Biomedical Engineering

Director of undergraduate studies: Lawrence Staib, N309 B TAC, 785-5958, lawrence.staib@yale.edu [F]; James Duncan, N309 D TAC, 785-2427, 313 MEC, 432-9917, james.duncan@yale.edu [S]; seas.yale.edu/departments/biomedical-engineering

FACULTY OF THE DEPARTMENT OF BIOMEDICAL ENGINEERING

Professors Richard Carson, †Nicholas Christakis, James Duncan, Jay Humphrey, Fahmeed Hyder, Andre Levchenko, †Laura Niklason, Douglas Rothman, Mark Saltzman, †Martin Schwartz, †Frederick Sigworth, †Brian Smith, Lawrence Staib, †Hemant Tagare, †Paul Van Tassel, Steven Zucker

Associate Professors †Robin de Graaf, Tarek Fahmy, Themis Kyriakides, †Evan Morris, †Xenophon Papademetris, †Corey Wilson

Assistant Professors †Joerg Bewersdorf, Stuart Campbell, †Michael Choma, Rong Fan, Anjelica Gonzalez, †Chi Liu, Kathryn Miller-Jensen, Michael Murrell, †Steven Tommasini, †Jiangbing Zhou

Lecturers †Liqiong Gui, †Jing Zhou

†A joint appointment with primary affiliation in another department or school.

Engineering methods and strategies are used to address biomedical problems ranging from studies of physiological function using images to the development of artificial organs and new biomaterials. The major in Biomedical Engineering is designed to provide students with an understanding of common fundamental methodologies and the ability to develop quantitative approaches to one of three biomedical engineering fields.

The flexible course structure of the major permits students to bridge basic concepts in the life sciences and traditional areas of engineering, while also gaining a comprehensive understanding of biomedical engineering as a field of study.

Prerequisites The following prerequisites are common to all tracks in the major: BIOL 101 and 102 (or a higher-level course in MCDB or MB&B, with permission of the director of undergraduate studies); a lecture course in chemistry numbered CHEM 161 or higher (or CHEM 112 or higher); ENAS 194; MATH 115; MATH 120 or ENAS 151; PHYS 180, 181, 205L, and 206L (or 165L and 166L, with permission of the director of undergraduate studies).

Requirements of the major The B.S. degree program in Biomedical Engineering offers three tracks: bioimaging, biomechanics, and molecular engineering.

During the freshman year, students study basic mathematics, chemistry, and biology. By the end of the sophomore year, they have taken physics, ENAS 194, Ordinary and Partial Differential Equations with Applications, BENG 249, Introduction to Biomedical Computation, and BENG 350, Physiological Systems. In the junior year, students gain a comprehensive grounding in the field through BENG 351, Biotransport and Kinetics, BENG 352, Biomedical Signals and Images, BENG 353, Introduction to Biomechanics, BENG 355L, Physiological Systems Laboratory, and BENG 356L, Biomedical Engineering Laboratory. During the junior and senior years students also acquire depth by taking electives in one of the three areas of concentration. A senior seminar and a senior project give students practical, detailed information about their chosen area of concentration.

Students must complete twelve term courses, totaling at least eleven course credits, beyond the prerequisites, including at least three required courses in the chosen track, two terms of a biomedical engineering laboratory (BENG 355L, 356L), and the two-term senior requirement.

Students in all tracks are required to take the following seven term courses: BENG 249, 350, 351, 352, 353, 355L, and 356L. Students in the Bioimaging track must also take three courses chosen from EENG 310, BENG 410, 421, 436, 445, 475, 476, or 485. Students in the Biomechanics track must also take three courses chosen from MENG 185, 280, 361, BENG 410, 434, 453, 455, 456457, or 458. Students in the Molecular Engineering track must also take three courses chosen from BENG 410, 434, 435, 464, 465, 467, or MENG 361. One relevant course may be substituted with the permission of the director of undergraduate studies. By the end of senior year, two term courses in the life sciences must have been included among the prerequisite and required courses for the major.

Senior requirement In their senior year, all students must complete a one-term senior project in their final term of enrollment (BENG 471 or 472) and the senior seminar (BENG 480).

