Math Courses for MS/PhD in Bioengineering

*Please note that not all courses will be offered every year/semester and it is up to the student to confirm they have the appropriate background/prerequisites for the course.

*Please also note that there may be alternative courses that will meet the requirement, they should be 500-level or greater and should generally be taught outside of SEAS.

• AMCS 6010 Algebraic Techniques for Applied Mathematics and Computational Science I
• AMCS 6020 Algebraic Techniques for Applied Mathematics and Computational Science II
• AMCS 6080 Analytic Techniques for Applied Math and Computational Science I
• AMCS 6090 Analytic Techniques for Applied Mathematics and Computation Science II
• BE 5040 Epigenomics
• BE 5100 Biomechanics and Biotransport
• BE 5160 High-performance Scientific Computing
• BE 5180 Optical Microscopy
• BE 5300 Theoretical and Computational Neuroscience
• BE/CIS 5370 – Biomedical Image Analysis
• BE/CBE 5400 Principles of Molecular and Cellular Bioengineering
• BE 5500 Continuum Tissue Mechanics
• BE 5590 Multiscale Modeling of Biological Systems
• BE 5660 Network Neuroscience
• BE 5670 Mathematical Computation Methods for Modeling Biological Systems
• BE 5840 Mathematics of Medical Imaging and Measurements
• BIOL 5510 Statistics for Biologists
• BIOL 5511 Biological Data Analysis
• BIOL 5560 Advanced Statistics
• BIOM 5200 Concepts and Methods in Biostatistics – Basic
• BIOM 5210 Concepts and Methods in Biostatistics – Intermediate
• BMIN 5020 Databases in Biomedical Research
• BMIN 5030 Data Science for Biomedical Informatics
• BMIN 5330, Statistics for Genomics and Biomedical Informatics
• BSTA 6200 Probability I
• BSTA 6210 Statistical Inference I
• BSTA 6220 Statistical Inference II
• BSTA 6300 Statistical Methods for Data Analysis I
• BSTA 6510 Introduction to Linear Models and Generalized Linear Models.
• BSTA 7510 Statistical Methods for Neuroimaging
• BSTA 7740 Statistical Methods for Evaluating Diagnostic Tests
• CBE 5080 Probability and Statistics for Biotechnology
• CBE 5200 Modeling, Simulations, and Optimization of Chemical Processes
• CBE 5220 Polymer Rheology and Processing
• CBE 6170 Control of Nonlinear Systems
• CHEM 5210 Statistical Mechanics 1
• CIS 5150 Fundamentals of Linear Algebra and Optimization
• CIS 5190 Applied Machine Learning
• CIS 5200 Machine Learning
• CIS 5360 Computational Biology
• ENM 5020 Numerical Methods and Modeling
• ENM 5030 Introduction to Probability and Statistics
• ENM 5100 Foundations of Engineering Mathematics I
• ENM 5110 Foundations of Engineering Mathematics II
• ENM 5200 Theory and Computation for ODE/PED-constrained optimization
• ENM 5200 Topics in Computational Science and Engineering
• ENM 6000 Functional Analysis
• ENM 6010 Special Topics in Engineering Mathematics – Nonlinear Dynamics and Chaos
• ESE 5000 Linear Systems Theory
• ESE 5020 Introduction to Spatial Analysis
• ESE 5040 Introduction to Optimization Theory
• ESE 5050 Control of Systems
• ESE 5300 Elements of Probability Theory and Random Processes
• ESE 5310 Digital Signal Processing
• ESE 6030 Simulation Modeling and Analysis
• ESE 6320 Random Process Models and Optimum Filtering
• ESE 6740 Information Theory
• MATH 5120 Advanced Linear Algebra
• MATH 5840 Mathematics of Medical Imaging
• MATH 5861/BIOL 5860 Mathematical Modeling in Biology
• MEAM 5220 Fundamentals of Sensor Technology
• MEAM 5270 Finite Element Analysis
• MEAM 5280 Advanced Kinematics
• STAT 5000 Applied Regression and Analysis of Variance
• STAT 5100 Probability
• STAT 5110 STATISTICAL INFERENCE
• STAT 5120 Mathematical Statistics
• STAT 5300 Probability
• STAT 5410 Statistical Methods
• STAT 5420 Bayesian Methods and Computation
• STAT 5500 Mathematical Statistics
• STAT 5710 Modern Data Mining

Biological Science Courses for MS/PhD in Bioengineering

*Please note that not all courses will be offered every year/semester and it is up to the student to confirm they have the appropriate background/prerequisites for the course.

*Please also note that there may be alternative courses that will meet the requirement, they should be 5000-level or greater and should generally be taught outside of SEAS.

