Carnegie Mellon University

Graduate Course Catalog

Graduate-Level Biomedical Engineering Courses

42-611/42-411/27-709/27-411/Engineering Biomaterials  
This course will cover structure-processing-property relationships in biomaterials for use in medicine. This course will focus on a variety of materials including natural biopolymers, synthetic polymers, and soft materials with additional treatment of metals and ceramics. Topics include considerations in molecular design of biomaterials, understanding cellular aspects of tissue-biomaterials interactions, and the application of bulk and surface properties in the design of medical devices. This course will discuss practical applications of these materials in drug delivery, tissue engineering, biosensors, and other biomedical technologies. This course is a project-based option for graduate students that is taught concurrently with 42-411.

42-612/27-520 Tissue Engineering 
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.

42-613/27-570 Polymeric Biomaterials 
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.

42-620 Engineering Molecular Cell Biology 
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.

42-624 Biological Transport and Drug Delivery 
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.

42-630/18-690 Introduction to Neuroscience for Engineers 
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) 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.

42-631/86-631 Neural Data Analysis
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. Those looking for broader neuroscience application (eg, fMRI) or more focus on regression analysis are encouraged to take 36-746. Those looking for more advanced techniques are encouraged to take 18-699.

42-632/18-698 Neural Signal Processing 
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. 

42-640/24-658 Image-Based Computational Modeling and Analysis
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.

42-643 Microfluids 
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.

42-645  Cellular Biomechanics
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.

42-647/24-659 Continuum Biomechanics: Solid and Fluid Mechanics of Physiological Systems 
This course provides a general survey of the solid and fluid mechanics of physiological systems, within the framework of continuum mechanics. The main objective of the course is to understand mathematical modeling of solid materials such as bone and tissues, and fluid mechanics of blood and other biofluids such as synovial fluid, etc. The course as a whole encourages class participation and discussion in a seminar-type fashion. 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 at the core of this course. Both analytical and to some extent 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 intent is to provide the basic ideas of continuum mechanics for engineering and science students with little or no background in biomechanics or mathematical modeling, with particular emphasis on the application of quantitative and system perspectives to fluid and solid mechanics problems. In addition to looking at various examples with physiological applications, the last few weeks of the course are dedicated to discussing individually-crafted research projects for the students.

42-648 Cardiovascular Mechanics
The primary objective of the course is to learn to model blood flow and mechanical forces in the cardiovascular system. After a brief review of cardiovascular physiology and fluid mechanics, the students will progress from modeling blood flow in a.) small-scale steady flow applications to b.) small-scale pulsatile applications to c.) large-scale or complex pulsatile flow applications. The students will also learn 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 students will learn various methods for modeling cardiac function. When applicable, students will apply these concepts to the design and function of selected medical devices (heart valves, ventricular assist devices, artificial lungs).

42-649: Introduction to Biomechanics
The purpose of this course is to achieve a broad overview of the application of mechanics to the human body. This includes solid, fluid, and viscoelastic mechanics applied to single cells, the cardiovascular system, lungs, muscles, bones, and human movement. The physiology of each system will be reviewed as background prior to discussing mechanics applications within that system. There are no firm prerequisites, but statics, fluid mechanics, and biology are helpful.

42-661 Surgery for Engineers 
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. 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 42-202 and one of the introductory engineering courses, 42-101, 06-100, 12-100. 18-100, 19-101, 24-101, or 27-100 Priority for enrollment is given to BME Graduate students and additional majors, followed by BME minors.

42-670 Special Topics: Biomaterial Host Interactions in Regenerative Medicine
Special Topics: 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.

42-673 Special Topics: Stem Cell Engineering 
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.

42-674 Special Topics: Engineering for Survival: ICU Medicine
Special Topics: Engineering for Survival: ICU Medicine The overall learning objective of this class is to expose students to acute care medicine and the fundamentals of acute illness. The lectures review the structure and function of different body systems. Typical modes of failure (disease) are then described and illustrated with examples using actual de-identified cases based on over 30 years of experiences in the intensive care unit (ICU) by Dr. Rosenbloom. Field trips are made to a local critical care and emergency medicine simulation facility at the University of Pittsburgh. An optional opportunity to participate in ICU rounds is also available

42-675 Fundamentals of Computational Biomedical Engineering
This goal of this course is to enable students with little or no programming background to use computational methods to solve basic biomedical engineering problems. Students will use MATLAB to solve linear systems of equations, model fit using least squares techniques (linear and nonlinear), interpolate data, perform numerical integration and differentiation, solve differential equations, and visualize data. Specific examples for each topic will be drawn from different areas of biomedical engineering, such as bioimaging and signal processing, biomechanics, biomaterials, and cellular and biomolecular technology.

