Biomedical Engineering - Carnegie Mellon University

Margaret Morrison

Graduate Course Catalog

Graduate-Level Biomedical Engineering Courses

42-611/27-709 Engineering Biomaterials | 12 units | Fall
Syllabus: 42-611
This course will cover structure-processing-property relationships in biomaterials for use in medicine. This course will focus on quantitative aspects of biomaterials design. Topics of study include surfaces, thermodynamics, receptor-binding kinetics, quantitative analysis of cell behavior, and transport phenomena. This course will discuss practical applications of these materials in medical devices, drug delivery, tissue engineering, biosensors, etc. This course is a project-based option for graduate students that is taught concurrently with 42-411.
Pre-requisite: Thermodynamics (06-221, 24-221, or 27-215 equivalent), graduate status in CIT or permission of instructor.

42-612/27-520 Tissue Engineering | 12 units | Spring
Syllabus: 42-612
This course will train students in advanced cellular and tissue engineering methods that apply physical, mechanical and chemical manipulation of materials in order to direct cell and tissue function. Students will learn the techniques and equipment of bench research including cell culture, immunofluorescent imaging, soft lithography, variable stiffness substrates, application/measurement of forces and other methods. Students will integrate classroom lectures and lab skills by applying the scientific method to develop a unique project while working in a team environment, keeping a detailed lab notebook and meeting mandated milestones. Emphasis will be placed on developing the written and oral communication skills required of the professional scientist. The class will culminate with a poster presentation session based on class projects. May count as practicum for practicum-option MS.
Pre-requisite: Cell biology and biomaterials, or permission of instructor. [Top]

42-613/27-570 Molecular and Micro-Scale Polymeric Biomaterials in Medicine | 9 units | Spring, every other year
This course will cover aspects of polymeric biomaterials in medicine from molecular principles to device scale design and fabrication. Topics include the chemistry, characterization, and processing of synthetic polymeric materials; cell-biomaterials interactions including interfacial phenomena, tissue responses, and biodegradation mechanisms; aspects of polymeric micro-systems design and fabrication for applications in medical devices. Recent advances in these topics will also be discussed.
Pre-requisite: Organic Chemistry (09-217, 09-219 or equivalent). [Top]

42-620 Engineering Molecular Cell Biology | 12 Units | Fall
Cells are not only basic units of living organisms but also fascinating engineering systems that exhibit amazing functionality, adaptability, and complexity. Applying engineering perspectives and approaches to study molecular mechanisms of cellular processes plays a critical role in the development of contemporary biology. At the same time, understanding the principles that govern biological systems provides critical insights into the development of engineering systems, especially in the micro- and nano-technology. The goal of this course is to provide basic molecular cell biology for engineering students with little or no background in cell biology, with particular emphasis on the application of quantitative and system perspectives to basic cellular processes. Course topics include the fundamentals of molecular biology, the structural and functional organization of the cell, the cytoskeleton and cell motility, the mechanics of cell division, and cell-cell interactions.
Pre-requisite: Differential Equations; knowledge of modern biology is suggested but not required. Proficiency in basic computation such as MATLAB programming is expected.

42-624 Biological Transport and Drug Delivery | 9 units | Spring
Analysis of transport phenomena in life processes on the molecular, cellular, organ and organism levels and their application to the modeling and design of targeted or sustained release drug delivery technologies. Coupling of mass transfer and reaction processes will be a consistent theme as they are applied to rates of receptor-mediated solute uptake in cells, drug transport and biodistribution, and drug release from delivery vehicles. Design concepts underlying new advances in nanomedicine will be described.
Pre-requisite: Mathematical Methods (06-262 equivalent) or Differential Equations (21-260 equivalent). [Top]

42-630/18-690 Introduction to Neuroscience for Engineers | 12 units | Spring
The first half of the course will introduce engineers to the neurosciences from the cellular level to the structure and function of the central nervous system (CNS) vis-a-vis the peripheral nervous system (PNS) and include a study of basic neurophysiology; the second half of the course will review neuroengineering methods and technologies that enable study of and therapeutic solutions for diseases or damage to the CNS. A goal of this course is to provide a taxonomy of neuroengineering technologies for research or clinical application in the neurosciences.
Pre-requisites: Graduate standing or permission of the instructor. [Top]

