### Biosignals and Systems

#### BME 33100 / 3 Cr.

This course applies mathematical analysis tools to biological signals and systems. Frequency analysis, Fourier and Laplace transforms, and state equations are used to represent and analyze continuous and discrete-time biosignals. Classic feedback analysis tools are applied to biological systems that rely on negative feedback for control and homeostasis.

**Available Online:** No

**Credit by Exam:** No

**Laptop required:** No

**Prerequisites/Co-requisites:**

P: MATH 26600, BIOL-K101 and BME 22200.

##### Textbooks

Signal Processing First. McClellan, Schafer and Yoder (2003) Prentice Hall. ISBN: 0-13-090999-8. Both electronic and printed handouts will also be distributed throughout the semester.

##### Goals

This course provides the foundational skills for the mathematical representation and analysis of biological signals. The basic analytical concepts for modeling and analysis of biological system dynamics are also presented. All computational homework assignments are carried out using MATLAB. All laboratory exercises are carried out using LabVIEW.

##### Outcomes

Upon completion of the course, students should be able to:

- Understand how electrical signals arise in the body, and explain the physiological function of such signals at a systems level. [a,g]
- Quantify the frequency content of bioelectrical signals using both continuous and discrete Fourier and Z transforms, and separate frequencies associated with physiological function from those associated with noise. [a]
- Apply state transition matrices to linear dynamic systems for studying the natural response of biological systems. [a]
- Define homeostasis and describe mechanisms of feedback that maintain homeostasis in physiological systems. [a]
- Determine the conditions for and study the stability of systems and convergence of signals (continuous- and discrete-time). [b]
- Determine and apply the appropriate methods and techniques to study transient responses and stability after determining the nature of the signals and systems. [a]
- Describe the typical impulse response of a neuron. [a]
- Design appropriate continuous and discrete-time filters for neural, cardiac and other biosignals, and determine their outputs. [a, b, c]
- Determine the applicability of different methods (e.g., Laplace transform, continuous and discrete-time, etc.) for linear and nonlinear dynamic systems with applications to the analysis of stability and dynamic responses of biological systems. [a]

##### Topics

BME 331 is comprised of three interrelated subject areas, all involving the use of mathematical and computational tools to extract meaningful information from biological signals and systems. The first subject area broadly introduces the topic of biological systems that rely on negative feedback for control and stability. Classical concepts of feedback system analysis and associated compensation techniques are introduced using root locus, Bode diagram, and Nyquist criterion as determinants of stability. The second subject area broadly introduces the topic of biological signals as an electrical event. Standard analytical methods of signal representation such as Fourier analysis and power spectrum are developed in order to quantify the information content of these biological signals. The third subject area utilizes recent articles from the scientific literature demonstrating the application of these and other mathematical processing techniques in the study of biological signals and physiological systems. Refer to the lecture schedule for specific topics and dates.

##### Additional Reference Materials

- Cooper, GR & McGillem, CD: Probabilistic Methods of signal and System Analysis, fourth edition or earlier, Oxford. ISBN: 0-190512354-9
- Kandel, ER & Schwartz, JH: Principles of Neuroscience. Second through fourth editions, Elsevier. ISBN: 0838577016
- Berne, RM (Editor), Levy, MN, Koeppen, BM & Stanton: Physiology. Fourth edition, Mosby, ISBN: 0815109520
- Bronzino, JD (Editor), The Biomedical Engineering Handbook, CRC Press, ISBN: 0849383463