BIOENGINEERING

BIOENGINEERING
(EG) {BE}

099. Independent Study in Bioengineering. (C) Prerequisite(s): Freshman or Sophomore standing in BE (Both BAS and BSE).

An individualized research-based learning experience on a biomedical research problem. Requires preparation of a proposal, literature evaluation, and preparation of a research paper and presentation. Regular progress reports and meetings with a faculty advisor are required.

L/L 100. Introduction to Bioengineering: What is Bioengineering?. (A) Corequisite(s): MATH 104, PHYS 140 or 150. Open to Freshmen only.

Covers, at an introductory level, a variety of topics such as cellular and molecular therapies, novel medical devices to diagnose and treat disease, engineering and computational models of the body, genomics, biomechanics, cell signalling, and tissue engineering. Students will do hands-on experiments in the Bioengineering Undergraduate Lab, learn about statistics and experimental design, government regulations, ethical and other professional considerations that affect bioengineering research and development. As an exercise, students will be asked to offer new bioengineering ideas and interventions, discuss and present them by applying the coure and lab material.

L/R 200. Bioengineering I: Introduction to Biomechanics and Biomaterials. (A) Prerequisite(s): Sophomore standing, MATH 104, 114, PHYS 140, 141 or PHYS 150, 151. Corequisite(s): MATH 240.

Application of statics and dynamics to simple force analyses of the musculoskeletal system. Introduction to the fundamentals of strength of materials. Biomechanics of soft and hard tissues: microstructure and mechanical properties. This course is intended to provide a solid foundation in statics and mechanics of materials with particular focus on human joint biomechanics. The first portion of the course will present fundamental concepts of force and mechanics of rigid and deformable bodies. The remainder of the course will consist of an introduction of materials science and engineering, including the classification and bulk properties of implantable materials, and will also address specific topics including torsional loading and bending. By the end of the course, it is anticipated that students will be able to integrate the origin of tissue mechanical properties with structure/function analyses of load-bearing tissues in the human body.

209. Bioengineering Lab I. (A) Corequisite(s): BE 200. Students taking BE 209 are required to be enrolled in BE 200 and to have completed the physics and chemistry laboratories scheduled during the freshmen year.

BE 209 is the first laboratory course in the Bioengineering curriculum. It is required for both BSE and BAS majors. It is intended for the fall semester of the semester.

210. Bioengineering Lab II. (B) Prerequisite(s): BE 209. Corequisite(s): Math 241.

Second term of a two-year sequence designed to integrate real world experiences into various Bioengienering Science courses. Experiments and projects in mechanics, material and chemical applications to Biomedical Engineering.

L/R 220. (MSE 220) Structure and Properties of Biomaterials. (B) Prerequisite(s): CHEM 101, BE 209. Corequisite(s): MATH 241, BE 210.

An examination of the structure of property, performance relationship for materials used in surgical implants and medical devices. Consideration is given to issues of biocompatibility, degradation of materials by biological systems, and biological response to artificial materials. Particular attention will be given to the materials of the total hip prosthesis and their relationship to the long-term outcomes for total hip arthoplasty.

SM 225. Technology and Engineering in Medicine. (C) Prerequisite(s): First year college physics, chemistry and biology or AP credit; Sophmore and higher standing only.

This course will provide an in-depth examination of technology and its impact on medicine, with an emphasis on the intersection of engineering with medicine and health. Basic foundations of historical perspective, constraints on technological development., and the promise and peril of technological impact on medicine will be discussed. Modules will also focus on specific tehnological advanceswhich have had significant impact on the field of medicine. These include: imaging and diagnosis of disease, genetic therapy and pharmacology, and rehabilitative devices, assistive devices and transplantation.

L/R 301. Bioengineering Signals and Systems. (A) Prerequisite(s): BE 210, MATH 241.

Properties of signals and systems and examples of biological and biomedical signals and systems; linear, time invariant systems; Fourier analysis of signals and systems with applications to biomedical signals such as ECG and EEG; frequency analysis of first and second order systems; the frequency response; of systems characterized by linear constant-coefficient differential equations; introduction to digital and analog filtering, sampling and sampling theorem and aliasing.