42-631 Neural Data Analysis | 9 units | Fall
The vast majority of behaviorally relevant information is transmitted through the brain by neurons as trains of action potentials. How can we understand the information being transmitted? This class will cover the basic engineering and statistical tools in common use for analyzing neural spike train data, with an emphasis on hands-on application. Topics will include neural spike train statistics, estimation theory (MLE, MAP), signal detection theory (d-prime, ROC analysis), information theory (entropy, mutual information, neural coding theories, spike-distance metrics), discrete classification (naïve Bayes), continuous decoding (PVA, OLE, Kalman), and white-noise analysis. Each topic covered will be linked back to the central ideas from undergraduate probability, and each assignment will involve actual analysis of neural data, either real or simulated, using Matlab. This class is meant for upper-level undergraduates or beginning graduate students, and is geared to the engineer who wants to learn the neurophysiologist's toolbox and the neurophysiologist who wants to learn new tools.
Pre-requisites: Undergraduate probability (36-217 or 36-225, or equivalent). [Top]

42-632/18-698 Neural Signal Processing | 12 units | Spring
Syllabus: 42-632
The brain is among the most complex systems ever studied. Underlying the brain's ability to process sensory information and drive motor actions is a network of 10^11 neurons, each making 10^3 connections with other neurons. Modern statistical and machine learning tools are needed to interpret the plethora of neural data being collected, both for (1) furthering our understanding of how the brain works, and (2) designing biomedical devices that interface with the brain. This course will cover a range of statistical methods and their application to neural data analysis. The statistical topics include latent variable models, dynamical systems, point processes, dimensionality reduction, Bayesian inference, and spectral analysis. The neuroscience applications include neural decoding, firing rate estimation, neural system characterization, sensorimotor control, spike sorting, and field potential analysis.
Pre-requisites: Introductory probability theory and random variables; introductory linear algebra. No prior knowledge of neuroscience is needed. [Top]

42-640/24-658 Image-Based Computational Modeling and Analysis | 12 units | Spring
Syllabus: 42-640
Biomedical modeling and visualization play an important role in mathematical modeling and computer simulation of real/artificial life for improved medical diagnosis and treatment. This course integrates mechanical engineering, biomedical engineering, computer science, and mathematics together. Topics to be studied include medical imaging, image processing, geometric modeling, visualization, computational mechanics, and biomedical applications. The techniques introduced are applied to examples of multi-scale biomodeling and simulations at the molecular, cellular, tissue, and organ level scales.
Pre-requisite: None. [Top]

42-643/24-615 Microfluidics | 12 units | Intermittent
This course offers an introduction to the emerging field of microfluidics with an emphasis on chemical and life sciences applications. During this course students will examine the fluid dynamical phenomena underlying key components of “lab on a chip” devices. Students will have the opportunity to learn practical aspects of microfluidic device operation through hands-on laboratory experience, computer simulations of microscale flows, and reviews of recent literature in the field. Throughout the course, students will consider ways of optimizing device performance based on knowledge of the fundamental fluid mechanics. Students will explore selected topics in more detail through a semester project. Major course topics include pressure-driven and electrokinetically-driven flows in microchannels, surface effects, micro-fabrication methods, micro/nanoparticles for biotechnology, biochemical reactions and assays, mixing and separation, two-phase flows, and integration and design of microfluidic chips.
Pre-requisites: Basic fluid mechanics or instructor permission. [Top]

42-645/24-655 Cellular Biomechanics | 9 units | Fall, every other year
Syllabus: 42-645
This course discusses how mechanical quantities and processes such as force, motion, and deformation influence cell behavior and function, with a focus on the connection between mechanics and biochemistry. Specific topics include: (1) the role of stresses in the cytoskeleton dynamics as related to cell growth, spreading, motility, and adhesion; (2) the generation of force and motion by moot molecules; (3) stretch-activated ion channels; (4) protein and DNA deformation; (5) mechanochemical coupling in signal transduction. If time permits, we will also cover protein trafficking and secretion and the effects of mechanical forces on gene expression. Emphasis is placed on the biomechanics issues at the cellular and molecular levels; their clinical and engineering implications are elucidated. 3 hours lecture.
Pre-requisite: None. [Top]

