Courses

BMEN E Lab-to-market: commercializing biomedical innovations. 0 points.

Not offered during 2018-19 academic year.

BMEN E1001 Engineering in medicine. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

The present and historical role of engineering in medicine and health care delivery. Engineering approaches to understanding organismic and cellular function in living systems. Engineering in the diagnosis and treatment of disease. Medical imaging, medical devices: diagnostic and surgical instruments, drug delivery systems, prostheses, artificial organs. Medical informatics and organization of the health care system. Current trends in biomedical engineering research.

BMEN E3010 Biomedical Engineering I. 3 points.

Lect: 3.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) or with instructor's permission
Corequisites: BMEN E3810,BMEN E4001

Various concepts within the field of biomedical engineering, foundational knowledge of engineering methodology applied to biological and/or medical problems through modules in biomechanics, biomaterials, and cell & tissue engineering.

BMEN E3020 Biomedical Engineering II. 3 points.

Lect: 3.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) or with instructor's permission.
Corequisites: BMEN E3820,BMEN E4002

Various concepts within the field of biomedical engineering, foundational knowledge of engineering methodology applied to biological and/or medical problems through modules in biomechanics, bioinstrumentation, and biomedical Imaging.

BMEN E3810 Biomedical engineering laboratory, I. 3 points.

Lab: 4.

Fundamental considerations of wave mechanics; design philosophies; reliability and risk concepts; basics of fluid mechanics; design of structures subjected to blast; elements of seismic design; elements of fire design; flood considerations; advanced analysis in support of structural design.

BMEN E3820 Biomedical engineering laboratory, II. 3 points.

Lab: 4.

Biomedical experimental design and hypothesis testing. Statistical analysis of experimental measurements. Analysis of experimental measurements. Analysis of variance, post hoc testing. Fluid shear and cell adhesion, neuro-electrophysiology, soft tissue biomechanics, biomecial imaging and ultrasound, characterization of excitable tissues, microfluidics.

BMEN E3910 Biomedical engineering design, I. 4 points.

Lect: 1. Lab: 3.

A two-semester design sequence to be taken in the senior year. Elements of the design process, with specific applications to biomedical engineering: concept formulation, systems synthesis, design analysis, optimization, biocompatibility, impact on patient health and comfort, health care costs, regulatory issues, and medical ethics. Selection and execution of a project involving the design of an actual engineering device or system. Introduction to entrepreneurship, biomedical start-ups, and venture capital. Semester I: statistical analysis of detection/classification systems (receiver operation characteristic analysis, logistic regression), development of design prototype, need, approach, benefits and competition analysis. Semester II: spiral develop process and testing, iteration and refinement of the initial design/prototype and business plan development. A lab fee of $100 each is collected.

BMEN E3920 Biomedical engineering design, II. 4 points.

Lect: 1. Lab: 3.

A two-semester design sequence to be taken in the senior year. Elements of the design process, with specific applications to biomedical engineering: concept formulation, systems synthesis, design analysis, optimization, biocompatibility, impact on patient health and comfort, health care costs, regulatory issues, and medical ethics. Selection and execution of a project involving the design of an actual engineering device or system. Introduction to entrepreneurship, biomedical start-ups, and venture capital. Semester I: statistical analysis of detection/classification systems (receiver operation characteristic analysis, logistic regression), development of design prototype, need, approach, benefits and competition analysis. Semester II: spiral develop process and testing, iteration and refinement of the initial design/prototype and business plan development. A lab fee of $100 each is collected.

BMEN E3998 Projects in biomedical engineering. 1-3 points.

Hours to be arranged.

Independent projects involving experimental, theoretical, computational, or engineering design work. May be repeated, but no more than 3 points of this or any other projects or research course may be counted toward the technical elective degree requirements as engineering technical electives.

BMEN E3999 Undergraduate Fieldwork. 1 point.

Prerequisites: Obtained internship and approval from faculty advisor. BMEN undergraduate students only.

May be repeated for credit, but no more than 3 total points may be used toward the 128-credit degree requirement. Only for BMEN undergraduate students who include relevant off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, and non-technical requirements. May not be taken for pass/fail credit or audited.

BMEN E4000 Special Topics. 3 points.

Lect: 3.

Additional current topics in biomedical engineering taught by regular or visiting faculty. The same subject matter is not usually considered in different years. Section 001: Gene and Drug Delivery (Fall); Section 002: Deep Learning for Biomedical Applications 

BMEN E4001 Quantitative Physiology, I: Cells and Molecules. 3 points.

Lect: 3.

Prerequisites: (BIOL UN2005) and (BIOL UN2006)
Corequisites: BMEN E3010,BMEN E3810

Physiological systems at the cellular and molecular level are examined in a highly quantitative context. Topics include chemical kinetics, molecular binding and enzymatic processes, molecular motors, biological membranes, and muscles.

BMEN E4002 Quantitative Physiology, II: Organ Systems. 3 points.

Lect: 3.

Prerequisites: (BIOL UN2005) and (BIOL UN2006)
Corequisites: BMEN E3020,BMEN E3820

Students are introduced to a quantitative, engineering approach to cellular biology and mammalian physiology. Beginning with biological issues related to the cell, the course progresses to considerations of the major physiological systems of the human body (nervous, circulatory, respiratory, renal).

BMEN E4010 Ethics for biomedical engineers. 2 points.

Lect: 2.Not offered during 2018-19 academic year.