L/R 303. (EAS 303) Ethics, Social and Professional Responsibility for Engineers. (A) Prerequisite(s): Junior Standing.

Provides an overview of the ethical and professional responsibilities of engineers, as engineerng professionals, as members of engineering organizations, and as participants in medical or scientific research. The course will make extensive use of student group presentations and role playing in the analysis of cases based on real-world problems with ethical dimensions. The case studies will vary from year to year, but will be chosen to reflect the full range of engineering fields and disciplines including areas of Bioengineering and Biomedical research.

305. Engineering Principles of Human Physiology. (B) Prerequisite(s): Junior Standing.

Analysis of cellular and systems-level human physiology with an emphaisis on clinical applications. Particular emphasis is on mechanisms of function in the neural and cardiovascular systems.

309. Bioengineering Lab III. (A) All students taking BE 309 are required to have satisfactorily completed BE 210 and be familiar with the operation and rules of the laboratory, use of the computer facilities and software, and safety regulations.

BE 309 is the first half of the third year continuation of BE 209 and BE 210. It is required for BSE majors and may be taken as an elective by BAS majors.

310. Bioengineering Lab IV. (B) Corequisite(s): BE 350.

Fourth semester of a two year sequence designed to integrate real world experiences into various Bioengineering and Bioengineering Science courses. Laboratory emphasizing biotransport and biomedical instumentaion.

L/R 324. Chemical Basis of Bioengineering II. (A) Prerequisite(s): PHYS 140, 141 or 150, 151, MATH 240, CHEM 101, 102.

Advanced topics in physical chemistry including solution and colloid chemistry, electrochemistry, surface phenomena, and macromolecules applied to biological systems.

330. (MSE 330) Soft Materials. (C)

L/R 350. Transport Processes in Living Systems. (B) Prerequisite(s): MATH 241 or equivalent, PHYS 140 or 150.

Introduction to basic principles of fluid mechanics and of energy and mass transport with emphasis on applications to living systems and biomedical devices.

400. Preceptorship in Clinical Bioengineering. (B)

Introduction to the integration of biomedical engineering in clinical medicine through lectures and a preceptorship with clinical faculty. This course is for BE majors ONLY, with preference given to BSE students.

402. (BE 502) From Biomedical Science to the Marketplace. (C) Prerequisite(s): Senior standing in Bioengineering or permission of the instructor.

Course Objectives and Relationship to Program Education. This course explores the transition from discovery of fundamental knowledge to its ultimate application in a clinical device or drug. Emphasis is placed upon factors that influence this transition and upon the integrative requirements across many fields necessary to achieve commercial success. Special emphasis is placed on entrepreneurial strategies, intellectual property, financing and the FDA process of proving safety and efficacy. Current public companies in the medical device and drug industry are studies in detail and critiqued against principles developed in class.

L/R 444. (BE 555, CBE 444, CBE 555, MEAM555) Nanoscale Systems Biology. Prerequisite(s): Background in Biology, Chemistry or Engineering with coursework in thermodynamics or permission of the instructor.

From single molecule studies to single cell manipulations, the broad field of cell and molecular biology is becoming increasingly quantitative and increasingly a matter of systems simplification and analysis. The elaboration of various stresses on cellular structures, influences of interaction pathways and convolutions of incessant thermal motions will be discussed via lectures and laboratory demonstration. Topics will range from, but are not limited to, protein folding/forced unfolding to biomolecule associations, cell and membrane mechanics, and cell motility, drawing from very recent examples in the literature. Frequent hands-on exposure to modern methods in the field will be a significant element of the course in the laboratory. Skills in analytical and professional presentations, papers and laboratory work will be developed.

450. (BE 550) Hemodynamics. (A) Prerequisite(s): BE 350 or equivalent, or permission of the instructor.

Development of concepts about the operation of the mammalian cardiovascular system as conceived in the years 198 (by Galenus), 1628 (by Harvey), and 1998 (at Penn by A. Noordergraaf).

455. (MEAM455, MEAM544) Continuum Biomechanics. (A)

Continuum mechanics with applications to biological systems. Fundamental engineering conservation laws are introduced and illustrated using biological and non-biological examples. Kinematics of deformation, stress, and conservation of mass, momentum, and energy. Constitutive equations for fluids, solids, and intermediate types of media are described and applied to selected biological examples. Class work is complemented by hands-on experimental and computational laboratory experiences.