42-646 Molecular Biomechanics | 9 units | Intermittent
Syllabus: 42-646
This class is designed to present concepts of molecular biology, cellular biology and biophysics at the molecular level together with applications. Emphasis will be placed both on the biology of the system and on the fundamental physics, chemistry and mechanics which describe the molecular level phenomena within context. In addition to studying the structure, mechanics and energetics of biological systems at the nano-scale, we will also study and conceptually design biomimetic molecules and structures. Fundamentals of DNA, globular and structured proteins, lipids and assemblies thereof will be covered.
Pre-requisite: Thermodynamics or instructor permission. [Top]

42-647/24-659 Continuum Biomechanics: Solid and Fluid Mechanics of Physiological Systems | 12 units | Spring
This course provides a general survey of the application of continuum mechanics to biomechanics. The objective of this course is to provide the basic ideas of continuum mechanics for engineering and science students with little or no background in biomechanics, with particular emphasis on the application of quantitative and system perspectives to fluid and solid mechanics problems. The course begins with a historical review of the subject followed by a review of vector and tensor analysis, before discussing various measures of deformation and stress formulations. The development and understanding of appropriate constitutive models for particular problems are emphasized. Both analytical and experimental results are presented through readings from recent literature and the relevance of these results to the solution of unsolved problems is highlighted. The course encourages class participation and discussion in a seminar fashion and includes individually-crafted research projects that will be discussed in class.
Pre-requisites: Differential Equations (21-260 equivalent) or Mathematical Methods (06-262 equivalent) or permission of instructor. Knowledge in mechanics of deformable solids (24-202) and fluid mechanics desirable but not required. [Top]

42-648 Cardiovascular Mechanics | 12 units | Fall, every other year
Syllabus: 42-648
The primary objective of the course is to teach how to model blood flow and mechanical forces in the cardiovascular system and medical devices. After a brief review of cardiovascular physiology and fluid mechanics, the course will progress from modeling blood flow and mechanical forces in a.) small-scale steady flow applications to b.) small-scale pulsatile applications to c.) large-scale or complex pulsatile flow applications. The course will also discuss how to calculate mechanical forces on cardiovascular tissue (blood vessels, the heart) and cardiovascular cells (endothelial cells, platelets, red and white blood cells), and the effects of those forces. Lastly, the course will focus on the biomechanical issues present in selected medical devices (heart valves, ventricular assist devices, artificial lungs).
Pre-requisite: Physiology and basic solid and fluid mechanics. [Top]

42-661 Surgery for Engineers | 9 units | Spring
This course explores the impact of engineering on surgery. Students will interact with clinical practitioners and investigate the technological challenges that face these practitioners. A number of visits to the medical center are anticipated for hands on experience with a number of technologies utilized by surgeons to demonstrate the result of advances in biomedical engineering. These experiences are expected to include microvascular surgery, robotic surgery, laparoscopic, and endoscopic techniques. Tours of the operating room and shock trauma unit will be arranged. If possible observation of an operative procedure will be arranged (if scheduling permits). Invited surgeons will represent disciplines including cardiovascular surgery, plastic and reconstructive surgery, surgical oncology, trauma surgery, minimally invasive surgery, oral and maxillofacial surgery, bariatric surgery, thoracic surgery, orthopedic surgery, and others. Specific engineering topics which may be relevant to each of these specialties as well as topics which span many specialties (for example imaging, biomaterials, biomechanics, etc) will be presented by various faculty members of the CMU Biomedical Engineering dept. Students will self-select into teams and present a broad topic overview that will augment the clinical speaker’s presentation. The topics and teams will be finalized on the first day of class and can be tailored to reflect the specific interests of the class but might include topics such as: pump functions of the heart, compliance of the vascular system, electrical map and function of the heart, surgical approaches to cancer, etc. A final paper/presentation will identify an unsolved surgical problem and a potential bioengineered solution for the problem. The possibility to extend this effort into an independent research endeavor will be discussed.
The Primary Instructor is Howard Edington, M.D., MBA System Chairman of Surgery, Allegheny Health Network. This course meets once a week for 3 hours. Several sessions will be held at the Medical Center, transport provided.
Pre-requisite: Physiology. [Top]

