Biological Systems Modeling & Simulation. Konstantinos P. Michmizos, PhD
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1 Biological Systems Modeling & Simulation 2 Konstantinos P. Michmizos, PhD June 25, 2012
2 Previous Lecture Biomedical Signal examples (1-d, 2-d, 3-d, ) Purpose of Signal Analysis Noise Frequency domain (1-d, 2-d) Filtering unwanted frequencies Sampling Kalman Filter Recursive Algorithm
3 Biological Signals Amplitude limited Distorted by colored noise Limited length Non-stationary The underlying system is unknown
4 Why do we need models? Insight Understanding the underlying system Testing bed for several hypotheses Description Design verification Explore linear behavior / non-linear nature of the biological physics (going beyond human senses) Control Predictions Functional limits
5 Definition of a Model abduction Difficulties 1. No access to the unconditional truth 2. No unbiased observer 3. Personal opinion on a hypothesis (abduction) 4. Abduction is not an infallible way for discovering truth
6 Modeling a System System (a collection of interconnected processes) Model (a representation that approximates the behavior of an actual system) Simulation (puts the model to work)
7 Goodness of a Model Accuracy Difference between predicted and true value Precision Reproducibility of the results
8 Model refinement
9 Classification of Models Level Sub-cellular Cellular Intercellular Tissue Organ Organism Behavior Dynamic Static Chance Deterministic Stochastic Parameters Parametric Compartments Single Compartment Multiple Compartments Linearity Linear Nonparametric Non- Linear Domain Time Frequency
10 Linear Modeling of Physiological Systems Why linear? Simple to implement Powerful analysis tools Transforming input into output Time variant Time invariant Linear Time-invariant Systems 1. Superposition 2. Impulse Response of a system Testing for linearity may be done using the principle of superposition (e.g. same input at different amplitudes) Response of a linear system to a sinusoidal input is a sinusoid at the same frequency Linearity of a system means nothing without its range
11 Impulse Response Function System Negative Values = System anticipation Positive Values = System memory Living systems frequently demonstrate predictive behavior (e.g. visual pursuit)
12 Coherence If Coherence is greater than 0 but not 1: 1. Extraneous noise is present in the measurements. 2. The system is not linear. 3. Output is due to the input as well as to other inputs.
13 Modeling Chaos in Physiology Chaos (χᾶος) = preponderant of all the others Physiological Systems are extremely complicated deterministic systems for their observers Stochastic determinism observed in biological signals (extraordinary sensitivity to internal conditions) Presence of order under the absence of periodicity (strange attractor) A chaotic system is not necessarily complex
14 Chaos in Physiological Systems Chaos in the heart Sinoatrial Node Sympathetic & parasympathetic fibers & respiration rate heart rate variability Chaos in the brain Neuron doctrine Feedbacks internal uncertainties are amplified over time
15 Why Chaos? Better adaptation capabilities (e.g. heart pumps blood in various circumstances) Adaptation in the brain = learning A never seen before stimulus in the brain, moves the brain to an un-patterned chaotic state. Chaos = normal function Disease = acute attack of order against chaos (e.g. the amount of chaos in the Parkinsonian brain decreases as neurons become more synchronized)
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