Courses

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

Not offered during 2023-2024 academic year.

BMEN E1001 ENGINEERING IN MEDICINE. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 health care system. Current trends in biomedical research

BMEN E2300 BIOMECHANICS TRACK. 0.00 points.

BMEN E2400 BIOSIGNAL ＆ BIOMED IMAG TRACK. 0.00 points.

BMEN E2500 CELLULAR ＆ TISSUE ENGIN TRACK. 0.00 points.

BMEN E3010 BIOMEDICAL ENGINEERING I. 3.00 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. 3.00 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 E3150 THE CELL AS A MACHINE. 3.00 points.

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 E3320 FLUID BIOMECHANICS. 3.00 points.

BMEN E3500 BIOL TRANSPORT ＆ RATE PROCESS. 3.00 points.

BMEN E3810 BIOMEDICAL ENGINEERING LAB I. 3.00 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 LAB II. 3.00 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 E3830 BIOMEDICAL ENGINEERING LAB III. 3.00 points.

BMEN E3899 Research Training. 0.00 points.

Research training course. Recommended in preparation for laboratory related research

BMEN E3910 BIOMEDICAL ENGINEERING DESIGN. 4.00 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 ENGIN DESIGN II. 4.00 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 ENGIN. 1.00-3.00 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. 1.00-2.00 points.

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 IN BIOMEDICAL ENGINEERING. 3.00 points.

Lect: 3.

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

BMEN E4001 QUANTITATIVE PHYSIOLOGY I. 3.00 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 QUANT PHYSIOLOGY II:ORGAN SYST. 3.00 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 BIOMEDICL ENGINEERS. 3.00 points.

Lect: 2.Not offered during 2023-2024 academic year.

Prerequisites: Senior status in biomedical engineering or the instructor's permission.
Covers a wide range of ethical 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 ELECTROPHYS OF HUM MEMORY * NAVIGATION. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 E4100 BMakE – Biomedical Device Design ＆ Fabrication. 3.00 points.

Hands-on course. Covers medical device design to develop basic fabrication skills. Includes central project theme, i.e., through individual modules, students create different components of a biomedical device. First offering focuses on creation of a device pertinent for COVID-19: a mechanical ventilator. The mechanical ventilator combines physics (fluid dynamics, pressure-flow relationships) with fabrication, (bio)materials, sensing, signal acquisition and processing, and controls. As a highly advanced, life-supporting device, its functional aspects can be decomposed into modules of this course to create a benchtop ventilator

BMEN E4103 ANATOMY OF THORAZ ＆ ABDOMEN. 2.00 points.

Lect: 2.

Prerequisites: Graduate standing in Biomedical Engineering.
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 LAB:THORAX ＆ ABDOMEN. 2.00 points.

Lect: 2.

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

BMEN E4105 ANATOMY OF THE EXTREMITIES. 2.00 points.

Lect: 2.

Prerequisites: Graduate standing in Biomedical Engineering.
Designed for 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 LAB: EXTREMITIES. 2.00 points.

Lab: 2.

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

BMEN E4107 ANATOMY OF THE HEAD ＆ NECK. 2.00 points.

Lect: 2.

Prerequisites: graduate standing in Biomedical Engineering.
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 LAB: HEAD ＆ NECK. 2.00 points.

Lab: 2.

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

BMEN E4110 BIOSTATISTICS FOR ENGINEERS. 4.00 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. 3.00 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 DRIVING FORCES OF BIOLOGICAL SYSTEMS. 4.00 points.

Lect: 4.

Prerequisites: (CHEM UN1404) and (MATH UN1202)
Corequisites: BIOL UN2005
Introduction to the statistical mechanics and thermodynamics of biological systems, with a focus on connecting 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 E4300 SOLID BIOMECHANICS. 3.00 points.

BMEN E4301 STRUCTURE/MECH ＆ ADAP OF BONE. 3.00 points.

Lect: 3.Not offered during 2023-2024 academic year.

