Topic 1: Mathematical Modeling in Biomedical Engineering. Conservation of mass, momentum, energy, and charge; first and second laws of thermodynamics; first- and second-order differential equations; nonlinear differential equations; partial differential equations as applied to biomedical engineering problems.

Topic 2: Quantitative Systems Physiology and Pathophysiology. Modeling of physiological systems from the molecular and cellular levels to the systems level; focus on the neuromuscular and cardiovascular systems. Additional prerequisite: An undergraduate physiology course or the equivalent, and consent of instructor.

Topic 3: Principles of Biomeasurement. Principles of signal measurement in the biomedical field; survey of transducers used for chemical, mechanical, electrical, and thermal biomedical measurements; analysis of how signals are converted into digital form; analysis of noise; aliasing; data storage.

Topic 4: Fields, Forces, and Flows. Introduction to mathematical models that integrate different energy domains and length scales, with an emphasis on the coupling between them. Additional prerequisite: Biomedical Engineering 380J (Topic 1) and 380J (Topic 2).

Topic 5: Biostatistics, Study Design, and Research Methodology. Principles for hypothesis testing; confidence limits; regression analysis; correlation; analysis of variance; experimental design and factorial analysis; discriminate analysis; applications of statistics. Additional prerequisite: An undergraduate probability theory course or the equivalent, and consent of instructor.

Topic 6: Analysis of Biomedical Engineering Systems I. Quantitative examination of the cardiovascular and respiratory systems from the cell to system levels. Presents the cardiovascular and respiratory systems in three phases: (1) anatomy and physiology; (2) energetics (thermodynamics), cellular processes, and engineering analysis; and (3) engineered devices, instrumentation, and imaging for therapeutics and diagnosis. Additional prerequisite: A course in physiology, proficiency in MATLAB, and consent of the graduate adviser.

Topic 7: Analysis of Biomedical Engineering Systems II. Computational techniques used in biomedical engineering. Students propose and conduct an engineering design study relevant to a selected medical problem. Additional prerequisite: Biomedical Engineering 380J (Topic 6).

Topic 8: Mathematical Methods for Biomedical Engineering. Analyze common mathematical techniques useful for biomedical engineering. Utilize vector calculus, linear algebra, Fourier and Laplace Transforms, and ordinary and partial differential equations. Explore common MATLAB (or Python) functions and manipulations for computationally implementing these mathematical techniques in biomedical engineering applications. Biomedical Engineering 380J (Topic: Mathematical Methods for BME) and 380J (Topic 8) may not both be counted. Restrictions: Required for first year biomedical engineering doctoral students.