Prerequisites: Senior status in biomedical engineering or the instructor's permission.

Covers a wide range of ethicical issues expected to confront graduates as they enter the biotechnology industry, research, or medical careers. Topics vary and incorporate guest speakers from Physicians and Surgeons, Columbia Law School, Columbia College, and local industry.

BMEN E4050 Electrophysiology of Human Memory and Navigation. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: Instructor's permission.

Human memory, including working, episodic and procedural memory. Electrophysiology of cognition, noninvasive and invasive recordings. Neural basis of spatial navigation, with links to spatial and episodic memory. Computational models of memory, brain stimulation, lesion studies.

BMEN E4103 Anatomy of the thorax and abdomen. 2 points.

Lect: 2.

Prerequisites: Graduate standing in Biomedical Engineering.

This course is designed for the Biomedical Engineering graduate student interested in acquiring in-depth knowledge of anatomy relevant to his/her doctoral research. Lectures and tutorial sessions may be taken with or without the associated laboratory (BMEN E4104). 

BMEN E4104 Anatomy laboratory: thorax and abdomen.. 2 points.

Lect: 2.

Prerequisites: Graduate standing in Biomedical Engineering.
Corequisites: BMEN E4103

BMEN E4105 Anatomy of the extremities. 2 points.

Lect: 2.

Prerequisites: Graduate standing in Biomedical Engineering.

This course is designed for the Biomedical Engineering graduate student interested in acquiring in-depth knowledge of anatomy relevant to his/her doctoral research. Lectures and tutorial sessions may be taken with or without the associated laboratory (BMEN E4106).

BMEN E4106 Anatomy laboratory: extremities. 2 points.

Lab: 2.

Prerequisites: graduate standing in Biomedical Engineering.
Corequisites: BMEN E4105

BMEN E4107 Anatomy of the head and neck. 2 points.

Lect: 2.

Prerequisites: graduate standing in Biomedical Engineering.

This course is designed for the Biomedical Engineering graduate student interested in acquiring in-depth knowledge of anatomy relevant to his/her doctoral research. Lectures and tutorial sessions may be taken with or without the associated laboratory (BMEN E4108).

BMEN E4108 Anatomy laboratory: head and neck. 2 points.

Lab: 2.

Prerequisites: Graduate standing in Biomedical Engineering.
Corequisites: BMEN E4107

BMEN E4110 Biostatistics for Engineers. 3 points.

Lect: 3.

Prerequisites: (MATH UN1202) and (APMA E2101) MATH V1202 and APMA E2101

Fundamental concepts of probability and statistics applied to biology and medicine. Probability distributions, hypothesis testing and inference, summarizing data and testing for trends. Signal detection theory and the receiver operator characteristic. Lectures accompanied by data analysis assignments using MATLAB as well as discussion of case studies in biomedicine.

BMEN E4150 The cell as a machine. 3 points.

Lect: 3.

Prerequisites: (MATH UN1101) or MATH V1101 or equivalent
Corequisites: One semester of BIOL C2005 or BIOC C3501, and one semester of PHYS C1401 or equivalent

Cells as complex micron-sized machines, basic physical aspects of cell components (diffusion, mechanics, electrostatics, hydrophobicity), energy transduction (motors, transporters, chaperones, synthesis complexes), basic cell functions. Biophysical principles, feedback controls for robust cell function, adaptation to environmental perturbations.

BMEN E4210 Thermodynamics of biological systems. 4 points.

Lect: 4.

Prerequisites: (CHEM UN1404) and (MATH UN1202)
Corequisites: BIOL UN2005

Introduction to the thermodynamics of biological systems, with a focus on connection microscopic molecular properties to macroscopic states. Both classical and statistical thermodynamics will be applied to biological systems; phase equilibria, chemical reactions, and colligative properties. Topics in modern biology, macromolecular behavior in solutions and interfaces, protein-ligand binding, and the hydrophobic effect.

BMEN E4301 Structure, mechanics, and adaptation of bone. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Introduction to structure, physiology, and biomechanics of bone. Structure, function, and physiology of skeletal bones; linear elastic properties of cortical and trabecular bone; anisotropy and constitutive models of bone tissue; failure and damage mechanics of bone; bone adaptation and fracture healing; experimental determination of bone properties; and morphological analysis of bone microstructure.

BMEN E4302 Biomechanics of musculoskeletal soft tissues. 3 points.

Lect.: 3.

Prerequisites: (ENME E3113) or equivalent. Restricted to seniors and graduate students.

Biomechanics of orthopaedic soft tissues (cartilage, tendon, ligament, meniscus, etc.). Basic and advanced viscoelasticity applied to the musculoskeletal system. Topics include mechanical properties, applied viscoelasticity theory, and biology of orthopaedic soft tissues.  

BMEN E4305 Cardiac mechanics. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (BMEN E4310) and (BMEN E4320) or equivalents.

Cardiac anatomy, passive myocardial constitutive properties, electrical activation, ventricular pump function, ventricular-vascular coupling, invasive and noninvasive measures of regional and global function, models for predicting ventricular wal stress. Alterations in muscle properites and ventricular function resulting from myocardial infarction, heart failure, and left ventricular assist.

BMEN E4310 Solid Biomechanics. 3 points.

Lect.: 3.