Introduction to structure, physiology of skeletal bones; linear elastic properties of cortical and trabecular bones; 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 TIS. 3.00 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 muscoskeletal system. Topics include mechanical properties, applied viscoelasticity theory, and biology of orthopaedic soft tissues

BMEN E4305 CARDIAC MECHANICS. 3.00 points.

Lect: 3.Not offered during 2023-2024 academic year.

Prerequisites: (BMEN E4310) and (BMEN E4320) or equivalents.
Cardiac anatomy, passive myocardial constitutive properties, electrical activation, ventricular-vascular coupling, invasive and noninvasive measures of regional and global function, models for predicting ventricular wall stress. Alterations in muscle properties and ventricular function resulting from myocardial infarction, heart failure, and felt ventricular assist

BMEN E4310 SOLID BIOMECHANICS. 3.00 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. 3.00 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. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 E4400 WAVELET APPL-BIOMED IMAGE PROC. 3.00 points.

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

BMEN E4410 PRIN OF ULTRASOUND IN MEDICINE. 3.00 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 SIGNAL MODELING. 3.00 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 PRIN OF MAG RESONANCE IMAGING. 3.00 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 examines both theory and experimental design techniques

BMEN E4440 PHYSIOLOGICAL CONTROL SYSTEM. 3.00 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 ＆ CRAN TISSUE ENG. 3.00 points.

Lect: 3.Not offered during 2023-2024 academic year.

Prerequisites: (MSAE E3103) and (BMEN E4210) and (BMEN E4501) or equivalent.
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 E4460 Deep Learning in Biomedical Imaging. 3.00 points.

Pre-requisites: MATH UN 1202 and APMA E2101. Background in Python programming is highly recommended.Not offered during 2023-2024 academic year.

Introduction to methods in deep learning, with focus on applications to quantitative problems in biomedical imaging and Artificial Intelligence (AI) in medicine. Network models: Deep feedforward networks, convolutional neural networks and recurrent neural networks. Deep autoencoders for denoising. Segmentation and classification of biological tissues and biomarkers of disease. Theory and methods lectures will be accompanied with examples from biomedical image including analysis of neurological images of the brain (MRI), CT images of the lung for cancer and COPD, cardiac ultrasound. Programming assignments will use tensorflow / Pytorch and Jupyter Notebook. Examinations and a final project will also be required

BMEN E4470 Deep Learning for Biomedical Signal Processing. 3.00 points.

Introduction to methods in deep learning, focus on applications to biomedical signals and sequences. Review of traditional methods for analysis of signals and sequences. Temporal convolutional neural networks and recurrent neural networks. Long-short term memory (LSTM) models and deep state-space models. Theory and methods lectures accompanied with examples from biomedical signal and sequence analysis, including analysis of electroencephalogram (EEG), electrocardiogram (ECG/EKG), and genomics. Programming assignments use tensorflow/keras. Exams and final project required

BMEN E4480 Statistical machine learning for genomics. 3.00 points.

Prerequisites: Intro to Applied Mathematics (APMA E2101), Calculus IV (MATH UN1202), Linear Algebra (MATH UN2010). Proficiency in Python/R programming. Background in probability/statistics. Intro to Machine Learning (COMS W4771) is recommended.

Prerequisites: see notes re: points
Introduction to statistical machine learning methods using applications in genomic data and in particular high-dimensional single-cell data. Concepts of molecular biology relevant to genomic technologies, challenges of highdimensional genomic data analysis, bioinformatics preprocessing pipelines, dimensionality reduction, unsupervised learning, clustering, probabilistic modeling, hidden Markov models, Gibbs sampling, deep neural networks, gene regulation. Programming assignments and final project will be required

BMEN E4490 Magnetic Resonance Spectroscopy: A Window to the Living Brain. 3.00 points.