470. Medical Devices. (B) Prerequisite(s): Junior or Senior standing in Bioengineering, or permission of the instructor.

This course discusses the design, development, and evaluation of medical devices. Emphasis is placed on the process of matching technological opportunities to medical needs. Medical devices are analyzed from three viewpoints: technology driven applications, competing technologies, and disease-related technology clusters.

480. Introduction to Biomedical Imaging. (A) Prerequisite(s): BE 301 or ESE 325.

Introduction to the mathematical, physical and engineering design principles underlying modern medical imaging systems including x-ray computed tomography, ultrasonic imaging, and magnetic resonance imaging. Mathematical tools including Fourier analysis and the sampling theorem. The Radon transform and related transforms. Filtered backprojection and other reconstruction algorithms. Bloch equations, free induction decay, spin echoes and gradient echoes. Applications include one-dimensional Fourier magnetic resonance imaging, three-dimensional magnetic resonance imaging and slice excitation.

483. (BE 583) Molecular Imaging. (C) Prerequisite(s): BIOL 215 or BE 305 or permission of the instructor.

This course will provide a comprehensive survey of modern medical imaging modalities with an emphasis on the emerging field of molecular imaging. The basic principles of X-ray, computed tomography, nuclear imaging, magnetic resonance imaging, and optical tomography will be reviewed. The emphasis of the course, however, will focus on the concept of contrast media and targeted molecular imaging. Topics to be covered include the chemistry and mechanisms of various contrast agents, approaches to identifying molecular markers of disease, ligand screening strategies, and the basic principles of toxicology and pharmacology relevant to imaging agents.

490. Research in Bioengineering. (C) Prerequisite(s): Junior/Senior Standing.

An intensive independent study experience on an engineering or biological science problem related to BE. Requires preparation of a proposal, literature evaluation, and preparation of a paper and presentation. Regular progress reports and meetings with faculty advisor are required.

492. Research in Biomedical Science. (C) Prerequisite(s): Junior or Senior Standing in ASBS or the BSE Program.

An intensive research experience on an engineering or biomedical science problem related to bioengineering. Requires preparation of a proposal, literature evaluation, and preparation of a research paper and presentation. Regular progress reports and meetings with a faculty advisor are required.

495. Senior Design Project. (A) Prerequisite(s): BE Senior Standing.

Design projects in various areas of bioengineering; projects are chosen by the students with approval of the instructor in the Spring semester of the Junior year; a proposal, three interim reports, a final report, and a presentation are required. Also emphasized are proposal and report writing, scheduling, project risk assessment, multidisciplinary environments and ethics.

496. Senior Design Project. (B) Prerequisite(s): BE Senior Standing.

Second semester of a year-long design project.

497. Senior Thesis in Biomedical Science. (C) Prerequisite(s): Senior Standing in Applied Science Biomedical Science Program (BAS students only).

An intensive independent project experience incorporating both technical and non-technical aspects of the student's chosen career path. Chosen topic should incorporate elements from the student's career path electives, and may involve advisors for both technical and non-technical elements. Topics may range from biomedical research to societal, technological and business aspects of Bioengineering. A proposal, regular progress reports and meetings with a faculty advisor, a written thesis, and a presentation are required.

498. Senior Thesis in Biomedical Science. (A) Prerequisite(s): Senior Standing in Applied Science Biomedical Science Program (BAS students only). Second semester of BE 497.

502. (BE 402) From Biomedical Science to the Marketplace. (A) Prerequisite(s): First year graduate level, or Senior standing in Bioengineering, or permission of the instructor.

This course explores the transition from discovery of fundamental knowledge to its ultimate application in a clinical device or drug. Emphasis is placed upon factors that influence this transition and upon the integrative requirements across many fields necessary to achieve commercial success. Special emphasis is placed on entrepreneurial strategies, intellectual property, financing and the FDA process of proving safety and efficacy. Current public companies in the medical device and drug industry are studies in detail and critiqued against principles developed in class.

