Departments and Academic Programs : Biomedical Engineering : Graduate Programs

Graduate Programs

The graduate curriculum in biomedical engineering is track-free at the master’s level while at the doctoral level, it consists of three tracks: biomechanics, cell and tissue engineering, and biosignals and biomedical imaging. Initial graduate study in biomedical engineering is designed to expand the student’s undergraduate preparation in the direction of the concentration of interest. In addition, sufficient knowledge is acquired in other areas to facilitate broad appreciation of problems and effective collaboration with specialists from other scientific, medical, and engineering disciplines. The Department of Biomedical Engineering offers a graduate program leading to the Master of Science degree (M.S.), the Doctor of Philosophy degree (Ph.D.), and the Doctor of Engineering Science degree (Eng.Sc.D.). Applicants who have a Master of Science degree or equivalent may apply directly to the doctoral degree program. All applicants are expected to have earned the bachelor’s degree in engineering or in a cognate scientific program. The Graduate Record Examination (General Test only) is required of all applicants. Students whose bachelor’s degree was not earned in a country where English is the dominant spoken language are required to take the TOEFL, IELTS, PTE Academic, or Duolingo English Test. In addition, for the doctoral program, the individual tracks require applicants to have taken the following foundation courses:

  • Biomechanics: One year of biology and/or physiology, solid mechanics, statics and dynamics, fluid mechanics, ordinary differential equations.
  • Cell and Tissue Engineering: One year of biology and/or physiology, one year of organic chemistry or biochemistry with laboratory, fluid mechanics, rate processes, ordinary differential equations.
    • Biomedical Imaging: Linear algebra, ordinary differential equations, Fourier analysis, digital signal processing, and one year of biology and/or physiology and/or biochemistry.

Applicants lacking some of these courses may be considered for admission with stipulated deficiencies that must be satisfied in addition to the requirements of the degree program. Columbia Engineering does not admit students holding the bachelor’s degree directly to doctoral studies; admission is offered either to the M.S. program or to the M.S. program/doctoral track. The Department of Biomedical Engineering also admits students into the 4-2 program, which provides the opportunity for students holding a bachelor’s degree from certain physical sciences to receive the M.S. degree after two years of study at Columbia.

M.S. students must complete the professional development and leadership course, ENGI E4000, as a graduation requirement. Doctoral students will be enrolled in ENGI E6001–6004 and should consult their program for specific PDL requirements. 

CURRICULUM AND EXAM REQUIREMENTS

Master’s Degree

In consultation with an appointed faculty adviser, M.S. students should select a program of 30 points of credit of graduate courses (4000-level or above) appropriate to their career goals. This program must include the course in computational modeling of physiological systems (BMEN E6003); two semesters of BMEN E9700: Biomedical engineering seminar; at least four other biomedical engineering courses where BME is in its call letters; and at least one graduate-level course in the Applied Mathematics department. Up to 6 credits of Master’s Research BMEN E9100 may be taken to fulfill degree requirements. Up to 3 credits of coursework outside of SEAS may count towards the MS degree. Students with deficiency in physiology coursework are required to take the BMEN E4001-E4002 sequence before taking BMEN E6003. Candidates must achieve a minimum grade-point average of 2.5. A thesis based on experimental, computational, or analytical research is optional. Students wishing to pursue the Master’s Thesis option are required to complete 6 credits of BMEN E9100 Master’s Research and consult with their BME faculty adviser.

MS concentrations are not required. The following grouped courses are a useful guide for students who wish to focus their studies in a particular Biomedical Engineering topic. If a student chooses to declare a concentration, the requirements for these elective concentrations are identical to those of the standard track (including BMEN 6003, Applied Math, BMEN 9700, four BMEN courses, three SEAS courses, and one 3 credit SEAS/non-SEAS course), with one exception: students must take at least 12 credits from a list of track-specific courses.