Introduction to use of magnetic resonance spectroscopy (MRS) with focus on brain. Covers all aspects of in vivo MRS from theory to experiment, from data acquisition to the derivation of metabolic signatures, from study design to clinical interpretation. Includes theoretical concepts, hands-on training in MRS data literacy and direct experimental experience using a 3T MR scanner

BMEN E4500 Functional Genomics: Methods and Applications. 3.00 points.

Introduces approaches for the functional genomic analysis of biological systems and their use to define genotype-phenotype relationships. Genetic variation, gene expression and regulation at the epigenome, chromatin organization level, and link between gene and protein expression covered. Case studies covered: study of cancer and cancer-associated processes, neuro-biology, and organismal development. The presented methods study these events at the genome, epigenome, transcriptome, and proteome levels.Approaches that increase the resolution of functional genomic assays to the level of individual cells, spatial profiling, integration with genetic and chemical screening methods, and their application to chemical genomic approaches also studied. Programming assignments and a final project required

BMEN E4501 Biomaterials and Scaffold Design. 3.00 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 ngineered grafts. Materials structuralfunctional 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 arameters critical in the design and selection of biomaterials for biomedical applications

BMEN E4502 TISSUE ENGINEERING II. 3.00 points.

BMEN E4510 TISSUE ENGINEERING. 3.00 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:PRIN GENETIC CIRCUITS. 3.00 points.

Not offered during 2023-2024 academic year.

Prerequisites: (BIOL UN2005) and (MATH UN2030) or (APMA E2101)
Basic principles of synthetic biology and 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. Knowledge of biology, ordinary differential equations, and MATLAB will be assumed. Intended for advanced undergraduate and graduate students

BMEN E4530 DRUG AND GENE DELIVERY. 3.00 points.

Prerequisites: BME I (BMEN E3010)
Application of polymers and other materials in drug and gene delivery, with focus on recent advances in field. Basic 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 format of assay responding to open-ended question. Term paper and 30-minute PowerPoint presentation required at end of semester

BMEN E4540 BIOELECTROCHEMISTRY. 3.00 points.

Lect: 3.Not offered during 2023-2024 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/NANO STRUCT CELL ENG. 3.00 points.

Lect: 3.Not offered during 2023-2024 academic year.

Prerequisites: (BIOL UN2005) and (BIOL UN2006) or BIOL C2005 and BIOL C2006 or equivalent
Design, fabrication, and application of micro-/nanostructured systems for cell engineering. Recognition and response of cells to spatial aspects of their extracellular environment. Focus on neural, cardiac, coculture, and stem cell systems. Molecular complexes at the nanoscale

BMEN E4560 DYNAMICS OF BIOLOGCL MEMBRANES. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 SCI ＆ ENGIN OF BODY FLUIDS. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 FOUND OF NANOBIOSCI/NANOBIOTECH. 3.00 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. Includes discussion of intermolecular forces and bonding, of kinetics and thermodynamics of self-assembly, of nanoscale transport processes arising from actions of biomolecular motors, computation and control in biomolecular systems, and of mitochondrium as an example of a nanoscale factory

BMEN E4590 BIOMEMS:CELL/MOLECULAR APPLIC. 3.00 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. 3.00 points.

Lect: 2. Lab: 1.Not offered during 2023-2024 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. Lab required

BMEN E4738 TRANSDUCTN/ACQ OF BIOMED DATA. 3.00 points.

Lect: 2. Lab: 1.Not offered during 2023-2024 academic year.

Data transduction and acquisition systems used in biomedicine. Assembly of biotransducers 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 biodata. Lab required

BMEN E4750 SOUND AND HEARING. 3.00 points.

Lect: 3.

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 E4810 ARTIFICIAL ORGANS. 3.00 points.

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

BMEN E4840 FUNCTIONAL IMAGING BRAIN. 3.00 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. 3.00 points.

Lect: 3.

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. 3.00 points.

Lect: 3.

Prerequisites: (BMEN E4894) and (PHYS UN1403) or instructor's permission.
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 E4899 Research Training. 0.00 points.

Research training course. Recommended in preparation for laboratory related research

BMEN E4999 FIELDWORK. 1.00-2.00 points.