505. Quantitative Human Physiology. (B) Prerequisite(s): BE 305.

Introduction to human physiology using the quantitative methods of engineering and physical science. Emphasis is on the operation of the major organ systems at both the macroscopic and cellular level.

510. Biomechanics and Biotransport. (A) Prerequisite(s): Math through 241; BE 350, BE 324 as pre-or corequisites.

The course is intended as an introduction to continuum mechanics in both solid and fluid media, with special emphasis on the application to biomedical engineering. Once basic principles are established, the course will cover more advanced concepts in biosolid mechanics that include computational mechanics and bio-constitutive theory. Applications of these advanced concepts to current research problems will be emphasized.

511. Analysis and Design of Bioengineering Signals. (B) Prerequisite(s): BE 301 or graduate status. Not intended for students with previous courses in digital signal processing.

This is a practically-oriented course in the analysis of biomedical signals focusing on medically significant applications. The specific applications will vary from year to year, but lectures will include the nature of major signals of biomedical importance, diginal signal processing including convolution, digital filtering, wavelet analysis. The course will include student experiments using Matlab and independent projects.

L/R 512. Bioengineering III: Biomaterials. (B)

This course provides a comprehensive background in biomaterials. It covers surface properties, mechanical behavior and tissue response of ceramics, polymers and metals used in the body. It also builds on this knowledge to address aspects of tissue engineering, particularly the substrate component of engineering tissue and organs.

513. Cell Biology. (A) Prerequisite(s): Graduate Standing or permission of the instructor.

Introduction to cell and molecular biology with emphasis on quantitative concepts and applications to multicellular systems.

517. (ESE 517) Optical Imaging. (C) Prerequisite(s): ESE 310 and ESE 325 or equivalent.

A modern introduction to the physical principles of optical imaging with biomedical applications. Propagation and interference of electromagnetic waves. Geometrical optics and the eikonal. Plane-wave expansions, diffraction and the Rayleigh criterion. Scattering theory and the Born approximation. Introduction to inverse problems. Multiple scattering and radiative transport. Diffusion approximation and physical optics of diffusing waves. Imaging in turbid media. Introduction to coherence theory and coherence imaging. Applications will be chosen from the recent literature in biomedical optics.

519. Cellular-Level Neural Simulation and Modeling. (M) Finkel.

Cellular level simulation of neurons at the biophysical level. Topics include cable theory, the Hodgkin-Huxley formalism for different channelspecies , synaptic interactions and plasticity, information measures in network activity, neuromodulation, and applications to modeling neurological disease.

520. (INSC594) Computational Neuroscience and Neuroengineering. (B) Finkel.

Computational modeling and simulation of the structure and function of brain circuits. A short survey of the major ideas and techniques in the neural network literature. Particular emphasis on models of hippocampus, basal ganglia and visual cortex. A series of lab exercises introduces techniques of neural simulation.

539. (ESE 539) Neural Networks, Chaos, and Dynamics: Theory and Application. (B)

Physiology and anatomy of living neurons and neural networks; Brain organization; Elements of nonlinear dynamics, the driven pendulum as paradigm for complexity, synchronicity, bifurcation, self-organization and chaos; Iterative maps on the interval, period-doubling route to chaos, universality and the Feigenbaum constant, Lyapunov exponents, entropy and information; Geometric characterization of attractors; Fractals and the Mandelbrot set; Neuron dynamics: from Hudgkin-Huxley to integrate and fire, bifurcation neuron; Artificial neural networks and connectionist models, Hopfield (attractor-type) networks,energy functions, convergence theorems, storage capacity, associative memory, pattern classification, pattern completion and error correction, the Morita network; Stochastic networks, simulated annealing and the Boltzmann machine, solution of optimization problems, hardware implementations of neural networks; the problem of learning, algorithmic approaches: Perception learning, back-propagation, Kohonnen's self-organizing maps and other networks; Coupled-map lattices; Selected applications including financial markets.

540. (BE 440, CBE 440, CBE 540) Biomolecular and Cellular Engineering.