Credit/D/Fail No course taken Credit/D/Fail may count toward the major, including prerequisites.

Preparation for graduate study The Biomedical Engineering curriculum is excellent preparation for graduate study in engineering, science, and medicine. In some cases, organic chemistry and/or certain biology courses may be substituted for one course in the major after consultation with the director of undergraduate studies.

REQUIREMENTS OF THE MAJOR

Prerequisites BIOL 101 and 102, or higher-level course in MCDB or MB&B with DUS permission; 1 lecture course in chemistry numbered CHEM 161 or higher (or CHEM 112 or higher); ENAS 194; MATH 115; MATH 120 or ENAS 151; PHYS 180, 181, and 205L, 206L (or 165L, 166L with DUS permission)

Number of courses 12 term courses, totaling at least 11 course credits, beyond prereqs (incl senior req)

Specific courses required All tracksBENG 249, 350, 351, 352, 353, 355L, 356L; Bioimaging track—3 from EENG 310, BENG 410, 421, 436, 445, 475, 476, or 485; Biomechanics track—3 from MENG 185, 280, 361, BENG 410, 434, 453, 455, 456457, or 458; Molecular engineering track—3 from BENG 410, 434, 435, 464, 465, 467, MENG 361.

Distribution of courses 2 term courses in life sciences among prereq and req courses

Substitution permitted Relevant course with DUS permission

Senior requirement Senior project in final term (BENG 471 or 472) and senior sem (BENG 480)

Courses

BENG 249b, Introduction to Biomedical Computation Richard Carson

Computational and mathematical tools used in biomedical engineering for the simulation of biological systems and the analysis of biomedical data. Basics of computational programming in MATLAB; applications to modeling, design, and statistical and data analysis. Prerequisite: MATH 120 or ENAS 151.  QR
MWF 10:30am-11:20am

* BENG 350a / MCDB 310a, Physiological Systems Mark Saltzman, Elizabeth Holt, Emile Boulpaep, Peter Aronson, and David Zenisek

Regulation and control in biological systems, emphasizing human physiology and principles of feedback. Biomechanical properties of tissues emphasizing the structural basis of physiological control. Conversion of chemical energy into work in light of metabolic control and temperature regulation. Prerequisites: CHEM 165 or 167 (or CHEM 113 or 115), or PHYS 180 and 181; MCDB 120, or BIOL 101 and 102.  SC
MWF 9:25am-10:15am

BENG 351a / CENG 351a, Biotransport and Kinetics Kathryn Miller-Jensen

Creation and critical analysis of models of biological transport and reaction processes. Topics include mass and heat transport, biochemical interactions and reactions, and thermodynamics. Examples from diverse applications, including drug delivery, biomedical imaging, and tissue engineering. Prerequisites: MATH 115, ENAS 194; BIOL 101 and 102; CHEM 161, 163, or 167; BENG 249.  QR
TTh 11:35am-12:50pm

BENG 352b, Biomedical Signals and Images Lawrence Staib

Principles and methods used to represent, model, and process signals and images arising from biomedical sources. Topics include continuous and discrete linear systems analysis, Fourier analysis and frequency response, metrics for signal similarity, and noise filtering. Biomedical examples range from one-dimensional electrical signals in nerves and muscles to two-dimensional images of organs and cells. Prerequisite: MATH 120 or ENAS 151. BENG 249, 350, and ENAS 194 strongly recommended.  QR
TTh 11:35am-12:50pm

BENG 353b, Introduction to Biomechanics Jay Humphrey

An introduction to the biomechanics used in biosolid mechanics, biofluid mechanics, biothermomechanics, and biochemomechanics. Diverse aspects of biomedical engineering, from basic mechanobiology to the design of novel biomaterials, medical devices, and surgical interventions. Prerequisites: PHYS 180, 181, MATH 115, and ENAS 194.  QR
TTh 2:30pm-3:45pm

* BENG 355La, Physiological Systems Laboratory Alyssa Siefert

Introduction to laboratory techniques and tools used in biomedical engineering for physiological measurement. Topics include bioelectric measurement, signal processing, and dialysis. Enrollment limited to majors in Biomedical Engineering, except by permission of the director of undergraduate studies.  SC½ Course cr
MF 1pm-5pm