42-670 Biomaterial Host Interactions in Regenerative Medicine | 12 units | Fall
This course will provide students with hands-on experience in investigating host responses to synthetic and naturally biomaterials used in regenerative medicine applications. Students will gain experience in the analysis of host responses to these biomaterials as well as strategies to control host interaction. Biomaterial biocompatibility, immune interactions, tissue healing and regeneration will be addressed. Students will integrate classroom lectures with laboratory skills evaluating host-material interactions in a laboratory setting. Laboratory characterization techniques will include cell culture techniques, microscopic, cytochemical, immunocytochemical and histological analyses. Prerequisite: junior or senior standing in Biomedical Engineering or consent of the instructor.
None. [Top]

42-671 Precision Medicine for Biomedical Engineers | 9 units | Fall
This course explores the opportunities for engineers in precision medicine of complex medical disorders. Students will interact with clinical practitioners and investigate the technological challenges that face these practitioners. The course will focus on common complex conditions and diseases such as inflammatory bowel disease (IBD), pancreatitis, diabetes mellitus and obesity, rheumatoid arthritis, multiple sclerosis, pain syndrome and pharmacogenetics. Improvement in care of these conditions requires a reverse engineering approach, and new tools because of the complexity and unpredictability of clinical course and best treatments on a case-by-case basis. Currently, the cost of medications for these conditions in Pittsburgh alone is >1 billion, with a large percent of patients being miss-treated because of lack of precision medicine tools. The course includes introduction to medical genetics, biomarkers of disease, health records, disease modeling, outcome predictions, therapies, remote monitoring and smart applications. Special lectures on health economics and career opportunities are also planned. Each session will include an hour of didactic lectures, followed by an hour-long workshop of applications. Specific engineering topics which may be relevant to each of these specialties as well as topics which span many specialties (for example biodetectors, computational biology, bioinformatics, integrated applications) will be presented by various faculty members of the CMU biomedical engineering and other dept. Students will gain experience exploring genetic variants associated with common diseases, including the opportunity to explore their own DNA. Instructors David C. Whitcomb, MD, PhD (UPMC) Philip Empey, PharmD, PhD (UPMC)
Physiology. [Top]

42-672 Special Topics: Fundamentals of Biomedical Imaging and Image Analysis | 9 units | Spring
This course introduces fundamentals of biological and medical imaging modalities and related image analysis techniques. It is organized into three units. The first unit introduces fundamental principles of biological imaging modalities, such as fluorescence microscopy, super-resolution microscopy, and electron microscopy. These modalities are used to visualize and record biological structures and processes at the molecular and cellular levels. The second unit introduces fundamental principles of imaging modalities, such as magnetic resonance imaging, x-ray computed tomography, and ultrasound. These modalities are used to visualize and record medical structures and processes at the tissue and organ levels. Recent developments in convergence of biological and medical imaging are briefly discussed. The third section introduces fundamentals of computational techniques used for analyzing and understanding biological and medical images, such as deconvolution, registration, segmentation, tracking, and pattern recognition. The introduction to these topics will draw on concepts and techniques from several related fields, including physics, statistics, signal processing, computer vision, and machine learning. As part of the course, students will complete several independent projects. Students will also have the opportunity to visit laboratories to see some of the actual biomedical imaging devices in action. Prerequisites: 18-290 Signals and Systems or permission of the instructor. Proficiency in basic programming is expected. Knowledge of image processing, computer vision, and/or MATLAB is helpful but not essential.
42-101 Introduction to Biomedical Engineering. [Top]

42-673 Stem Cell Engineering | 9 units | Fall, every other year
This course will give an overview over milestones of stem cell research and will expose students to current topics at the frontier of this field. It will introduce students to the different types of stem cells as well as environmental factors and signals that are implicated in regulating stem cell fate. The course will highlight techniques for engineering of stem cells and their micro-environment. It will evaluate the use of stem cells for tissue engineering and therapies. Emphasis will be placed on discussions of current research areas and papers in this rapidly evolving field. Students will pick a class-related topic of interest, perform a thorough literature search, and present their findings as a written report as well as a paper review and a lecture. Lectures and discussions will be complemented by practical lab sessions, including: stem cell harvesting and culture, neural stem cell transfection, differentiation assays, and immunostaining, polymeric microcapsules as advanced culture systems, and stem cell integration in mouse brain tissue. The class is designed for graduate students and upper undergraduates with a strong interest in stem cell biology, and the desire to actively contribute to discussions in the class.
Pre-requisites: None. [Top]