This course provides an introduction to the quantitative methods used in characterizing and engineering biomolecular properties and cellular behavior, focusing primarily on receptor-mediated phenomena. The thermodynamics and kinetics of protein/ligand binding are covered, with an emphasis on experimental techniques for measuring molecular parameters such as equilibrium affinities, kinetic rate constants, and diffusion coefficients. Approaches for probing and altering these molecular properties of proteins are also described, including site-directed mutagenesis, directed evolution, rational design, and covalent modification. Equilibrium, kinetic, and transport models are used to elucidate the relationships between the aforementioned molecular parameters and cellular processes such as ligand/receptor binding and trafficking, cell adhesion and motility, signal transduction, and gene regulation.

545. (CIS 537) Biomedical Image Analysis. (C)

546. (BMB 546) Quantitative Image Analysis. (H)

Most of the time will be spent on different kinds of analysis methods (e.g., intensity measurements and approaches to segmentation) along with brief reviews of necessary mathematical background (e.g., transforms) and examples of specific areas of application (primarily biomedical). While traditional image processing techniques will be reviewed as a means of preparing images for analysis, they will not be a principal focus of this course.

550. (BE 450) Hemodynamics. (A) Prerequisite(s): BE 350 or equivalent, or permission of the instructor.

Development of concepts about the operation of themammalian cardiovascular system as conceived in the years 198 (by Galenus), 1628 (by Harvey), and 1998 (at Penn by A. Noordergraaf).

L/R 552. (CBE 552) Cellular Engineering. (M) Prerequisite(s): Math through 241; BE 350, BE 324 as pre- or corequisites. Molecular & cellular biology.

The goal of this course is to introduce students quantitative concepts in understanding and manipulating the behavior of biological cells. We will try to understand the interplay between molecules in cells and cell function. A particular focus is on receptors - cell surface molecules that mediate cell responses. We will also try to understand processes such as adhesion, motility, cytoskeleton, signal transduction, differentiation, and gene regulation.

553. Principles, Methods, and Applications of Tissue Engineering. (B) Gooch. Prerequisite(s): Graduate Standing or instructor's permission.

Tissue engineering demonstrates enormous potential for improving human health. While there is an extensive body of literature discussing the state of the art of tissue engineering, the majority of this literature is descriptive and does little to address the principles that govern the success or failure of an engineering tissue. This course explores principles of tissue engineering, drawing upon diverse fields such as developmental biology, immunology, cell biology, physiology, transport phenomena, material science, and polymer chemistry. Current and developing methods of tissue engineering as well as specific applications will be discussed in the context of these principles.

554. (CBE 554) Engineering Biotechnology. (M)

Advanced study of re DNA techniques; bioreactor design for bacteria, mammalian and insect culture; separation methods; chromatography; drug and cell delivery systems; gene therapy; and diagnostics.

L/R 555. (BE 444, CBE 444, CBE 555, MEAM555) Nanoscale Systems Biology. (A) Prerequisite(s): Background in Biology, Chemistry or Engineering with coursework in thermodynamics or permission of the instructor.

556. Mechanical Forces: Cells/Tissue. (M)

This course will explore the biological effects of mechanical forces at the molecular, cellular and tissue level in specific tissues (blood vessels, cartilage, bone, brain, lung, and skeletal and cardiac muscle). The importance of physical forces in the health, disease, development, remodeling and injury of these tissues will be highlighted. An understanding of these specific systems will provide a foundation for discussions of the molecular basis of mechanotransduction, mechanically induced trauma, as well as the manipulation of the mechanical environment in biotechnology and tissue engineering applications. Throughout the course, the use of engineering principles and methods to understand and model mechanically induced biological phenomena will be stressed.

L/R 557. From Cells to Tissue: Engineering Structure and Function. (C) Faculty. Prerequisite(s): Math through 241; BE350, BE324 as pre- or corequisites; Molecular & cellular biology.

The goal of this course is to introduce students to quantitative concepts in understanding and manipulating the behavior of biological cells. We will try to understand the interplay between molecules in cells and cell function. A particular focus is on receptors - cell surface molecules that mediate cell responses. We will also try to understand processes such as adhesion, motility, cytoskeleton, signal transduction, differentiation, and gene regulation.

559. Multiscale Modeling/Bio Systems. (C) Prerequisite(s): Quantum mechanics, statistical physics (undergrad level) or permission of instructor.