Prerequisites: (ENME E3105) and (ENME E3113) and

Applications of continuum mechanics to the understanding of various biological tissues properties. The structure, function, and mechanical properties of various tissues in biolgical systems, such as blood vessels, muscle, skin, brain tissue, bone, tendon, cartilage, ligaments, etc. are examined. The establishment of basic governing mechanical principles and constitutive relations for each tissue. Experimental determination of various tissue properties. Medical and clinical implications of tissue mechanical behavior.

BMEN E4320 Fluid Biomechanics. 3 points.

Prerequisites: (APMA E2101) and (ENME E3105) and (MECE E4100) APMA E2101, ENME E3105, and MECE E4100.

The principles of continuum mechanics as applied to biological fluid flows and transport. Continuum formulations of basic conservation laws, Navier-Stokes equations, mechanics of arterial and venous blood flow, blood rheology and non-Newtonian properties, flow and transport in the microcirculation, oxygen diffusion, capillary filtration.

BMEN E4340 Biomechanics of cells. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (BMEN E3320) and (BMEN E4300) or equivalents.

Survey of experiments and theoretical analyses of the mechanical behavior of individual living nonmuscle cells. Emphasis on quantitative analytic description using continuum mechanics and molecular level theory from the standpoint of statistical mechanics and mechanical models. Mechanics of erythrocytes, leukocytes, endothelial cells, and fibroblasts; models of aggregation, adhesion, locomotion, amoeba motility, cell division and morphogenesis; molecular level models of actin, myosin, microtubules, and intermediate filaments and relation to mechanical properties of cells and cytoskeleton. Alternative models of cytoskeletal mechanics, foam theory, tensegrity. Analysis of experimental techniques including micropipette studies, optical and magnetic cytometry, and nanoindentation.

BMEN E4410 Ultrasound in diagnostic imaging. 3 points.

Lect: 3.

Prerequisites: (MATH UN1202) or MATH V1202 or equivalent,

Fourier analysis. Physics of diagnostic ultrasound and principles of ultrasound imaging instrumentation. Propagation of plane waves in lossless medium; ultrasound propagation through biological tissues; single-element and array transducer design; pulse-echo and Doppler ultrasound instrumentation, performance evaluation of ultrasound imaging systems using tissue-mimicking phantoms, ultrasound tissue characterization; ultrasound nonlinearity and bubble activity; harmonic imaging; acoustic output of ultrasound systems; biological effects of ultrasound.

BMEN E4420 Biomedical signal processing and signal modeling. 3 points.

Lect: 3.

Prerequisites: (ELEN E3801) and (APMA E2101) or (APMA E3101) or ELEN E3801 and either APMA E2101 or E3101 or instructor's permission

Fundamental concepts of signal processing in linear systems and stochastic processes. Estimation, detection and filtering methods applied to biomedical signals. Harmonic analysis, auto-regressive model, Wiener and Matched filters, linear discriminants, and independent components. Methods are developed to answer concrete questions on specific data sets in modalities such as ECG, EEG, MEG, Ultrasound. Lectures accompanied by data analysis assignments using MATLAB.

BMEN E4430 Principles of magnetic resonance imaging. 3 points.

Lect: 3.

Prerequisites: (PHYS UN1403) and (APMA E2101) or PHYS C1403 and APAM E2101 or instructors' permission.

Fundamental principles of Magnetic Resonance Imaging (MRI), including the underlying spin physics and mathematics of image formation with an emphasis on the application of MRI to neuroimaging, both anatomical and functional. The course will examine both theory and experimental design techniques.

BMEN E4440 Physiological control systems. 3 points.

Lect: 3.

Prerequisites: (MEBM E4439) and (APMA E2101)

Fundamentals of time and frequency domains analyses and stability. Frequency domain controller design. Cardiovascular and respiratory systems simulation. Endogenous control systems: baroreflex, chemoreflex, thermoregulation, pupillary light reflex. Open and closed loop physiological systems. Exogenous control systems: ventilators, infusion pumps. Nonlinear actuators and delayed feedback systems. Acute disease simulation and clinical decision support in the intensive care unit. MATLAB and Simulink environments utilized.

BMEN E4450 Dental and craniofacial tissue engineering. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (MSAE E3103) and (BMEN E4210) and (BMEN E4501) or equivalent.

Principles of dental and craniofacial bioengineering, periodontal tissue engineering: beyond guided tissue regeneration, craniofacial regeneration by stem cells and engineered scaffolds, biomaterials: Engineering approaches in tissue regeneration, bone biology and development: instructive cues for tissue engineers.

BMEN E4501 Biomaterials. 3 points.

Lect: 3.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) and (BMEN E4001) and (BMEN E4002)

An introduction to the strategies and fundamental bioengineering design criteria in the development of biomaterials and tissue engineered grafts. Material structural-functional relationships, biocompatibility in terms of material and host responses. Through discussions, readings, and a group design project, students acquire an understanding of cell-material interactions and identify the parameters critical in the design and selection of biomaterials for biomedical applications.

BMEN E4510 Tissue Engineering. 3 points.

Lect: 3

Prerequisites: (BIOL UN2005) and (BIOL UN2006) and (BMEN E4001) and (BMEN E4002)

An introduction to the strategies and fundamental bioengineering design criteria behind the development of cell-based tissue substitutes. Topics include biocompatibility, biological grafts, gene therapy-transfer, and bioreactors.

BMEN E4520 Synthetic Biology: Principles of Genetic Circuits. 3 points.

Not offered during 2018-19 academic year.