42-702 Advanced Physiology | 12 units | Spring
Syllabus: 42-702
This course is an introduction to human physiology and includes units on all major organ systems. Particular emphasis is given to the musculoskeletal, cardiovascular, respiratory, digestive, excretory, and endocrine systems. Modules on molecular physiology, tissue engineering, and physiological modeling are also included. Due to the close relationship between structure and function in biological systems, each functional topic will be introduced through a brief exploration of anatomical structures. Basic physical laws and principles will be explored as they relate to physiologic function. (This course is designed to bring graduate students without prior undergraduate courses in physiology to a level of understanding suitable for various graduate research projects. It is not recommended for undergraduate students and cannot be counted toward the BME additional major).
Pre-requisite: Graduate standing. Modern Biology or permission of the instructor. [Top]

42-744 Medical Devices | 12 units | Fall and Spring
Syllabus: 42-744
This course is an introduction to the engineering, clinical, legal and regulatory aspects of medical device performance and failure. Topics covered include a broad survey of the thousands of successful medical devices in clinical use, as well as historical case studies of devices that were withdrawn from the market. In-depth study of specific medical devices will include: cardiovascular medicine (pacemakers, heart valves, vascular grafts, heart-assist pumps..), orthopedics (fixation devices, prostheses…), and general medicine (defibrillators, blood pressure cuffs, stethoscopes…) We will study the principles of operation (with hands-on examples), design evolution, and modes of failure. Additional lectures will provide basic information concerning biomaterials used for implantable medical devices (metals, polymers, ceramics) and their biocompatibility, mechanisms of failure (wear, corrosion, fatigue, fretting, etc.). Guest lectures will be provided by practicing engineers from regional medical device companies to provide real-world perspective of the development process.
In addition to a mid-term and final exam covering topics presented in class, students will prepare a written report that critically investigates a particular medical device that has been recalled by the FDA, of the student’s choosing. The report will include the design history, engineering analysis, and recommendations for future improvements (re-design). [Students enrolled in 42-744 will also be required to produce a lo-fi prototype, which they will present in class at the end of the semester.]
The ultimate objectives of this course are to (1) provide students with a broad understanding of the medical device industry, (2) stimulate critical analysis of medical device design, and (3) convey practical knowledge and skills that are valuable for a future career in the medical device industry.
Pre-requisites: Graduate standing for MCS and CIT students. For non- MCS or CIT graduate students, a degree in a science or engineering. For all other students, permission of the instructor. [Top]

42-772 Special Topics: Applied Nanoscience and Nanotechnology | 12 units | Spring
Have you ever wondered what is nanoscience and nanotechnology and their impact on our lives? In this class we will go through the key concepts related to synthesis (including growth methodologies and characterizations techniques) and chemical/physical properties of nanomaterials from zero-dimensional (0D) materials such as nanoparticles or quantum dots (QDs), one-dimensional materials such as nanowires and nanotubes to two-dimensional materials such as graphene. The students will then survey a range of applications of nanomaterials through problem-oriented discussions, with the goal of developing design strategies based on basic understanding of nanoscience. Examples include, but are not limited to, biomedical applications such as nanosensors for DNA and protein detection, nanodevices for bioelectrical interfaces, nanomaterials as building blocks in tissue engineering and drug delivery, and nano materials in cancer therapy.
Pre-requisite: Graduate standing. College level chemistry or physical chemistry, and thermodynamics. [Top]