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 E6001 TOPICS IN BIOMED NANOTECHNOLOGY. 3.00 points.

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 E6003 COMP MODELING-PHYSIOL SYSTEMS. 3.00 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 DESIGN II. 3.00 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 E6007 LAB-TO-MARKET. 3.00 points.

Introduction to and application of commercialization of biomedical innovations. Topics include needs clarification, stakeholder analysis, market analysis, value proposition, business models, intellectual property, regulatory, and reimbursement. Development of path-to-market strategy and pitch techniques

BMEN E6301 MODELING OF BIOL TISS WITH FEM. 3.00 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 E6410 Principles and Practices of In Vivo Magnetic Resonance Spectroscopy. 3.00 points.

Prerequisites: Quantitative Physiology I or II
Magnetic resonance spectroscopy (MRS) allows the detection and quantification of chemical compounds from localized regions in living tissue, e.g., the brain, in a noninvasive fashion. It thereby provides a powerful tool to assess key aspects of brain metabolism and function. The repertoire of measurable compounds along with the quantitative character of the derived information makes MRS a versatile tool for the identification of clinical conditions, for longitudinal patient monitoring and for treatment control and monitoring of virtually all disorders with a metabolic signature. This educational course comprises all aspects of in vivo MRS from theory to experiment, from data acquisition to the derivation of metabolic signatures, and from study design to clinical interpretation, with special focus on applications in the human brain. Anyone interested in gaining an understanding of MRS techniques, their potential and the limitations of their application in vivo will find this course useful. The course bridges the gap between theoretical concepts, hands-on training in MRS data literacy and direct experimental experience on a human 3T MR scanner. This combined academic course and practical “boot-camp” will provide novices in MRS the requisite know-how for future engagement in MRS research and diagnostics

BMEN E6420 ADV MICROSCOPY APPLICATIONS. 3.00 points.

Lect: 3.Not offered during 2023-2024 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/MOLECULAR ENGI LAB. 4.00 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. Lab required

BMEN E6505 Advanced Biomaterials for Tissue Engineering. 3.00 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 E6510 STEM CELL, GENOME ENG ＆ REGEN MED. 3.00 points.

Lect: 3.

Prerequisites: (BMEN E4001) or (BMEN E4002) and Biology, Cell Biology
General lectures on stem cell biology followed by student presentations and discussion of the primary literature. Themes presented include: basic stem cell concepts; basic cell and molecular biological characterization of endogenous stem cell populations; concepts related to reprogramming; directed differentiation of stem cell populations; use of stem cells in disease modeling or tissue replacement/repair; clinical translation of stem cell research

BMEN E8001 TOPICS IN NANOBIOTCEHNOLOGY. 3.00 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. 1.00-6.00 points.

Candidates for the M.S. degree may conduct an investigation of some problem in biomedical engineering. No more than 6 points in this course may be counted for graduate credit

BMEN E9500 DOCTORAL RESEARCH. 1.00-6.00 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. 0.00 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. 3.00-12.00 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. 0.00 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 students course work has been completed and until the dissertation has been accepted

BMCH E3500 BIOL TRANSPORT ＆ RATE PROCESS. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 BIOL TRANSPORT ＆ RATE PROCESS. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 hetergeneous 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 ARTIFICAL ORGANS. 3.00 points.

Lect: 3.

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

BMEE E4030 NEURAL CONTROL ENGINEERING. 3.00 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 electrohysiological recording methods, sensorimotor integration and optimal state estimation, operant conditioning of neural activity, nonlinear modelling 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 2023-2024 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. 3.00 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 ＆ NEUROENGIN. 3.00 points.

Lect: 3.Not offered during 2023-2024 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 includes 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 ADV MUSCULOSKELETAL BIOMECHNCS. 3.00 points.

Lect: 2.5. Lab: 0.5.Not offered during 2023-2024 academic year.

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

CBMF W4761 COMPUTATIONAL GENOMICS. 3.00 points.