42-676/27-514 Bio-nanotechnology: Principles and Applications
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 biological 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 nanomaterials in cancer therapy.

42-677 Rehabilitation Engineering
Rehabilitation engineering is the systematic application of engineering sciences to design, develop, adapt, test, evaluate, apply, and distribute technological solutions to problems confronted by individuals with disabilities. This course focuses on assistive technologies - technologies designed for use in the everyday lives of people with disabilities to assist in the performance of activities of daily living. The course surveys assistive technologies designed for a variety of functional limitations - including mobility, communication, hearing, vision, and cognition - as they apply to activities associated with employment, independent living, education, and integration into the community. This course considers not only technical issues in device development, but also the psychosocial factors and market forces that influence device acceptance by individuals and the marketplace. 

42-678/49-732 Medical Device Innovation and Realization
The increasing pace of medical discoveries and emerging technologies presents a unique and exciting time for medical devices. Medical devices range from biomaterials that stimulate the body to repair itself to drug eluting stints to robotic surgical systems. Because they seek to improve and prolong human health, there are unique requirements and challenges for medical device development compared to most other industries. This class will look at how medical device innovation is currently practiced as well as the drivers which govern it, such as the FDA, intellectual property, reimbursement, and funding. By the end of this course, students should be able to: (1) obtain a broad understanding of medical devices; (2) identify new product opportunities; (3) understand the drivers that affect medical device development; (4) develop strategies to address those drivers within the overall medical device development plan; and (5) conceptualize and develop a working prototype.

42-679/49-735 Medical Device Realization
This course is a companion to 42-678, Medical Device Innovation, which is a pre-requisite for this course. Medical Device Realization will take the research and early conceptualization work in 42-678and use it to further conceptualize and develop a prototype.

42-681 Engineering and Analysis of Complex Disease Models
One of the key challenges in the fields of tissue engineering and disease modelling is a disconnect between the use of robust bioengineering tools and our limited understanding of pathobiology. The future of these fields depends on biomedical engineers using their technical skill sets to study normal physiology and disease mechanisms. In this class, we will explore current state-of-the-art methods for creating tissue and disease models, including: 2D/3D tissue cultures, bioreactors, organs-on-a-chip, microfluidic models, disease-in-a-dish models (with discussions on coupling multiple tissue systems), animal models of disease, and CRISPR/CAS9. The first few weeks of the semester will focus on learning the state-of-the-art methods with 1 exam as an assessment. The rest of the class will focus on specific disease modules with journal reviews and experts sharing their research on disease models with the class. For assessment, students will read 1 journal article each week and provide a brief critique. In addition, they will write a grant and present to the class methods for creating a disease model of their choice. At the end of the class, students will be able to critically assess and design models of normal and pathobiological disease mechanisms. Prior knowledge of basic physiology is required.

42-682 Bioinstrumentation and Measurement
This course aims to build the understanding of basic concepts and applications of instrumentation used for biomedical research and patient care. The course will follow a fast track, using a flipped format to cover components ranging from simple resistors, capacitors, transistors, sensors, actuators, to operational amplifiers and microcontrollers, using a combination of lectures, guided tutorials, lab exercises, and term projects. Students will gain hands-on skills of how to integrate components into functional instruments, based on physiological measurements such as temperature, humidity, oxygen concentration, blood pressure, and EKG signals. MATLAB programming will be used throughout the course. The course is designed for advanced undergraduate and graduate students with a knowledge in basic physics of electricity and magnetism. 

42-683 Introduction to Machine Learning for Biomedical Engineers
This course introduces fundamental concepts, methods and applications in machine learning and datamining. We will cover topics such as parametric and non-parametric learning algorithms, support vector machines, neural networks, clustering, clustering and principal components analysis. The emphasis will be on learning high-level concepts behind machine learning algorithms and applying them to biomedical-related problems. This course is intended for advanced undergraduate and graduate students in Biomedical Engineering or related disciplines. Students should have experience with high-level programming language such as Matlab, basic familiarity with probability, statistics and linear algebra, and should be comfortable with manipulating vectors and matrices.