42-775 Special Topics: Graduate Biomedical Engineering Design | 12 units | Spring
This project course will involve students working in small teams (2 or 3) to design a product or process related to healthcare and employing principles and methods of (biomedical) engineering. The emphasis will be on translation of a technology to practice. This is contrasted with Inventive Problem Solving (42773) which is all about the ideation phase of design. The students will be offered the option to pursue a project from scratch, to continue development of a well-defined problem, starting from a final report of a previous class’s capstone project (e.g. 42401/402 or 42773.) Although these courses are not prerequisites for attending this class. The course provides students with an opportunity to exercise, hence develop, their skills in engineering modeling (mathematics + physics), optimization, human factors, prototyping, play-testing. It will also offer an introduction to other practical aspects of product development, such as intellectual property protection, regulatory affairs, reimbursement, supply chain, and project management. Critical design reviews will be held multiple times during the semester which will be attended by guest speakers from medicine or business, including several entrepreneurs who have successfully started companies in the healthcare industry. The final deliverables of the course will be a design report (e.g. design history file), and possibly a prototype and/or a patent application.
Pre-requisite: Graduate standing. [Top]

Selected Undergraduate-Level Biomedical Engineering Courses

Depending on the graduate degree program and option, a limited number of undergraduate courses relevant to biomedical engineering is allowed to count toward the degree requirements. The purpose is to allow students to develop breadth in an unfamiliar area. Courses other than those listed below may be accepted upon petition.

42-302 Biomedical Engineering Systems Modeling and Analysis | 9 units | Fall and Spring
This course is designed to enable students to develop mathematical models for biological systems and for biomedical engineering systems, devices, components, and processes and to use models for data reduction and for system performance analysis, prediction and optimization. Models considered will be drawn from a broad range of applications and will be based on algebraic equations, ordinary differential equations and partial differential equations. The tools of advanced engineering mathematics comprising analytical, computational and statistical approaches will be introduced and used for model manipulation.
Pre-requisite: Graduate standing. [Top]

42-341/24-334 Introduction to Biomechanics | 9 units | Spring
This course provides a general survey of the application of solid mechanics and rigid body dynamics to the study of the human cardiovascular and musculoskeletal systems. The mechanical properties and behavior of heart, blood vessel, bone, muscle and connective tissues are discussed and methods for the analysis of human motion are developed. Both analytic and experimental results are presented through readings from reports in recent journals and the relevance of these results to the solution of unsolved problems is highlighted. The development of appropriate models for particular problems is also considered. [Top]

Graduate Courses Offered by Other CMU Departments

The courses below offered by other departments have been preapproved to be eligible for BME course requirement. Descriptions of these courses may be found in the University Course Catalog. Students are urged to contact the instructor if they are uncertain about the background required. Additional courses may be approved as electives upon petition, which must be submitted before taking the course. Regardless of the approval of individual courses, the overall course selection must reflect a clear theme in biomedical engineering.

02-730 Cell and Systems Modeling | 12 units

02-750 Automation of Biological Research: Robotics and Machine Learning | 12 units

03-534 Biological Imaging and Fluorescence Spectroscopy | 9 units

03-712 Computational Methods for Biological Modeling and Simulation | 12 units

03-730 Advanced Genetics | 12 units | Spring

03-741 Advanced Cell Biology | 12 units

03-742 Advanced Molecular Biology | 12 units

03-620 Techniques in Electron Microscopy | 9 units

03-751 Advanced Developmental Biology and Human Health | 12 units

03-762 Advanced Cellular Neuroscience | 12 units

03-763 Advanced Systems Neuroscience | 12 units

03-871 Structural Biophysics | 12 units

06-804 Drug Delivery Systems | 9 units

09-741 Organic Chemistry of Polymers | 12 units

09-801 Special Topics: Molecular Biophysics and Biochemistry | 12 units

15-883 Computational Models of Neural Systems | 12 units

16-725 Medical Image Analysis | 12 units

16-868 Biomechanics and Motor Control | 12 units

18-612 Neural Technology: Sensing and Stimulation | 12 units

24-674 Design of Biomechatronic Systems for Humans | 12 units

33-441 Introduction to BioPhysics | 10 units

33-767 Biophysics: From Basic Concepts to Current Research | 12 units

45-906 The Business of Healthcare Innovation | 6 units

49-850 Grand Challenge Innovation | 12 units | Spring

The following courses may be taken to supplement courses in biomedical engineering and count toward BME degree requirement. However no more than one such course, or other course unrelated to biomedical engineering, may be taken each semester by MS students. PhD students should consult the thesis advisor about the suitability of these courses.