This course aims to provide theoretical, conceptual, and hands-on modeling experience on three different length and time scales that are crucial to biochemical phenomena in cells and to nanotechnology applications. Applications will include nuclear magnetic resonance; electron transfer; enzyme catalysis; synthesis and characterization of quantum dots; diffusion and transport in ion-channels, semiconductors, nano-wires; protein folding and conformational changes; signal transduction in cells.

L/R 562. (CBE 562, MEAM562) Robotics and Cominatorial Experimentation. (B)

An introduction to the use of robotics for large-scale experimentation. The course will cover micropositioning, micromanipulation, liquid handling, combinatorial chemistry, microfluidics and lob-on-a-chip design, DNA biochips and microarrary technologies. A special emphasis is placed on: drug discovery, detection systems; and the generation and analysis of biological diversity. Examples from material discovery will also be covered. Working knowledge in biology or fluid mechanics is not assumed, but helpful.

L/R 567. Modeling Biological Systems. (A) Prerequisite(s): Graduate Standing or instructor's permission.

This course will present a comprehensive account of the application of modeling methodology to the investigation of biological systems. The emphasis will be on an organized overview of the tools and techniques rather than the detailed mathematical structures upon which they may rely. The course will draw examples widely from the current literature in an attempt to not only show the topical relevance of the subject matter but also to equip participants with an understanding of the diversity of domains to which the techniques and methodologies apply.

575. Injury Biomechanics. (B) Prerequisite(s): ENM 500 or 510, BE 510 or MEAM 519 or equivalent. A background in physiology and anatomy is also recommended.

This course is intended as an introduction to investigating the mechanics of injury, from the organism to the tissue level. The students will be exposed to both formal didactic instruction and selected field work. The course will cover principles in continuum and analytical mechanics, and will use application in injury research to illustrate these concepts. The course will be divided into three major units. The first unit will be an introduction to variational principles of mechanics and calculus of variations, and will apply these concepts to injury problems (e.g., occupant kinematics during a collision, vehicle kinematics, impact to padded surfaces). Special emphasis will be placed on converting a system input into a body response. The second unit of the course will be used to discuss the effect of gross body motion on tissue and organ mechanical response. Material models of biological tissue will be discussed, and examples relating body motion to tissue response will be reviewed. In the final unit of this course, students are required to research and review a problem of their choice and present a report detailing an engineering based solution to the problem.

580. (PHYS582) Medical Radiation Engineering. (B) Prerequisite(s): Junior standing.

This course in medical radiatioin physics investigates electromagnetic and particulate radiation and its interaction with matter. The theory of radiation transport and the basic concept of dosimetry will be presented. The principles of radiation detectors and radiation protection will be discussed.

581. (BMB 581) Techniques of Magnetic Resonance Imaging. (M)

Detailed survey of the physics and engineering of magnetic resonance imaging as applied to medical diagnosis. Covered are: history of MRI, fundamentals of electromagnetism, spin and magnetic moment, Bloch equations, spin relaxation, image contrast mechanisms, spatial encoding principles, Fourier reconstruction,imaging pulse sequences and pulse design, high-speeding imaging techniques, effects of motion, non-Cartesian sampling strategies, chemical shift encoding, flow encoding, susceptibility boundary effects, diffusion and perfusion imaging.

583. (BE 483) Molecular Imaging. (C) Prerequisite(s): BIOL 215 or BE 305 or permission of the instructor.

584. (MATH584) Mathematics of Medical Imaging and Measurements. (M) Prerequisite(s): Math through 241 as well as some familiarity with linear algebra and basic physics.

In the last 25 years there as has been a revolution in image reconstruction techniques in fields from astrophysics to electron microscopy and most notably in medical imaging. In each of these fields one would like to have a precise picture of a 2 or 3 dimensional object, which cannot be obtained directly. The data that is accessible is typically some collection of weighted averages. The problem of image reconstruction is to build an object out of the averaged data and then estimate how close the reconstruction is to the actual object. In this course we introduce the mathematical techniques used to model measurements and reconstruct images. As a simple representative case we study transmission X-ray tomography (CT). In this contest we cover the basic principles of mathematical analysis, the Fourier transform, interpolation and approximation of functions, sampling theory, digital filtering and noise analysis.