BIOINFORMATICS AND MACHINE LEARNING

BINF G4006: Translational bioinformatics (3)
BINF G4015: Computational systems biology: proteins, networks, functions (3)
ECBM E4040: Neural networks and deep learning (3)
STAT GU4241: Statistical machine learning (3)
COMS W4252: Introduction to computational learning theory (3)
BMEN E4420: Biomedical signal processing and signal modeling (3)
BMEN E4520: Synthetic biology: principles of genetic circuits (3)
BMEN E4460: Deep learning in biomedical imaging (3)
COMS W4701: Artificial intelligence (3)
CBMF W4761: Computational genomics (3)
COMS W4771: Machine learning (3)
COMS W4772 (E6772): Advanced machine learning (3)
BMEN E4895: Analysis and quantification of medical images (3)
BMEN E9100: Master's research (3)

BIOMATERIALS AND TISSUE ENGINEERING

BMEN E4210: Driving forces of biological systems (3)
BMCH E4500: Biological transport and rate processes (3)
BMEN E4501: Biomaterials and scaffold design (3)
BMEN E4510: Tissue engineering (3)
BMEN E4530: Drug and gene delivery (3)
BMEN E4550: Micro- and nanostructures in cellular engineering (3)
BMEN E4580: Fundamentals of nanobioscience and nanobiotechnology (3)
BMEN E4590: BioMems: cellular and molecular applications (3)
BMEN E6001: Current topics in nanbiotechnology and synthetic biology (3)
BMEN E6500: Tissue and molecular engineering laboratory (4)
BMEN E6505: Advanced biomaterials for tissue engineering (3)
BMEN E9100: Master's research (3)

BIOMECHANICS

MECE E4100: Mechanics of fluids (3)
BMEN E4301: Structure, mechanics, and adaptation of bone (3)
BMEN E4302: Biomechanics of musculoskeletal soft tissues (3)
BMEN E4305: Cardiac mechanics (3)
BMEN E4310: Solid biomechanics (3)
BMEN E4570: Science and engineering of body fluids (3)
BMME E4702: Advanced musculoskeletal biomechanics (3)
MEBM E4703: Molecular mechanics in biology. (3)
MEBM E4710: Morphogenesis: shape and structure in biological materials (3)
BMEN E4750: Sound and hearing (3)
MECE E6100: Advanced mechanics of fluids (3)
BMEN E6301: Modeling of biological tissues with finite elements (3)
MEBM E6310-E6311: Mixture theories for biological tissues, I and II (3)
MECE E6422-E6423: Introduction to the theory of elasticity, I and II (3)
MECE E8501: Advanced continuum biomechanics (3)
BMEN E9100: Master's research (3)

BIOMEDICAL IMAGING

BMEN E4410: Ultrasound in diagnostic imaging(3)
BMEN E4420: Biomedical signal processing and signal modeling (3)
BMEN E4430: Principles of magnetic resonance imaging (3)
BMEE E4740: Bioinstrumentation (3)
ELEN E4810: Digital signal processing (3)
BMEN E4840: Functional imaging for the brain(3)
BMEN E4894: Biomedical imaging (3)
BMEN E4895: Analysis and quantification of medical images (3)
BMEN E4898: Biophotonics (3)
BMEN E6410: Principles and practices of in vivo magnetic resonance spectroscopy (3)
BMEN E9100: Master's research (3)

NEURAL ENGINEERING

BMEB W4020: Computational neuroscience: circuits in the brain (3)
BMEE E4030: Neural control engineering (3)
BMEN E4050: Electrophysiology of human memory and navigation (3)
BMEN E4420: Biomedical signal processing and signal modeling (3)
BMEN E4430: Principles of magnetic resonance imaging (3)
ELEN E4810: Digital signal processing (3)
BMEN E4894: Biomedical imaging (3)
BMEN E9070: Massively parallel neural computation (3)
BMEN E9100: Master's research (3)

DESIGN, INNOVATION, AND ENTREPRENEURSHIP

ENGI W4100: Research to revenue (3)
BIOT GU4180: Entrepreneurship in biotechnology (3)
BIOT W4200: Biopharmaceutical development and regulation (3)
IEME E4200: Intro to human centered design (3)
IEME E4310: Manufacturing enterprise (3)
MECE E4604: Product design for manufacturability (3)
MECE E4610: Advanced manufacturing processes (3)
IEOR E4570: Entrepreneurship bootcamp (1.5)
BMEE E4740: Bioinstrumentation (3)
BMEN E6005: Biomedical innovation I (3)
BMEN E6006: Biomedical innovation II (3)
BMEN E6007: Lab-to-market: commercializing biomedical innovations (3)