06-607 Physical Chemistry of Colloids and Surfaces | 9 units

06-609 Physical Chemistry of Macromolecules | 9 units

06-610 Rheology and Structure of Complex Fluids | 9 units

09-707 Nanoparticles | 12 units

10-601 Introduction to Machine Learning | 12 units

10-701 Introduction to Machine Learning | 12 units

10-702 Statistical Machine Learning | 12 units

10-708 Probabilistic Graphical Models | 12 units

11-785 Introduction to Deep Learning | 12 units | Fall | Spring

15-853 Algorithms in the Real World | 12 units

16-711 Kinematics, Dynamic Systems and Control | 12 units

16-720 Computer Vision | 12 units

16-722 Sensing and Sensors | 12 units

16-764 Finding Opportunities for Technology | 12 units

16-824 Visual Learning and Recognition | 12 units | Spring

18-491 Fundamentals of Signal Processing | 12 units | Spring

18-614 Microelectromechanical Systems | 12 units

18-751 Applied Stochastic Process | 12 units

18-752 Estimation, Detection and Learning | 12 units | Spring

18-792 Advanced Digital Signal Processing | 12 units

18-793 Optical Image and Radar Processing | 12 units

18-794 Pattern Recognition Theory | 12 units

18-799K Special Topics in Signal Processing: Advanced Machine Learning | 12 units | Spring

21-690 Methods of Optimization | 12 units

24-614 Microelectromechanical Systems | 12 units

24-673 Soft Robots: Mechanics, Design and Modeling | 12 units

24-688 Introduction to CAD and CAE Tools | 12 units

24-703 Numerical Methods in Engineering | 12 units | Fall | Spring

24-778 Mechatronic Design | 12 units

24-780 Engineering Computation | 12 units

24-787 Machine Learning and Artificial Intelligence for Engineers | 12 units | Fall

27-565 Nanostructured Materials | 12 units

27-715 Applied Magnetism and Magnetic Materials | 12 units

27-718 Soft Materials | 12 units

36-700 Probability and Mathematical Statistics I | 12 units | Fall

36-759 Statistical Models of the Brain | 12 units

85-765 Cognitive Neuroscience | 9-12 units

86-675 Computational Perception | 12 units


Graduate Courses Offered by the University of Pittsburgh

Carnegie Mellon graduate students may register for one course per semester at the University of Pittsburgh except for the last semester before graduation (see cross-registration page), where courses offered by the Department of Bioengineering and in the School of Medicine may be of particular interest. Students who plan to register for a course at the University of Pittsburgh must petition the Biomedical Engineering Department then apply through the Carnegie Mellon Enrollment Services. Plenty of time should be allowed for processing.

Special Courses for Biomedical Engineering Graduate Degree Requirements

42-701 Biomedical Engineering Seminar | 0 units | Fall and Spring
The Biomedical Engineering Seminar is required each semester for all students in residence. It provides opportunities to learn about research in various and related fields being conducted at other universities and in industry. All graduate students must register for either 42-701 or 42-801 during each semester of full-time study. Attendance is mandatory. Students may register for either 0 unit as 42-701 Biomedical Engineering Seminar or 3 units as Biomedical Engineering Seminar with Self-Study. Students registering for 42-701 receive a pass/fail grade based on the submission of notes taken at the seminars. Students registering for 42-801 receive a letter grade based on both notes taken at the seminar and reports from 2 hours of self-study following each seminar. [Top]

42-790 Practicum in Biomedical Engineering | 12 units | Fall and Spring
This course must be taken by practicum-option M.S. students for at least one semester. Students will work with a faculty member, local biomedically-oriented company or local clinical researcher on a technical research, development or outreach project.  A faculty member affiliated with the Department of Biomedical Engineering will either serve as the advisor for an internal project or as a liaison for an external industrial/clinical project.  This course may count as an elective for MS and PhD students if taken at a medical center.
Pre-requisite: Graduate standing and consent of faculty advisor/liaison. [Top]