42-684/06-500  Principles of Immunoengineering and Development of Immunotherapy Drugs
This course will provide context for the application of engineering principles to modulate the immune system to approaches problems in human health. Basic understanding of the components and function of the innate and adaptive immune system. Students will leave with a basic understanding of immunology and of the engineering techniques used to develop and characterize immunotherapy systems. Where appropriate, we will discuss how immunoengineering fits into other disciplines of engineering such as mechanical, chemical, and materials science. Because the purpose of immunoengineering is disease treatment, we will discuss, the therapy pipeline, development of clinical trials and the FDA approval process. Immunotherapy will also be assessed within different disease contexts including cancer, infectious disease, allergies, prosthetics and implants, neuro and musculoskeletal disorders.

42-685 Biostatistics: Computational Course/Biostatistics
This course introduces statistical methods for making inferences in engineering, biology and medicine. Students will learn how to select the most appropriate methods, how to apply these methods to actual data, and how to read and interpret computer output from a commonly used statistical package. The topics covered are descriptive statistics; elementary probability; discrete and continuous random variables and their distributions; hypothesis testing involving interval (continuous and discrete) and categorical (nominal and ordinal) variables, for two and three or more treatments; simple and multiple linear regression; time-series analysis; clustering and classification; and time-to-event (survival) analysis. Students will also learn how to write the statistical component of a Results section for a scientific paper and learn about the limitations of the statistical analyses. Basic familiarity with probability and probability distribution preferred but not required.

42-686 Biomedical Ultrasound
In this course, emerging technologies using sound waves and their biomedical applications will be introduced. The course will cover the fundamental physics of the propagation and the interaction of sound waves with biological tissues, acoustic devices and sensors, and associated core signal processing for imaging, stimulation, and therapy. Their applications in biomedicine in different scales from cell, tissue, organ to whole body, and from structural to functional assessment will be discussed. Students should have a background in Physics II and differential equations.

42-688 Introduction to Neural Engineering
Neural engineering sits at the interface between neuroscience and engineering, applying classical engineering approaches and principles to understand the nervous system and its function. Modern neural engineering techniques have been used to measure neural activity using tools based on light, electricity, and magnetism. The same tools for measurement can be redirected to modulate neural activity, and manipulate how an organism perceives, thinks, and acts. The course objectives are to familiarize students with a range of neural engineering approaches to investigating and intervening in the nervous system, emphasizing quantitative understanding and fundamental engineering concepts. The course will pair lectures and discussion with projects involving real neural data (Matlab-based exercises). Example projects could include finding visual responses in EEG data, or determining how groups of individual neurons interact based on spiking data. Overall, the goal is to give the student a deep understanding of select topics in neuroscience and the application of quantitative neural engineering approaches to these topics. This course is intended for advanced undergraduate and entering graduate students. Familiarity with linear algebra, signal processing, and introductory Matlab programming is helpful. This course is suitable for students coming from diverse backgrounds: (1) Students with non-engineering backgrounds seeking quantitative skills, and wanting to learn an engineering approach to neuroscience problems, and (2) students with engineering or other quantitative backgrounds who are seeking ways to apply their skills to scientific questions in neuroscience.

42-689 Introduction to Bioimaging
The field of medical imaging describes methods of seeing the interior of the human body, as well as visual representation of tissue and organ function. The materials covered in this course will give an overview of existing medical imaging devices used in a clinical and pre-clinical setting. The course presents the principles of medical imaging technologies, explaining the mathematical and physical principles, as well as describing the fundamental aspects of instrumentation design. Students will gain a thorough understanding of how these methods are used to image morphological and physiological features. Imaging methods will include Ultrasound, X-ray, computed tomography (CT), and magnetic resonance imaging (MRI), as well as optical methods. For each method, the fundamental imaging principles will be discussed, and examples of clinical applications will be presented. No prior knowledge of imaging methods is required.

42-690 BME in Everyday Life
This course focuses on how biomedical engineering technologies are used in everyday life. The objective is to develop an understanding of the clinical need for these technologies, and past and current solutions to meet these clinical needs. Topics covered include artificial organs, tissue engineering, brain-control interfaces, and immunoengineering. For each medical condition being addressed, biology physiology, and anatomy concepts will be applied in the context of biomedical engineering technology. This course is suitable for non-engineering majors who have an interest in biomedical engineering.

42-691 Biomechanics of Human Movement
This course provides an overview of the mechanical principles underlying human movement biomechanics and the experimental and modeling techniques used to study it. Specific topics will include locomotion, motion capture systems, force plates, muscle mechanics, musculoskeletal modeling, three dimensional kinematics, inverse dynamics, forward dynamic simulations, and imaging-based biomechanics. Homework and final class projects will emphasize applications of movement biomechanics in orthopedics, rehabilitation, and sports.