• BE 5300 Theoretical and Computational Neuroscience
• BE 5400 Principles of Molecular and Cellular Bioengineering
• BE 5530 Principles, Methods, and Applications of Tissue Engineering
• BE 5550 Nanoscale Systems Biology
• BE 5580 Principles of Biol Fabrication
• BE 5610 Musculoskeletal Biology & Bioengineering
• BE 5650 Systems Biology of Tissues and Organogenesis
• BE 5660 Network Neuroscience
• BE 5670 Modeling Biological Systems
• BE 5690 Systems Biology of Cell Signaling and Behavior
• BE 5760 The Cell as a Machine
• BE 5780 – Principles of Controlled Release Systems
• BMIN 5010 Introduction to Biomedical and Health Informatic
• BIOL 5210 Molecular Biology and Genetics
• BIOL 5220 Human Evolutionary Genomics
• BIOL 5240 Genetic Analysis
• BIOM 5010 Mechanisms of Disease and Therapeutics
• BIOM 6000 Cell Biology
• BIOM 5020 Mechanisms of Disease
• BIOM 5100 Case Studies in Translational Research
• BMB 5080 Molecular Biophysics I
• BMB 5090 Macromolecular Biophysics II
• BMB 5100 Data Analysis and Scientific Inference
• BMB 5670 Bioinorganic Chemistry
• BMB 5850 Macromolecular Biophysics: Principles and Methods
• BMB 5900 Biological Physics
• BMB 6140 Membrane Structural Biology
• BMB 6160 Medical Problems in Modern Biochemistry
• BMB 6220 Physical Principles of Mechano-Enzymes
• BMB 6240 Ion Channels and Pumps
• BMB 6250 Optical Methods in Cell Physiology
• BMB 6260 Mass Spectrometry and Proteomics
• BMIN 5010 Introduction to Biomedical and Health Informatics
• BSTA 5090 Introduction to Epidemiology
• BSTA 5100 Introduction to Anatomy and Physiology
• BSTA 7510 Statistical Methods for Neuroimaging
• CAMB 5110 Principles of Development
• CAMB 5220 Human Evolutionary Genomics
• CAMB 5260 Experimental Principles in Cell and Molecular Biology
• CAMB 5320 Human Physiology
• CAMB 5500 Genetic Principles
• CAMB 5970 Developmental Neuroscience
• CAMB 6090 Vaccines and Immunization Therapy
• CAMB 6100 Molecular Basis of Gene Therapy
• CAMB 6380 Advanced Seminar in Cell Death and Survival
• CAMB 6970 Biology of Stem Cells
• CAMB 7520 Genomics
• CBE 5170 Principles of Genome Engineering
• CIS 5350 Introduction to Bioinformatics (also offered as GCB 5350 and MTR 5350)
• GCB 5270 Genetics for Computational Biology
• IMUN 5060 Immune Mechanisms
• IMUN 5080 Immune Responses
• IMUN 6090 Vaccines and Immune Therapeutics
• INSC 5750 Neurobiology of Learning and Memory
• MEAM 5550 Nanoscale Systems Biology
• MMP 5110 Image- Based Anatomy
• MMP 5120 Radiation Biology
• NGG 5720 Neuroscience Core Ii
• NGG 5730 Neuroscience Core III
• NGG 5750 Neurobiology of Learning and Memory
• NGG 5870 Neurobiology of Disease
• NGG 5880 Topics in Translational Neuroscience
• NGG 5920 Cognitive Neuroscience of Memory
• NGG 5930 Structural Neurobiology
• NGG 5940 Theoretical and Computational Neuroscience
• NGG 5980 Advanced Systems Neuroscience
• NGG 6180 Recovery after Neural Injury
• NGG 6310 Cognitive Neuroscience Affect
• NGG 6320 Cognitive Neuroscience Vision
• PHRM 5310 Intro to Genome Science
• PHRM 5700 Principles of Cardiovascular Biology
• PHRM 6000 Medical Pharmacology
• PHRM 6230 Fundamentals of Pharmacology
• REG 6180 Introduction to Vaccine Development

BE 5020 From Biomedical Science to the Marketplace

This course explores, through own work (this is, own discovery) the transition from 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 upon entrepreneurial strategies, intellectual property, and the FDA process of proving safety and efficacy. Graduate students or permission of the instructor.

• Course usually offered in fall term Activity: Lecture
• 1.0 Course Unit

BE 5040 Biological Data Science II: Data Mining Principles for Epigenomics

This course will teach upper level undergraduates and graduate students how to answer biological questions by harnessing the wealth of genomic and epigenomic data sets generated by high-throughput sequencing technologies. Graduate students or permission of the instructor

• Course usually offered in spring term Activity: Lecture
• 1.0 Course Unit

BE 5100 Biomechanics and Biotransport

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.

• Course usually offered in spring term
• Prerequisites: MATH 241, BE 200, 350
• Activity: Lecture
• 1.0 Course Unit

BE 5120 Bioengineering III: Biomaterials

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. General Chemistry, basic biomechanics.

• Course usually offered in fall term Activity: Lecture
• 1.0 Course Unit

BE 5140 Rehab Engineering and Design

Students will learn about problems faced by disabled persons and medical rehabilitation specialists, and how engineering design can be used to solve and ameliorate those problems. The course combines lectures, multiple design projects and exercises, and field trips to clinical rehabilitation facilities. Students will have substantial interaction with clinical faculty, as well as with patients. Prerequisite: Graduate students or permission of the instructor.