Prerequisites: (BIOL UN2005) and (MATH UN2030) or (APMA E2101)

Basic principles of synthetic biology and a survey of the field. Fundamentals of biological circuits, including circuit design, modern techniques for DNA assembly, quantitative characterization of genetic circuits, and ODE modeling of biological circuits with MATLAB. Intended for advanced undergraduate and graduate students.

BMEN E4530 Drug and Gene Delivery. 3 points.

Prerequisites: BME I (BMEN E3010)

Prerequisites: BME I. The course covers the application of polymers and other materials in drug and gene delivery, with focus on recent advances in the field. It covers basics of polymer science, pharmacokinetics, and biomaterials, cell-substrate interactions, drug delivery system fabrication from nanoparticles to microparticles and electrospun fibrous membranes. Applications include cancer therapy, immunotherapy, gene therapy, tissue engineering, and regenerative medicine. Course readings include textbook chapters and journal papers. Homework assignments take the format of an assay responding to an open-ended question. A term paper and a 30-minute PowerPoint presentation are required at the end of the semester.

BMEN E4540 Bioelectrochemistry. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (CHEM UN3079) and (CHEM UN2443) or equivalent.

Application of electrochemical kinetics to interfacial processes occurring in biomedical systems. Basics of electrochemistry, electrochemical instrumentation, and relevant cell and electrophysiology reviewed. Applications to interpretation of excitable and nonexcitable membrane phenomena, with emphasis on heterogeneous mechanistic steps. Examples of therapeutic devices created as a result of bioelectrochemical studies.

BMEN E4550 Micro- and nano-structures in cellular engineering. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) or BIOL C2005 and BIOL C2006 or equivalent

Design, fabrication, and application of micro-/nano-structured systems for cell engineering. Recognition and response of cells to spatial aspects of their extracellular environment. Focus on neural, cardiac, co-culture, and stem cell systems. Molecular complexes at the nanoscale.

BMEN E4560 Dynamics of biological membranes. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (BIOL UN2005) and (BMEN E4001) or equivalent.

 The structure and dynamics of biological (cellular) membranes are discussed, with an emphasis on biophysical properties. Topics include membrane composition, fluidity, lipid asymmetry, lipid-protein interactions, membrane turnover, membrane fusion, transport, lipid phase behavior. In the second half of the semester, students will lead discussions of recent journal articles.

BMEN E4570 Science and engineering of body fluids. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: General chemistry, organic chemistry, and basic calculus.

Body fluids as a dilute solution of polyelectrolyte molecules in water. Study of physical behavior as affected by the presence of ions in surrounding environments. The physics of covalent, ionic, and hydrogen bonds are reviewed, in relation to the structure/properties of the body fluid. Selected physiological processes are examined in physical-chemical terms for polymers.

BMEN E4580 Fundamentals of Nanobioscience and Nanobiotechnology. 3 points.

Lect: 3.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) and (BMEN E4001) or (BMEN E4002) instructor permission

Fundamentals of nanobioscience and nanobiotechnology, scientific foundations, engineering principles, current and envisioned applications. This includes the discussion of intermolecular forces and bonding, of the kinetics and thermodynamics of self-assembly, of nanoscale transport processes arising from the actions of biomolecular motors, computation and control in biomolecular systems, and of the mitochondrium as an example of a nanoscale factory.

BMEN E4590 BioMems: cellular and molecular applications. 3 points.

Lect: 3.

Prerequisites: (MATH UN1201) and (BIOL UN2005) and (BIOL UN2006) and (CHEM UN3443) or (CHEM UN2545) or or equivalent. Chemistry.

Topics include biomicroelectromechanical, microfluidic, and lab-on-a-chip systems in biomedical engineering, with a focus on cellular and molecular applications. Microfabrication techniques, biocompatibility, miniaturization of analytical and diagnostic devices, high-throughput cellular studies, microfabrication for tissue engineering, and in vivo devices.

BMEN E4601 Cellular electricity. 3 points.

Lect: 2. Lab: 1.Not offered during 2018-19 academic year.

Bioelectricity of the cell membrane. Basis of cell resting voltage, voltage changes that lead to the action potential and electrical oscillations used in sensing systems. Laboratory includes building electronic circuits to measure capacitance of artificial membranes and ion pumping in frog skin.

BMEN E4737 Computer control of medical instrumentation. 3 points.

Lect: 2. Lab: 1.Not offered during 2018-19 academic year.

Prerequisites: Basic knowledge of the C programming language.

Acquisition and presentation of data for medical interpretation. Operating principles of medical devices: technology of medical sensors, algorithms for signal analysis, computer interfacing and programming, interface design. Laboratory assignments cover basic measurement technology, interfacing techniques, use of Labview software instrument interrogation and control, automated ECG analysis, ultrasonic measurements, image processing applied to x-ray images and CAT scans.

BMEN E4738 Transduction and acquisition of biomedical data. 3 points.

Lect: 2. Lab: 1.Not offered during 2018-19 academic year.

Data transduction and acquisition systems used in biomedicine. Assembly of bio-transducers and the analog/digital circuitry for acquiring electrocardiogram, electromyogram, and blood pressure signals. Each small group will develop and construct a working data acquisition board, which will be interfaced with a signal generator to elucidate the dynamics of timing constraints during retrieval of bio-data.

BMEN E4750 Sound and hearing. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (PHYS UN1401) and (MATH UN1105) and (MATH UN1106) PHYS C1401 and MATH V1105 - MATH V1106.