42-693: Special Topics in Integrated systems Technology: Micro/Nano Biomedical Devices
Biomedical devices constantly call for innovations. Micro/nano fabrication not only miniaturizes devices and instruments, but also can enable new biomedical devices and significantly boost device performance. This course introduces fundamental micro/nano fabrication technologies and related materials of biomedical devices. The biomedical background and design principles of various biomedical devices will be presented. Both diagnostic and therapeutic devices will be discussed, including point-of-care diagnostic devices, biosensors, DNA sequencers, medical implants, prosthetic devices, drug delivery systems, medical robots, etc.

42-702 Advanced Physiology 
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 interrelationship between structure and function in biological systems, each functional topic will be introduced through a brief exploration of anatomical structure. Basic physical laws and principles will be explored as they relate to physiologic function. Prerequisite: 03-121 Modern Biology, or permission of instructor.

42-737/42-437 Biomedical Optical Imaging
Biophotonics, or biomedical optics, is a field dealing with the application of optical science and imaging technology to biomedical problems, including clinical applications. The course introduces basic concepts in electromagnetism and light tissue interactions, including optical properties of tissue, absorption, fluorescence, and light scattering. Imaging methods will be described, including fluorescence imaging, Raman spectroscopy, optical coherence tomography, diffuse optical spectroscopy, and photoacoustic tomography. The basic physics and engineering of each imaging technique are emphasized. Their relevance to human disease diagnostic and clinical applications will be included, such as breast cancer imaging and monitoring, 3D retinal imaging, ways of non-invasive tumor detection, as well as functional brain imaging in infants.

42-744 / 42-444 Medical Devices
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, orthopedics, and general medicine. 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.). The level of technical content will require junior standing for MCS and CIT students, a degree in science or engineering for non-MCS or non-CIT graduate students, or permission of the instructor for all other students.

42-781 Professional Issues in Biomedical Engineering
This course exposes students to many of the issues that biomedical engineers face. It provides an overview of professional topics including bioethics, regulatory issues, communication skills, teamwork, and other contemporary issues. Outside speakers and case studies will describe real world problems and professional issues in biotechnology and bioengineering, and progress toward their solution. A term paper describing on now the topics in class are applicable to a specific biomedical industry.

42-782/42-302 Biomedical Engineering Systems Modeling and Analysis
This course will prepare 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. There will be an extra project.

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.

42-341/24-334 Introduction to Biomechanics 
This course covers the application of solid and fluid mechanics to living tissues. This includes the mechanical properties and behavior of individual cells, the heart, blood vessels, the lungs, bone, muscle and connective tissues as well as methods for the analysis of human motion.

42-401/42-402 Foundation of BME Design
This course sequence introduces Biomedical Engineering students to the design of useful biomedical products to meet a specific medical need. Students will learn to identify product needs, how to specify problem definitions and to use project management tools. Methods to develop creativity in design will be introduced. The course sequence is comprised of two parts: 42-401 is offered in the Fall semester and provides the students the opportunity to form project teams, select and define a project, create a development plan, and complete an initial prototype. 42-402 is offered in the Spring semester is a full semester course and completes the plan that was developed in the fall semester. This course culminates in the completion of multiple prototypes, a poster presentation, and a written report.

42-437 Biomedical Optical Imaging
Biophotonics, or biomedical optics, is a field dealing with the application of optical science and imaging technology to biomedical problems, including clinical applications. The course introduces basic concepts in electromagnetism and light tissue interactions, including optical properties of tissue, absorption, fluorescence, and light scattering. Imaging methods will be described, including fluorescence imaging, Raman spectroscopy, optical coherence tomography, diffuse optical spectroscopy, and photoacoustic tomography. The basic physics and engineering of each imaging technique are emphasized. Their relevance to human disease diagnostic and clinical applications will be included, such as breast cancer imaging and monitoring, 3D retinal imaging, ways of non-invasive tumor detection, as well as functional brain imaging in infants.

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.