42-792 Extramural Practicum | 3-12 units | Fall, Spring, and Summer
This course may be taken by M.S. or Ph.D. students as part of the arrangement to work in an outside organization during the summer, for the purpose of gaining experience in the real-world practice of biomedical engineering. In exceptional cases it may be performed during the academic year in conjunction with other courses on campus. Students should register for Section R during the summer or Section A during the academic year. A written report is required at the end of tthe semester.
Pre-requisite: Graduate standing, require special arrangement through the advisor and approval of the department, and approval of the Office of International Education for international students. [Top]

42-798 Current Readings in Biomedical Engineering | 1 or 2 units | Fall or Spring, intermittent
This course takes the "Journal Club" format involving at least three interacting research groups. Students are required to participate regularly and actively in discussing current literatures and make at least one presentation. The number of units is determined by the weekly or biweekly frequency. Students may receive at most 2 units over the entire period of training in each of the following broad areas - fundamental principles of biomedical engineering, technologies for biomedical research, technologies at the interface of biological and artificial materials, and clinical applications of biomedical engineering.
Pre-requisite: Students must obtain consent of the instructor before registering. Limited to graduate students and advanced undergraduate students. [Top]

42-799 Directed Study | 1-48 units | Fall and Spring
Students work with a faculty member of Biomedical Engineering to gain knowledge in areas where formal courses are not available. Emphasizing resourcefulness and initiative, the students with their advisors evolve a project with both research and development aspects. By permission only.
Pre-requisite: Consent of advisor. [Top]

42-801 Biomedical Engineering Seminar with Self Study| 3 units | Fall and Spring
The Biomedical Engineering Seminar is required each semester for all students in residence. It provides opportunities to learn about research in various and related fields being conducted at other universities and in industry. All graduate students must register for either 42-701 or 42-801 during each semester of full-time study. Attendance is mandatory. Students may register for either 0 unit as 42-701 Biomedical Engineering Seminar or 3 units as Biomedical Engineering Seminar with Self-Study. Students registering for 42-701 receive a pass/fail grade based on the submission of notes taken at the seminars. Students registering for 42-801 receive a letter grade based on both notes taken at the seminar and reports from 2 hours of self-study following each seminar. [Top]

42-890 M.S. Research | 12-48 units | Fall, Spring, and Summer
Research culminating in a M.S. thesis. All research-option M.S. students must register for at least 12 units of this course each semester. [Top]

42-899 M.S. Project Report | 0 units
Research culminating in a M.S. research report. Research-option M.S. students must register for this course only during the final semester. [Top]

42-990 Ph.D. Thesis Research | 5-48 units | Fall, Spring and Summer
Research culminating in a Ph.D. thesis. All Ph.D. students must register for this course each semester, normally for at least 20 units while taking formal courses or 48 units thereafter. [Top]

42-996 Teaching Assistantship | 2 units | Fall and Spring
This 2-unit course is the vehicle for PhD students serving teaching assignments. PhD students must register for this course upon notification of the assignment as a teaching assistant (TA). MS students should not register for this course regardless of TA appointment. The units received for this course are not counted toward M.S. or Ph.D. degree requirements. Assignments are made by the department office and announced at the beginning of each semester. The duties generally consist of grading problem sets and holding office hours. An instructor may ask a TA to fill for a lecture in a lecture if the instructor is unavoidably away from campus during the class period. This might occur for no more than a couple lectures for a given class. This course is a requirement for graduation and must be taken by all PhD students for a total of three semesters. [Top]

42-997 Ph.D. Qualifying Examination | 0 unit
Ph.D. students should register for this course during the semester scheduled for the qualifying examination. The purpose of the exam is given to determine the student's general knowledge of the fields of engineering appropriate to the individual's research plan, and to assess the student’s ability to use this knowledge in the solution of problems and in the execution of original research. The examination comprises written and/or oral parts. Students must take the qualifying examination at the time specified by the department. Upon satisfactorily passing the examination, the student will be accepted as a candidate for the degree of Doctor of Philosophy for up to six calendar years. [Top]

42-998 Ph.D. Proposal Examination | 0 units
Ph.D. students should register for this course during the semester scheduled for the proposal examination. The exam includes a written proposal for thesis research and an oral examination. [Top]

42-999 Ph.D. Thesis Defense | 0 units
Thesis defense examination for the Ph.D. in Biomedical Engineering. Ph.D. students must register for this course only during the final semester. [Top]