Introductory acoustics, basics of waves and discrete mechanical systems. The mechanics of hearing -- how sound is transmitted through the external and middle ear to the inner ear, and the mechanical processing of sound within the inner ear.

BMEN E4840 Functional Imaging for the Brain. 3 points.

Lect: 3. Lab: 1.

Prerequisites: (APMA E2101) and (APMA E4200) and (ELEN E3801) or instructor's permission.

Fundamentals of modern medical functional imaging. In depth exploration of functional magnetic resonance imaging (fMRI), arterial spin labeling (ASL), and positron emission tomography (PET). Human brain anatomy, physiology, and neurophysiological bases underlying each functional imaging. Statistical and digital signal processing methods specific for functional image analysis. Final cumulative project requiring coding in MATLAB, Python, R, or C.

BMEN E4894 Biomedical imaging. 3 points.

Lect: 3.

This course covers image formation, methods of analysis, and representation of digital images. Measures of qualitative performance in the context of clinical imaging. Algorithms fundamental to the construction of medical images via methods of computed tomography, magnetic resonance, and ultrasound. Algorithms and methods for the enhancement and quantification of specific features of clinical importance in each of these modalities.

BMEN E4895 Analysis and Quantification of Medical Images. 3 points.

Lect: 3.

Prerequisites: (BMEN E4894)
Corequisites: BMEN E4894

Novel methods of mathematical analysis applied to problems in medical imaging. Design requirements for screening protocols, treatment therapies, and surgical planning. Sensitivity and specificity in screening mammography and chest radiographs, computer aided diagnosis systems, surgical planning in orthopaedics, quantitative analysis of cardiac performance, functional magnetic resonance imaging, positron emission tomography, and echocardiography data.

BMEN E4898 Biophotonics. 3 points.

Lect: 3.

Prerequisites: (BMEN E4894) and (PHYS UN1403) or instructor's permission.

This course provides a broad-based introduction into the field of Biophotonics. Fundamental concepts of optical, thermal, and chemical aspects of the light-tissue interactions will be presented. The application of these concepts for medical therapy and diagnostics will be discussed. The course includes theoretical modeling of light-tissue interactions as well as optical medical instrument design and methods of clinical data interpretation.

BMEN E4999 Graduate Fieldwork. 1 point.

Prerequisites: Obtained internship and approval from faculty advisor. BMEN graduate students only.

Only for BMEN graduate students who need relevant work experience as part of their program of study. Final reports required. May not be taken for pass/fail credit or audited.

BMEN E6000 Graduate Special Topic. 3 points.

Lect: 3.

Current topics in biomedical engineering. Subject matter will vary by year. Instructors may impose prerequisites depending on the topic.

BMEN E6003 Computational modeling of physiological systems. 3 points.

Lect: 3.

Prerequisites: (BMEN E4001) and (BMEN E4002) and (APMA E4200) or equivalent.

Advanced computational modeling and quantitative analysis of selected physiological systems from molecules to organs. Selected systems are analyzed in depth with an emphasis on modeling methods and quantitative analysis. Topics may include cell signaling, molecular transport, excitable membranes, respiratory physiology, nerve transmission, circulatory control, auditory signal processing, muscle physiology, data collection and analysis.

BMEN E6005 Biomedical Innovation I. 3 points.

Lect: 3.

Prerequisites: Master's students only.

Project-based design experience for graduate students. Elements of design process, including need identification, concept generation, concept selection, and implementation. Development of design prototype and introduction to entrepreneurship and implementation strategies. Real-world training in biomedical design and innovation.

BMEN E6006 Biomedical Innovation II. 3 points.

Lect. 3.

Second semester of project-based design experience for graduate students. Elements of design process, with focus on skills development, prototype development and testing, and business planning. Real-world training in biomedical design, innovation, and entrepreneurship. 

BMEN E6301 Modeling of biological tissues with finite elements. 3 points.

Lect: 3.

Prerequisites: (MECE E6422) or (ENME E6315) or equivalent.

Structure-function relations and linear/nonlinear constitutive models of biological tissues: anisotropic elasticity, viscoelasticity, porous media theories, mechano-electrochemical models, infinitesimal and large deformations. Emphasis on the application and implementation of constitutive models for biological tissues into existing finite element software packages. Model generation from biomedical images by extraction of tissue geometry, inhomogeneity and anisotropy. Element-by-element finite element solver for large-scale image based models of trabecular bone. Implementation of tissue remodeling simulations in finite element models.

BMEN E6420 Advanced microscopy: fundamentals and applications. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (PHYS UN1401) and (PHYS UN1402) and (PHYS UN1403) or (PHYS UN1601) and (PHYS UN1602) and (PHYS UN2601) or (PHYS UN2801) and (PHYS UN2802) or equivalent (general Physics sequence).

Fundamentals of techniques including confocal, two-photon, atomic force and electron microscopy.  Application of methods to modern biomedical imaging targets. Analysis and interpretation of microscopy data. Enrollment beyond the cap must be completed using an add/drop form in consultation with class instructor.

BMEN E6500 Tissue and molecular engineering laboratory. 4 points.

Lect: 1. Lab: 4.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) or permission of instructor.

Hands-on experiments in molecular and cellular techniques, including fabrication of living engineered tissues. Covers sterile technique, culture of mammalian cells, microscopy, basic subcloning and gel electrophoresis, creation of cell-seeded scaffolds, and the effects of mechanical loading on the metabolism of living cells or tissues. Theory, background, and practical demonstration for each technique will be presented.

