BIEN 269 – Modeling Rehabilitative Biosystems

Course description: Mathematical modeling is a widely used tool for gaining insight into mechanisms underlying complex rehabilitative biosystems. This course introduces students to large-scale mathematical models of various physiological systems of interest in rehabilitation (e.g., musculoskeletal, cardiovascular, pulmonary, neurorehabilitative). For each, simulations are used to further our understanding of the adaptive processes of these systems in response to physiological/pathophysiological stresses and rehabilitative interventions.

Prerequisites:

• Systems physiology (e.g., BIEN 180: Systems Physiology)
• Exposure to rehabilitation systems (e.g., BIEN 267 or BIEN 169)
• Basic systems/modeling background (e.g., BIEN 155 or BIEN 152 or equiv.)
• Experience using Matlab (used in class for graphing, simple programming)

Instructors:

• Prof. Jack Winters (Schroeder North A115A, 8-6640, jack.winters@mu.edu)
• Prof. Said Audi (Schroeder North A115B, 8-xxxx, said.audi@mu.edu)

Reading Material:

Assigned via Blackboard, and an extensive web site at www.eng.mu.edu/rehab/rehab167/home.htm

Grading:

• Homework projects for Modules 1-4 (40% total, 10% each)
• Exams for Modules 1-4 (40% total, 10% each)
• Final presentation & report (20%)

Textbooks:

• Lecture notes for each Module
• Helpful: Mathematical and Computer Modeling of Physiological Systems. Vincent C. Rideout. Prentice Hall, New Jersey, 1991.

Course Outline:

Introduction:

• Rehabilitation and modeling: motivation
• Modeling approaches and tools
• Mathematical modeling terminology and approaches (general nonlinear, linear)
• Basics of numerical methods for simulation of ODE’s
• Terminology of control/homeostatic/adaptive systems

Module 1: Neuromusculoskeletal Modeling and Simulation (Dr. Winters):

1. Structure and functional foundations of neuromuscular systems
2. Dynamic modeling of excitation-activation-contraction coupling (e.g., calcium kinetics)
3. Lumped-parameter mechanical model elements: springs, masses, dashpots, sources
4. Viscoelastic models for soft connective tissues (using Matlab)
5. Muscle modeling with Hill-based models
   1. linearized model (using Matlab)
   2. nonlinear model (using JAMM model)
6. Use of muscle-joint models to study simple goal-directed human movement tasks
   1. Point-to-point, isotonic, isokinetic, systems perturbation simulations
7. Feedback pathways and neurocontrol strategies (using JAMM)
   1. Position, velocity, force feedback; effect of time delays
8. Sensitivity analysis of neurocontrols/parameters for goal-directed tasks, and adaptive processes

Module 2: Cardiovascular Hemodynamics and Homeostasis (Dr. Winters)

• Background: Structure (anatomy) and normal function (physiology) of the cardiovascular system (heart, systemic & pulmonary circulations, blood)
• Cardiac cycle, volume-pressure diagram, factors influencing cardiac output
• Model for a blood vessel: transmission line equations
• Classic Windkessel model for the aorta and major arteries
• Full model of uncontrolled/controlled cardiovascular system (examples using Matlab)
• Neuromuscular regulation of heart pumping
• Adaptation of the cardiovascular system to exercise
• Pathogenesis of cardiovascular diseases
• Simulations of the cardiovascular response to physiological (e.g., exercise) and pathophysiological (e.g., congenital heart disease, heart failure) stresses

Module 3: Respiratory System (Dr. Audi)

• Introduction: Pulmonary rehabilitation, chronic obstructive lung diseases (COPD)
• Review of respiration anatomy and histology: Conducting airways, tracheobronchial tree, lung parenchyma, bronchial circulation
• Mechanics of pulmonary ventilation
• Dynamic lung compliance
• Dynamic flow compression, flow limitation
• Regulation of respiration (respiratory center)
• Function of the diseased lung
• Multiple modeling: modeling of the mechanics of breathing and the transport of oxygen and carbon dioxide in the respiratory system
• Simulation of system response to physiological (e.g., exercise, aging) and pathophysiological (e.g., COPD) stresses

Module 4: Modeling Rehabilitative Adaptive Processes (Dr. Winters):

1. Review of spontaneous recovery mechanisms after biomechanical and neural trauma
2. Challenge of modeling rehabilitative (adaptive parametric) change
3. Basics of dynamic neurofuzzy systems as relevant to Med-Predict dynamic model
4. Med-Predict model structure (applied to neurorehab, cardiopulmonary rehab, exercise)
   1. inputs: facts, contexts, interventions (pharmacological, therapy)
   2. states (e.g., physiologic, impairment) = f(inputs, states)
   3. rules (using fuzzy expert systems tools to create systems of nonlinear ODE’s)
   4. outputs (e.g., predictions of performance metrics) = f(states, possibly inputs)
   5. outcomes (e.g., predictions of scalars to be optimized, such as FIM score)
5. Use of an interactive Med-Predict model for simulating adaptive dynamics of:
   1. spontaneous healing processes after neural trauma, based on evidence and expert knowledge (“prognosis”)
   2. use of rules to model muscle biology of hypertropy/atrophy
   3. use of rules to estimate dynamic effects of pharmacological inputs such as BOTOX
   4. use of rules to estimate adaptive changes in JAMM muscle-joint model parameters (Med-Predict states) as a function of use history (rehabilitation, exercise)

back to Rehab Courses Page