* BENG 356Lb, Biomedical Engineering Laboratory Tarek Fahmy

Continuation of BENG 355L, introducing laboratory techniques and tools used in biomedical engineering. Topics include image processing, ultrasound, and microscopy. Enrollment limited.  SC½ Course cr
MF 1pm-5pm

BENG 404a / MENG 404a, Medical Device Design and Innovation Joseph Zinter and Ying Zheng

The engineering design, project planning, prototype creation, and fabrication processes for medical devices that improve patient conditions, experiences, and outcomes. Students develop viable solutions and professional-level working prototypes to address clinical needs identified by practicing physicians. Some attention to topics such as intellectual property, the history of medical devices, documentation and reporting, and regulatory affairs.
MW 2:30pm-3:45pm

* BENG 410a, Physical and Chemical Basis of Bioimaging and Biosensing Douglas Rothman, Frederick Sigworth, Fahmeed Hyder, and Richard Carson

Basic principles and technologies for sensing the chemical, electrical, and structural properties of living tissues and of biological macromolecules. Topics include magnetic resonance spectroscopy, microelectrodes, fluorescent probes, chip-based biosensors, X-ray and electron tomography, and MRI. Prerequisites: BENG 351 and 352 or permission of instructor.  QR, SC
TTh 1pm-2:15pm

BENG 434a, Biomaterials Anjelica Gonzalez

Introduction to the major classes of biomedical materials: ceramics, metals, and polymers. Their structure, properties, and fabrication connected to biological applications, from implants to tissue-engineered devices and drug delivery systems. Prerequisite: CHEM 165 (or CHEM 113 or 115); organic chemistry recommended.  SC
MW 11:35am-12:50pm

* BENG 435b, Biomaterial-Tissue Interactions Themis Kyriakides

Study of the interactions between tissues and biomaterials, with an emphasis on the importance of molecular- and cellular-level events in dictating the performance and longevity of clinically relevant devices. Attention to specific areas such as biomaterials for tissue engineering and the importance of stem/progenitor cells, as well as biomaterial-mediated gene and drug delivery. Prerequisites: CHEM 161, 165, or 167 (or CHEM 112, 114, or 118); MCDB 120, or BIOL 101 and 102; or equivalents.  SC
TTh 9am-10:15am

BENG 444b, Fundamentals of Medical Imaging Michael Choma, Chi Liu, and Christoph Juchem

Review of basic engineering and physical principles of common medical imaging modalities including X-ray, CT, PET, SPECT, MRI, and echo modalities (ultrasound and optical coherence tomography). Additional focus on clinical applications and cutting-edge technology development. BENG 352 or similar background.  QR, SC
MF 11:35am-12:50pm

[ BENG 445, Biomedical Image Processing and Analysis ]

BENG 455a, Vascular Mechanics Jay Humphrey

Methods of continuum biomechanics used to study diverse vascular conditions and treatments from an engineering perspective. Topics include hypertension, atherosclerosis, aneurysms, vein grafts, and tissue engineered constructs. Emphasis on mechanics driven by advances in vascular mechanobiology. Prerequisite: BENG 353.  QR
TTh 2:30pm-3:45pm

BENG 456b, Molecular and Cellular Biomechanics Michael Murrell

The basic mechanical principles at the molecular and cellular level that underlie the major physical behaviors of the cell, from cell division to cell migration. Basic cellular physiology, methodology for studying cell mechanical behaviors, models for understanding the cellular response under mechanical stimulation, and the mechanical impact on cell differentiation and proliferation. Prerequisites: MENG 211 and 280 or equivalents, and experience with MATLAB. Recommended preparation: BENG 353 and MCDB 205.  QR, SC
TTh 2:30pm-3:45pm

BENG 459a / MENG 459a, Neuromuscular Biomechanics Madhusudhan Venkadesan

Mechanics and control of animal movement, including skeletal muscle mechanics, systems-level neural and sensory physiology, elements of feedback control, and optimal control. Deriving equations of motion for multibody mechanical systems that are actuated by muscles or muscle-like motors; incorporating sensory feedback; analyzing system properties such as stability and energetics. Prerequisites: MENG 383 and MATH 222 or equivalents, and familiarity with MATLAB or a similar scientific computing environment.  QRRP
MW 1pm-2:15pm