02-718 Computational Medicine

02-730 Cell and Systems Modeling 

02-750 Automation of Scientific Research

03-534 Biological Imaging and Fluorescence Spectroscopy

03-712 Computational Methods for Biological Modeling and Simulation 

03-730 Advanced Genetics 

03-741 Advanced Cell Biology 

03-742 Advanced Molecular Biology 

03-620 Techniques in Electron Microscopy 

03-751 Advanced Developmental Biology and Human Health

03-762 Advanced Cellular Neuroscience

03-763 Advanced Systems Neuroscience 

03-871 Structural Biophysics 

06-804 Drug Delivery Systems 

09-741 Organic Chemistry of Polymers 

09-801 Special Topics in Physical Chemistry: Computational Tools for Molecular Science

15-883 Computational Models of Neural Systems 

16-725 (Bio)Medical Image Analysis 

16-868 Biomechanics and Motor Control 

18-612 Neural Technology: Sensing and Stimulation

24-674 Design of Biomechatronic Systems for Humans 

27-565 Nanostructured Materials

33-441 Introduction to BioPhysics

33-767 Biophysics: From Basic Concepts to Current Research 

45-906 The Business of Healthcare Innovation

49-850 Grand Challenge Innovation

06-607 Physical Chemistry of Colloids and Surfaces 

06-609 Physical Chemistry of Macromolecules

06-610 Rheology and Structure of Complex Fluids 

09-707 Nanoparticles

10-601 Introduction to Machine Learning for M.S.

10-701 Introduction to Machine Learning for Ph.D 

10-702 Statistical Machine Learning 

10-708 Probabilistic Graphical Models 

11-785 Introduction to Deep Learning 

15-853 Algorithms in the Real World 

16-711 Kinematics, Dynamic Systems and Control

16-720 Computer Vision 

16-722 Sensing and Sensors 

16-824 Visual Learning and Recognition

18-491 Fundamentals of Signal Processing

18-614 Microelectromechanical Systems 

18-751 Applied Stochastic Process 

18-752 Estimation, Detection and Learning 

18-792 Advanced Digital Signal Processing

18-793 Image and Video Processing

18-794 Pattern Recognition Theory

18-799K Special Topics in Signal Processing: Advanced Machine Learning 

21-690 Methods of Optimization 

24-614 Microelectromechanical Systems

24-673 Soft Robots: Mechanics, Design and Modeling 

24-688 Introduction to CAD and CAE Tools 

24-703 Numerical Methods in Engineering

24-778 Mechatronic Design 

24-780 Engineering Computation

24-787 Machine Learning and Artificial Intelligence for Engineers

36-759 Statistical Models of the Brain

85-765 Cognitive Neuroscience 

86-675 Computational Perception

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 
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. 

42-790 Practicum in Biomedical Engineering 
Students will work with a local clinical researcher on a technical research, development or outreach project performed at a medical center with clinical exposure. The project will culminate in an oral presentation and an internally-archived written report which documents the project and its results. The presentation and report will be reviewed by the faculty advisor/liaison; this review will serve as the basis for the assignment of the course grade. Research Option MS and PhD students should not register for research us­ing this course and instead utilize their respective research courses, 42-890 and 42-990.

42-792 Extramural Practicum  
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 the semester. Research Option MS and PhD students should not register for research using this course and instead utilize their respective research courses, 42-890 and 42-990.

Require special arrangement through the advisor and approval of the department, and approval of the Office of International Education for foreign students.

42-798 Current Readings in Biomedical Engineering 
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. Require special arrangement through the advisor and approval of the department,

42-799 Directed Study 
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. This course is intended for directed study only with permission of the Associate Department Head.

42-801 Biomedical Engineering Seminar
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. 

42-890 M.S. Research 
M.S. students engaged in Lab research should register for 42-890. All research-option M.S. students must register for at least 12 units of this course each semester.

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

42-990 Ph.D. Thesis Research 
This course is designed to give students enrolled in the Ph.D. program an opportunity to conduct extensive research over the course of their studies 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.

42-996 Teaching Assistantship 
The 2-unit course is the vehicle for these teaching assignments. All students must register for this course only during semesters they are a Teaching Assistant (TA). 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 students; it is in no way linked to a student’s source of financial support. Additional compensation is provided for any TA who volunteers to assist beyond the required three semesters.

42-997 Ph.D. Qualifying Examination 
Ph.D. students should register for this course during the semester scheduled for the qualifying examination. The purpose of the exam is 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 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. If, at the end of this six-year period, the Ph.D. has not been awarded, the student must reapply for admission to the graduate program and will be judged competitively with other students applying at the same time. If the student is re-admitted, he or she may, at the discretion of the department, be requested to pass the qualifying examination again before the Ph.D. is awarded. A student may petition for extension of the six-year limit under extenuating circumstances such as a forced change of advisor, military service, or prolonged illness.

42-998 Ph.D. Proposal
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. 

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