                       - The student may choose to have it either in English or in Italian.

The open questions (generally in sequences of 2-4 items) and the oral discussion are aimed to assess the comprehension of mathematical tools and models and the acquired capabilities in properly handling them.