BMEN E6505 Advanced scaffold design and engineering complex tissues. 3 points.

Prerequisites: (BMEN E4501) or BMEN E4501 or equivalent.
Corequisites: BMEN E4001 or BMEN E4002

Advanced biomaterial selection and biomimetic scaffold design for tissue engineering and regenerative medicine. Formulation of bio-inspired design criteria, scaffold characterization and testing, and applications on forming complex tissues or organogenesis. Laboratory component includes basic scaffold fabrication, characterization and in vitro evaluation of biocompatibility. Group projects target the design of scaffolds for select tissue engineering applications.

BMEN E8001 Current Topics in nanobiotechnology and synthetic biology. 3 points.

Lect: 3.

Targeted toward graduate students; undergraduate student may participate with permission of the instructor. Review and critical discussion of recent literature in nanobiotechnology and synthetic biology. Experimental and theoretical techniques, critical advances. Quality judgments of scientific impact and technical accuracy. Styles of written and graphical communication, the peer review process.

BMEN E9100 Masters research. 1-6 points.

Candidates for the M.S. degree may conduct an investigation of some problem in biomedical engineering culminating in a thesis describing the results of their work. No more than 6 points in this course may be counted for graduate credit, and this credit is contingent upon the submission of an acceptable thesis.

BMEN E9500 Doctoral research. 1-6 points.

Doctoral candidates are required to make an original investigation of a problem in biomedical engineering, the results of which are presented in the dissertation.

BMEN E9700 Biomedical engineering seminar. 0 points.

0 pts. Sem: 1.

All matriculated graduate students are required to attend the seminar as long as they are in residence. No degree credit is granted. The seminar is the principal medium of communication among those with biomedical engineering interests within the University. Guest speakers from other institutions, Columbia faculty, and students within the Department who are advanced in their studies frequently offer sessions.

BMEN E9800 Doctoral research instruction. 3-12 points.

A candidate for the Eng.Sc.D. degree in biomedical engineering must register for 12 points of doctoral research instruction. Registration may not be used to satisfy the minimum residence requirement for the degree.

BMEN E9900 Doctoral dissertation. 0 points.

0 pts.

A candidate for the doctorate in biomedical engineering or applied biology may be required to register for this course in every term after the student's course work has been completed and until the dissertation has been accepted.

BMCH E3500 Transport in biological systems. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (CHEM UN3443) and (MATH UN2030) CHEM C3443 and MATH V2030.
Corequisites: BIOL C2005.

Convective and diffusive movement and reaction of molecules in biological systems.  Kinetics of homogeneous and heterogeneous reactions in biological environments.  Mechanisms arid models of transport across membranes.  Convective diffusion with and without chemical reaction.  Diffusion in restricted spaces.  Irreversible thermodynamic approaches to transport and reaction in biological systems.

BMCH E4500 Biological transport and rate processes. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (CHEM UN2443) and (APMA E2101)
Corequisites: BIOL UN2005

Convective and diffusive movement and reaction of molecules in biological systems. Kinetics of homogeneous and heterogeneous reactions in biological environments. Mechanisms and models of transport across membranes. Convective diffusion with and without chemical reaction. Diffusion in restricted spaces. Irreversible thermodynamic approaches to transport and reaction in biological systems. 

BMCH E4810 Artificial organs. 3 points.

Lect: 3.

Analysis and design of replacements for the heart, kidneys, and lungs. Specification and realization of structures for artificial organ systems.

BMEE E4030 Neural control engineering. 3 points.

Lect: 3.

Prerequisites: (ELEN E3801) ELEN E3801

Topics include: basic cell biophysics, active conductance and the Hodgkin-Huxley model, simple neuron models, ion channel models and synaptic models, statistical models of spike generation, Wilson-Cowan model of cortex, large-scale electrophysiological recording methods, sensorimotor integration and optimal state estimation, operant conditioning of neural activity, nonlinear modeling of neural systems, sensory systems: visual pathway and somatosensory pathway, neural encoding model: spike triggered average (STA) and spike triggered covariance (STC) analysis, neuronal response to electrical micro-stimulation, DBS for Parkinson's disease treatment, motor neural prostheses, and sensory neural prostheses.

BMEE E4400 Wavelet applications in biomedical image and signal processing. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (APMA E2101) or (APMA E3101) or equivalent.

An introduction to methods of wavelet analysis and processing techniques for the quantification of biomedical images and signals. Topics include: frames and overcomplete representations, multiresolution algorithms for denoising and image restoration, multiscale texture segmentation and classification methods for computer aided diagnosis.

BMEE E4740 Bioinstrumentation. 3 points.

Lect: 1. Lab: 3.

Prerequisites: (ELEN E1201) and (COMS W1005)

Hands-on experience designing, building, and testing the various components of a benchtop cardiac pacemaker. Design instrumentation to measure biomedical signals as well as to actuate living tissues. Transducers, signal conditioning electronics, data acquisition boards, the Arduino microprocessor, and data acquisition and processing using MATLAB will be covered. Various devices will be discussed throughout the course, with laboratory work focusing on building an emulated version of a cardiac pacemaker.

BMEE E6030 Neural modeling and neuroengineering. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (ELEN E3801) and (APMA E2101) or (APMA E3101) or equivalent, or instructor's permission.