BENG 463a / CENG 320a, Immunoengineering Staff

Introduction to immunoengineering, a field combining immunology with the physical sciences and engineering. Focus on biophysical principles and biomaterial applications for understanding and engineering immunity.  SC

BENG 464b, Tissue Engineering Laura Niklason

Introduction to the major aspects of tissue engineering, including materials selection, scaffold fabrication, cell sources, cell seeding, bioreactor design, and tissue characterization. Class sessions include lectures and hands-on laboratory work. Prerequisite: CHEM 161, 165, or 167 (or CHEM 112, 114, or 118). Recommended preparation: organic chemistry, cell biology, and physiology.  SC1½ Course cr
MW 9:25am-10:15am; W 2:30pm-4:20pm

BENG 465a / MCDB 361a, Dynamical Systems in Biology Thierry Emonet, Damon Clark, and Kathryn Miller-Jensen

Advanced topics related to dynamical processes in biological systems. Processes by which cells compute, count, tell time, oscillate, and generate spatial patterns. Time-dependent dynamics in regulatory, signal-transduction, and neuronal networks; fluctuations, growth, and form. Comparisons between models and experimental data. Dynamical models applied to neurons, neural systems, and cellular biophysical processes. Use of MATLAB to create models. Prerequisite: MCDB 261 or equivalent, or a 200-level biology course, or with permission of instructor.  QR
TTh 2:30pm-3:45pm

BENG 467b, Systems Biology of Cell Signaling Andre Levchenko

Approaches from systems biology to the fundamental processes underlying both the sensory capability of individual cells and cell-to-cell communication in health and disease. Prerequisites: BENG 249 and ENAS 194, or equivalents.  QR, SC
MW 4pm-5:15pm

* BENG 471a and BENG 472b, Special Projects Staff

Faculty-supervised individual or small-group projects with emphasis on research (laboratory or theory), engineering design, or tutorial study. Students are expected to consult the director of undergraduate studies and appropriate faculty members about ideas and suggestions for suitable topics. This course is usually taken during the spring term of the senior year but with permission of the director of undergraduate studies can be taken any time during a student's career, and may be taken more than once. Permission of both the instructor and the director of undergraduate studies is required.
HTBA

* BENG 474b, Senior Project James Duncan

Faculty-supervised biomedical engineering projects focused on research (laboratory or theory) or engineering design. Students should consult with the director of undergraduate studies and appropriate faculty mentors for suitable projects. This course is taken during the spring term of the senior year. Permission of both the faculty mentor and the director of undergraduate studies is required.
HTBA

BENG 475a / CPSC 475a / EENG 475a, Computational Vision and Biological Perception Steven Zucker

An overview of computational vision with a biological emphasis. Suitable as an introduction to biological perception for computer science and engineering students, as well as an introduction to computational vision for mathematics, psychology, and physiology students. After CPSC 112 and MATH 120, or with permission of instructor.  QR, SCRP
TTh 2:30pm-3:45pm

BENG 476b / CPSC 476b, Advanced Computational Vision Steven Zucker

Advanced view of vision from a mathematical, computational, and neurophysiological perspective. Emphasis on differential geometry, machine learning, visual psychophysics, and advanced neurophysiology. Topics include perceptual organization, shading, color and texture analysis, and shape description and representation. After CPSC 475.  QR, SC
MW 2:30pm-3:45pm

* BENG 480a, Seminar in Biomedical Engineering Xenophon Papademetris

Oral presentations and written reports by students analyzing papers from scientific journals on topics of interest in biomedical engineering, including discussions and advanced seminars from faculty on selected subjects.
T 4pm-5:50pm

* BENG 485b, Fundamentals of Neuroimaging Fahmeed Hyder

The neuroenergetic and neurochemical basis of several dominant neuroimaging methods, including fMRI. Technical aspects of different methods, interpretation of results, and controversies or challenges regarding the application of fMRI and related methods in medicine.  SC
W 3:30pm-5:20pm