Lect: 3.

Prerequisites: Working knowledge of at least one programming language, and some background in probability and statistics.
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 2023-2024 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 COMPUT NEUROSCIENCE. 4.50 points.

Lect: 3.Not offered during 2023-2024 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 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Lect: 2.

Prerequisites: The instructor's permission.
Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090-6099

EEBM E6091 TPCS IN COMP NEUROSCI/ENGINEERING. 3.00 points.

Lect: 2.

Prerequisites: The instructor's permission.
Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090-6099. Topic: Devices and Analysis for Neural Circuits

EEBM E6092 TOPICS IN COMP NEUROSI ＆ ENG. 3.00 points.

Not offered during 2023-2024 academic year.

Prerequisites: The instructor's permission.
Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6093 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6094 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6095 TOPICS IN COMP NEUROSI ＆ ENG. 3.00 points.

Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6096 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6097 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6098 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Selected advanced topics in computational neuroscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090 to 6099

EEBM E6099 TPCS:COMPUT NEUROSCI/NEUROENGI. 3.00 points.

Lect: 2.

Prerequisites: The instructor's permission.
Selected advanced topics in computational neurscience and neuroengineering. Content varies from year to year, and different topics rotate through the course numbers 6090-6099

EEBM E9070 SEM IN COMP NEURO SCI＆NEUROENGINEERING. 3.00 points.

Lect: 3.

Prerequisites: (BMEB W4020) or permission of instructor.
Study of recent developments in computational neuroscience and neuroengineering

APBM E4650 ANATOMY FOR PHYSICISTS ＆ ENGR. 3.00 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 womens 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 INTRO-GENOMIC INFO SCI ＆ TECH. 3.00 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 NETWRKS ＆ DEEP LEARNING. 3.00 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 INTRO-GENOMIC INFO SCI ＆ TECH. 3.00 points.

Lect: 3.

Introduction to computational biology with emphasis on genomic data science tools and methodologies for analyzing data, such as genomic sequences, gene expression measurements and the presence of mutations. Applications of machine learning and exploratory data analysis for predicting drug response and disease progression. Latest technologies related to genomic information, such as single-cell sequencing and CRISPR, and the contributions of genomic data science to the drug development process

ECBM E4070 Computing with Brain Circuits of Model Organisms. 3.00 points.

Building the functional map of the fruit fly brain. Molecular transduction and spatio-temporal encoding in the early visual system. Predictive coding in the Drosophila retina. Canonical circuits in motion detection. Canonical navigation circuits in the central complex. Molecular transduction and combinatorial encoding in the early olfactory system. Predictive coding in the antennal lobe. The functional role of the mushroom body and the lateral horn. Canonical circuits for associative learning and innate memory. Projects in Python

ECBM E4090 BRAIN COMPUTER INTERFACES LAB. 3.00 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 E6020 METHODS COMP NEUROSCIENCE. 3.00 points.

ECBM E6040 NEUR NET ＆ DEEP LEAR RSRCH. 3.00 points.

Lect: 3.

Prerequisites: (ECBM E4040) or ECBM E4040 or the 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 TPC NEUROSCI ＆ DEEP LEARN. 3.00 points.

Lect: 2. Not offered during 2023-2024 academic year.

Prerequisites: Instructor's permission.
Selected advanced topics in neuroscience and deep learning. Content varies from year to year, and different topics rotate through the course numbers 6070 to 6079

MEBM E4439 MODELING ＆ ID OF DYNAMIC SYST. 3.00 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 E4440 Physiological Controls. 3.00 points.

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

MEBM E4703 MOLECULAR MECHANICS IN BIOLOGY. 3.00 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 superresolution imaging, for understanding molecular mechanics and dynamics

MEBM E4710 MORPHOGENESIS:BIOL MAT SHP/STR. 3.00 points.

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 engineering approach emphasizing 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 collection of research papers

MEBM E6311 MIXT THEORIES FOR BIOL TISSUES. 3.00 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