Engineering perspective on the study of multiple levels of brain organization, from single neurons to cortical modules and systems. Mathematical models of spiking neurons, neural dynamics, neural coding, and biologically-based computational learning. Architectures and learning principles underlying both artificial and biological neural networks. Computational models of cortical processing, with an emphasis on the visual system. Applications of principles in neuroengineering; neural prostheses, neuromorphic systems and biomimetics. Course will include a computer simulation laboratory. Lab required.

BMEB W4020 Computational neuroscience: circuits in the brain. 3 points.

Lect: 3.

Prerequisites: (ELEN E3801) or (BIOL UN3004)

The biophysics of computation: modeling biological neurons, the Hodgkin-Huxley neuron, modeling channel conductances and synapses as memristive systems, bursting neurons and central pattern generators, I/O equivalence and spiking neuron models.  Information representation and neural encoding: stimulus representation with time encoding machines, the geometry of time encoding, encoding with neural circuits with feedback, population time encoding machines.  Dendritic computation: elements of spike processing and neural computation, synaptic plasticity and learning algorithms, unsupervised learning and spike time-dependent plasticity, basic dendritic integration.  Projects in MATLAB.

BMME E4702 Advanced musculoskeletal biomechanics. 3 points.

Lect: 2.5. Lab: 0.5.Not offered during 2018-19 academic year.

Advanced analysis and modeling of the musculoskeletal system. Topics include advanced concepts of 3-D segmental kinematics, musculoskeletal dynamics, experimental measurements of joint kinematics and anatomy, modeling of muscles and locomotion, multibody joint modeling, introduction to musculoskeletal surgical simulations.

CBMF W4761 Computational Genomics. 3 points.

Lect: 3.

Prerequisites: Working knowledge of at least one programming language, and some background in probability and statistics.

Computational techniques for analyzing genomic data including DNA, RNA, protein and gene expression data. Basic concepts in molecular biology relevant to these analyses. Emphasis on techniques from artificial intelligence and machine learning. String-matching algorithms, dynamic programming, hidden Markov models, expectation-maximization, neural networks, clustering algorithms, support vector machines. Students with life sciences backgrounds who satisfy the prerequisites are encouraged to enroll. 

CHBM E4321 The genome and the cell. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (BIOL UN2005) and (MATH UN2030)

The utility of genomic information lies in its capacity to predict the behavior of living cells in physiological, developmental, and pathological situations. The effect of variations in genome structure between individuals within a species, including those deemed healthy or diseased, and among species, can be inferred statistically by comparisons of sequences with behaviors, and mechanistically, by studying the action of molecules whose structure is encoded within the genome. This course examines known mechanisms that elucidate the combined effect of environmental stimulation and genetic makeup on the behavior of cells in homeostasis, disease states, and during development, and includes assessments of the probable effect of these behaviors on the whole organism.  Quantitative models of gene translation and intracellular signal transduction will be used to illustrate switching of intracellular processes, transient and permanent gene activation, and cell commitment, development, and death.

EEBM E6020 Methods of computational neuroscience. 4.5 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (BMEB W4020)

Formal methods in computational neuroscience including methods of signal processing, communications theory, information theory, systems and control, system identification and machine learning. Molecular models of transduction pathways. Robust adaptation and integral feedback. Stimulus representation and groups. Stochastic and dynamical systems models of spike generation. Neural diversity and ensemble encoding. Time encoding machines and neural codes. Stimulus recovery with time decoding machines. MIMO models of neural computation. Synaptic plasticity and learning algorithms. Major project(s) in MATLAB.

EEBM E6090 Topics in computational neuroscience and neuroengineering. 3 points.

Lect: 2.

Prerequisites: The instructor's permission.

EEBM E6091 Topics in computational neuroscience and neuroengineering. 3 points.

Lect: 2.

Prerequisites: The instructor's permission.

Topic: Devices and Analysis for Neural Circuits.

EEBM E6092 Topics in computational neuroscience and neuroengineering. 3 points.

Not offered during 2018-19 academic year.

Prerequisites: The instructor's permission.

Topic: Big Data in Neurscience.

EEBM E6099 Topics in computational neuroscience and neuroengineering: Brian/Computer Interfaces. 3 points.

Lect: 2.

Prerequisites: The instructor's permission.

EEBM E9070 Seminar in computational neuroscience and neuroengineering. 3 points.

Lect: 3.

Prerequisites: (BMEB W4020) or permission of instructor.

Drosophila connectomics. Detailed description of the fruit fly's olfactory and vision systems. Parallel processing on GPSs. 

APBM E4650 Anatomy for physicists and engineers. 3 points.

Lect: 3.

Prerequisites: Engineering or physics background

Systemic approach to the study of the human body from a medical imaging point of view: skeletal, respiratory, cardiovascular, digestive, and urinary systems, breast and women's issues, head and neck, and central nervous system. Lectures are reinforced by examples from clinical two- and three-dimensional and functional imaging (CT, MRI, PET, SPECT, U/S, etc.).

ECBM E3060 Introduction to genomic information science and technology. 3 points.

Lect: 3.

Introduction to the information system paradigm of molecular biology. Representation, organization, structure, function and manipulation of the biomolecular sequences of nucleic acids and proteins. The role of enzymes and gene regulatory elements in natural biological functions as well as in biotechnology and genetic engineering. Recombination and other macromolecular processes viewed as mathematical operations with simulation and visualization using simple computer programming. This course shares lectures with ECBM E4060, but the work requirements differ somewhat.