ROBOTICS AND CONTROL OF BIOLOGICAL SYSTEMS

BMEE E4030: Neural control engineering (3)
MECE E4058: Mechatronics and embedded microcomputer control (3)
BMEN E4420: Biomedical signal processing and signal modeling (3)
MEBM E4439: Modeling and identification of dynamic systems (3)
EEME E4601: Digital control systems (3)
MECE E4602: Introduction to robotics (3)
MECS E4603: Applied robotics: algorithms and software (3)
MECE E4606: Digital manufacturing (3)
BMME E4702: Advanced musculoskeletal biomechanics (3)
BMEE E4740: Bioinstrumentation (3)
MECE E6400: Advanced machine dynamics (3)
EEME E6601: Introduction to control theory (3)
EEME E6602: Modern control theory (3)
EEME E6610: Optimal control theory (3)
MECE E6614: Advanced topics in robotics and mechanism synthesis (3)
MECE E6615: Robotic manipulation (3)
BMEN E9100: Master's research (3)

 

Doctoral Degree

Doctoral students must complete a program of 30 points of credit beyond the M.S. degree. The core course requirements (9 credits) for the doctoral program include the course in computational modeling of physiological systems (BMEN E6003), plus at least one graduate-level course from the Applied Mathematics department and one graduate-level course in the following departments: Statistics, Applied Mathematics, or a graduate-level Biostatistics course such as BMEN E4110. If BMEN E6003 has already been taken for the master’s degree, a technical elective can be used to complete the core course requirement. If one or both graduate level applied mathematics courses have been taken for the master's degree, technical elective(s) can be used as a substitution. Students must register for BMEN E9700: Biomedical engineering seminar and for research credits during the first two semesters of doctoral study. Remaining courses should be selected in consultation with the student’s faculty adviser to prepare for the doctoral qualifying examination and to develop expertise in a clearly identified area of biomedical engineering. Students should not receive more than two “C” or below letter grades.

All graduate students admitted to the doctoral degree program must satisfy the equivalent of two semesters’ experience in teaching (one semester for M.D./Ph.D. students). This may include supervising and assisting undergraduate students in laboratory experiments, grading, and preparing lecture materials to support the teaching mission of the department. This requirement must be completed by the 3rd year of graduate studies. The Department of Biomedical Engineering is the only engineering department that offers Ph.D. training to M.D./Ph.D. students. These candidates are expected to complete their Ph.D. program within 3.5 years, with otherwise the same requirements as those outlined for the Doctoral Degree program.    

Doctoral Qualifying Examination

Doctoral candidates are required to pass a qualifying examination. This examination is given once a year, and it should be taken after the student has completed 30 points of graduate study. The qualifying examination consists of an oral exam during which the student presents an analysis of assigned scientific papers, as well as answers to questions in topics covering applied mathematics, quantitative biology and physiology, and track-specific material. The committee consists of the thesis advisor and two BME core faculty members approved by the graduate studies committee. A written analysis of the assigned scientific papers must be submitted prior to the oral exam. A minimum cumulative grade-point average of 3.2 without research credit grades is required to register for this examination.

Doctoral Committee and Thesis

Students who pass the qualifying examination must have a core BME faculty member who will serve as their primary research adviser or co-adviser. Each student is expected to submit a research proposal and present it to a committee that consists of three BME faculty members (two must be core BME faculty members, including research adviser) before the end of year 4. The committee considers the scope of the proposed research, its suitability for doctoral research and the appropriateness of the research plan. The committee may approve the proposal without reservation or may recommend modifications. In general, the student is expected to submit his/her research proposal after five semesters of doctoral studies. In accordance with regulations of the Graduate School of Arts and Sciences, each student is expected to submit a thesis and defend it before a committee of five faculty, one of whom holds primary appointment in another department or school or university. Every doctoral candidate is required to have had at least one first-author full-length paper accepted for publication in a peer-reviewed journal prior to recommendation for award of the degree.