591. Anatomy and Biomechanics of Synovial Joints. (B)

Anatomy and Biomechanics of Synovial Joints in Health and Disease.

612. Materials Affecting Cell and Molecular Function. (B)

This course provides advanced knowledge regarding the effect of the various classes of materials on tissues, cells and molecules, with the emphasis on musculoskeletal tissues. Topics include the effect of particulate matter, controlled release carriers and scaffolds for tissue repair. Emphasis is placed on recent developments in tissue engineering of bone and cartilage. The course discusses the use of materials science techniques in the study of tissue-engineered constructs. Data in the literature related to the subject matter will be extensively discussed and the students will write two articles on selected topics.

619. (BMB 604) Statistical Mechanics. (C) Prerequisite(s): CBE 618 or equivalent.

A modern introduction to statistical mechanics with biophysical applications. Theory of ensembles. Noninteracting systems. Liquid theory. Phase transitions and critical phenomena Nonequilibrium systems. Applications to reaction kinetics, polymers and membranes.

630. (EE 630) Elements of Neural Computation, Complexity and Learning. (M) Prerequisite(s): A semester course in probability or equivalent exposure to probability (e.g. ESE 530).

Non-linear elements and networks: linear and polynomial threshold elements, sigmoidal units, radial basis functions. Finite (Boolean) problems: acyclic networks; Fourier analysis and efficient computation; projection pursuit; low frequency functions. Network capacity: Feedforward networks; Vapnik-Chervnenkis dimension. Learning theory: Valiant's learning model; the sample complexity of learning. Learning algorithms: Perception training, gradient descent algorithms, stochastic approximation. Learning complexity: the intractability of learning; model selection.

645. Biological Elasticity. (C) Prerequisite(s): BE 510 or equivalent.

Large deformation mechanics of biological materials. Nonlinear elasticity theory, strain energy functions, constitutive laws of hyperelastic and viscoelastic biological materials. Applications to heart, lung, and arteries.

655. (MSE 655) Advanced Topics in Biomaterials. (M) Prerequisite(s): BE 512 and MSE 506 or permission of instructor.

The effect of nearly inert and bioactive materials on surrounding tissues. Mechanisms of bone tissue growth enhancement with bioactive ceramics. Elasticity and strength of porous coated and ceramic coated implants. Tissue remodeling around coated implants.

L/R 662. (CBE 618, MEAM662) Advanced Molecular Thermodynamics.

Review of classical thermodynamics. Phase and chemical equilibrium for multicomponent systems. Prediction of thermodynamic functions from molecular properties. Concepts in applied statistical mechanics. Modern theories of liquid mixtures.

SM 699. Bioengineering Seminar. (C)

700. Special Topics in Bioengineering. (M)

The research areas discussed will be those of the participating BE faculty who will direct the discussions and present background material. The purpose of the course is to present current research being done in the bioengineering Graduate Group and study relevant literature. The grade will be based on class participation and a final paper or presentation. Course content and staffing varies from year to year.

799. Research Rotation. (C)

895. Methods in Bioengineering Education. Bioengineering PHD students only.

This course provides training in the practical aspects of teaching. The students will attend seminars emphasizing basic pedagogical skills. Depending on the course setting for the practicum portion, student will obtain handson experience developing and delivering lectures, leading recitations, developing and supervising instructional laboratories, preparing and grading homework, grading laboratory reports, and preparing and grading examinations. Practicum experiences will be supervised by a faculty mentor. Students will meet during the practicum portion of the course to discuss difficult situations encountered in the classroom/laboratory and to constructively review each other. Final evaluations will be based on mentor, peer, and student feedback.

899. Independent Study. (C) Graduate Students Only.

For students who are studying a specific advance subject area in fulfillment of the Bioengineering rotation requirements. Students must submit a proposal outlining the study area along with the faculty supervisors approval. A paper or presentation is required.

990. Masters Thesis. (C)

For students working on a Masters Thesis project leading to the completion of a M.S.E. degree.

995. Dissertation. (C)

999. Thesis/Dissertation Research. (C)

For students working on an advanced research program leading to the completion of master's thesis or Ph.D. dissertation requirements.