ECBM E4040 Neural networks and deep learning. 3 points.

Lect: 3.

Prerequisites: (BMEB W4020) or (BMEE E4030) or (ECBM E4090) or (EECS E4750) or (COMS W4771) or equivalent.

Developing features & internal representations of the world, artificial neural networks, classifying handwritten digits with logistics regression, feedforward deep networks, back propagation in multilayer perceptrons, regularization of deep or distributed models, optimization for training deep models, convolutional neural networks, recurrent and recursive neural networks, deep learning in speech and object recognition.

ECBM E4060 Introduction to Genomic Information. 3 points.

Lect: 3.

Introduction to the information system paradigm of molecular biology. Representation, organization, structure, function, and manipulation of the biomolecular sequences of nucleic acids and proteins. The role of enzymes and gene regulatory elements in natural biological functions as well as in biotechnology and genetic engineering. Recombination and other macromolecular processes viewed as mathematical operations with simulation and visualization using simple computer programming. 

ECBM E4090 Brain computer interfaces (BCI) laboratory. 3 points.

Lect: 2. Lab: 3.

Prerequisites: (ELEN E3801)

Hands on experience with basic neural interface technologies. Recording EEG (electroencephalogram) signals using data acquisition systems (non-invasive, scalp recordings). Real-time analysis and monitoring of brain responses. Analysis of intention and perception of external visual and audio signals.

ECBM E6040 Neural networks and deep learning research. 3 points.

Lect: 3.

Prerequisites: (ECBM E4040) or equivalent.

Regularized autoencoders, sparse coding and predictive sparse decomposition, denoising autoencoders, representation learning, manifold perspective on representation learning, structured probabilistic models for deep learning, Monte Carlo methods, training and evaluating models with intractable partition functions, restricted Boltzmann machines, approximate inference, deep belief networks, deep learning in speech and object recognition.

ECBM E6070 Topics in neuroscience & deep learning. 3 points.

Lect: 2. Not offered during 2018-19 academic year.

Prerequisites: Instructor's permission.

Selected advanced topics in neuroscience & deep learning. Content varies from year to year, and different topics rotate through the course numbers 6070 to 6079. Current topic for 6070: Fruit Fly Brain as Neuroinformation Processor.

MEBM E4439 Modeling and identification of dynamic systems. 3 points.

Prerequisites: (APMA E2101) and (ELEN E3801) or instructor's permission.
Corequisites: EEME E3601

Generalized dynamic system modeling and simulation. Fluid, thermal, mechanical, diffusive, electrical, and hybrid systems are considered. Nonlinear and high order systems. System identification problem and Linear Least Squares method. State-space and noise representation. Kalman filter. Parameter estimation via prediction-error and subspace approaches. Iterative and bootstrap methods. Fit criteria. Wide applicability: medical, energy, others. MATLAB and Simulink environments.

MEBM E4702 Advanced musculoskeletal biomechanics. 3 points.

Lect: 3.

Advanced analysis and modeling of the musculoskeletal system. Topics include advanced concepts of 3-D segmental kinematics, musculoskeletal dynamics, experimental measurements of joints kinematics and anatomy, modeling of muscles and locomotion, multibody joint modeling, introduction to musculoskeletal surgical simulations.

MEBM E4703 Molecular mechanics in biology. 3 points.

Lect: 3.

Prerequisites: (ENME E3105) and (APMA E2101) or instructor's permission.

Mechanical understanding of biological structures including proteins, DNA and RNA in cells and tissues. Force response of proteins and DNA, mechanics of membranes, biophysics of molecular motors, mechanics of protein-protein interactions.  Introduction to modeling and simulation techniques, and modern biophysical techniques such as single molecule FRET, optical traps, AFM, and super-resolution imaging, for understanding molecular mechanics and dynamics.

MEBM E4710 Morphogenesis: Shape and structure in biological materials.

Prerequisites: Courses in mechanics, thermodynamics, and ordinary differential equations (for example, ENME E3113, MECE E3301 and MATH UN3027) at the undergraduate level or instructor's permission.

Introduction to how shape and structure are generated in biological materials using an engineering approach that emphasizes the application of fundamental physical concepts to a diverse set of problems. Mechanisms of pattern formation, self-assembly, and self-organization in biological materials, including intracellular structures, cells, tissues, and developing embryos. Structure, mechanical properties, and dynamic behavior of these materials. Discussion of experimental approaches and modeling. Course uses textbook materials as well as a collection of research papers.

MEBM E6310 Mixture theories for biological tissues, I. 3 points.

Lect: 3.Not offered during 2018-19 academic year.

Prerequisites: (MECE E6422) and (APMA E4200) or equivalent.

Development of governing equations for mixtures with solid matrix, interstitial fluid, and ion constituents. Formulation of constitutive models for biological tissues. Linear and nonlinear models of fibrillar and viscoelastic porous matrices. Solutions to special problems, such as confined and unconfined compression, permeation, indentation and contact, and swelling experiments.

MEBM E6311 Mixture theories for biological tissues, II. 3 points.

Lect: 3.

Prerequisites: (MECE E6422) and (APMA E4200) or equivalent.

Development of governing equations for mixtures with solid matrix, interstitial fluid, and ion constituents. Formulation of constitutive models for biological tissues. Linear and nonlinear models of fibrillar and viscoelastic porous matrices. Solutions to special problems, such as confined and unconfined compression, permeation, indentation and contact, and swelling experiments.