• Course usually offered in fall term
• Also Offered As: IPD 504
• Activity: Lecture
• 1.0 Course Unit

BE 5150 Bioengineering Case Studies

This course has the unofficial title “What Makes Medical Technology Work?” We will examine biomedical devices and technologies with significant engineering components for use in breast cancer detection, for minimally invasive treatment of cancer and other disease, and applied neuroscience technologies for rehabilitation. Various factors that determine the success of particular medical systems will be discussed, including the “fit” of the technology with a medical need, testing for safety and efficacy, FDA premarket approval requirements, clinical studies used to assess the technology for evidence-based medicine. The class will examine successful and unsuccessful examples of these technologies. The course will require extensive reading of papers from the professional literature , group presentations and papers. BE seniors and graduate students are encouraged to enroll. Graduate students or permission of the instructor.

• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 5160 Introduction to High-Performance Scientific Computing

Research problems in the domain of physical, biological and biomedical sciences and engineering often span multiple time and length-scales from the molecular to the organ/organism, owing to the complexity of information transfer underlying biological mechanisms. Multiscale modeling (MSM) and high-performance scientific computing (HPC) have emerged as indispensable tools for tackling such complex problems. However, a paradigm shift in training is now necessary to leverage the rapid advances, and emerging paradigms in HPC — GPU, cloud, exascale supercomputing, quantum computing — that will define the 21st century. This course is a collaboration between Penn, UC Berkeley, and the Extreme Science and Engineering Discovery Environment (XSEDE) which administers several of the federally funded research purpose supercomputing centers in the US. It will be taught as a regular 1 CU course at Penn by adopting a flip-classroom/active learning format. The course is designed to teach students how to program parallel architectures to efficiently solve challenging problems in science and engineering, where very fast computers are required either to perform complex simulations or to analyze enormous datasets. The course is intended to be useful for students from many departments and with different backgrounds, e.g., scholar of Penn Institute for Computational Science, although we will assume reasonable programming skills in a conventional (non-parallel) language, as well as enough mathematical skills to understand the problems and algorithmic solutions presented.

• Taught by: Ravi Radhakrishnan
• One-term course offered either term Also Offered As: CBE 506
• Activity: Lecture
• 1.0 Course Unit

BE 5180 Optical Microscopy

An introduction to the fundamental concepts of optics and microscopy. Geometrical optics: ray tracing, optical elements, imaging systems, optical aberrations. Physical optics: the electromagnetic spectrum, the wave equation, diffraction, interference and interferometers, optical resolution limits, optical coherence, lasers. Microscopy methods: phase contrast, differential interference contrast, fluorescence microscopy, confocal microscopy, multiphoton microscopy, optical coherence tomography, superresolution microscopy.

• Course usually offered in fall term Prerequisite: MATH 240
• Activity: Lecture
• 1.0 Course Unit

BE 5210 Brain-Computer Interfaces

The course is geared to advanced undergraduate and graduate students interested in understanding the basics of implantable neuro-devices, their design, practical implementation, approval, and use. Reading will cover the basics of neuro signals, recording, analysis, classification, modulation, and fundamental principles of Brain- Machine Interfaces. The course will be based upon twice weekly lectures and “hands-on” weekly assignments that teach basic signal recording, feature extraction, classification and practical implementation in clinical systems.

Assignments will build incrementally toward constructing a complete, functional BMI system. Fundamental concepts in neurosignals, hardware and software will be reinforced by practical examples and in-depth study. Guest lecturers and demonstrations will supplement regular lectures. BE 301 (Signals and Systems) or equivalent, computer programming experience, preferably MATLAB (e.g., as used the BE labs, BE 310). Some basic neuroscience background (e.g. BIOL 215, BE 305, INSC core course), or independent study in neuroscience, is required. This requirement may be waived based upon practical experience on a case by case basis by the instructor.

• Course usually offered in spring term
• Also Offered As: NGG 521
• Activity: Lecture
• 1.0 Course Unit

BE 5270 Immune Engineering

This course would target graduate students and upper level undergraduate students. This course introduces to students the concept of immune engineering that ranges from vaccine design to cancer immunotherapy and cutting edge tools recently developed in these areas. It is best suited for graduate students and upper level undergraduate students who have had cell biology and immunology. We will build on the topics covered in Immunology and explore deeper questions and applications in cancer immunotherapy, infection, and auto-immune diseases, and high-throughput immune profiling technologies. The course will use a combination of lectures, journal clubs, and a final project presentation that will be discussed mirroring NIH study section format. The course is open to graduate students and upper level undergraduate students who have taken courses in biochemistry and/or cell biology.

• Taught by: N. J. Jiang, PhD
• One-term course offered either term Activity: Lecture
• 1.0 Course Unit

BE 5280 Applied Medical Innovation I

Applied Medical Innovation I: Bedside to Bench is a hands-on, project-based team design experience for graduate students, offered in partnership with the Center for Health, Devices, and Technology (Penn Health Tech). The course acts as an idea INCUBATOR for projects originating from unmet clinical needs, identified by clinical collaborators, industry sponsors, and Penn Health Tech partners. By the end of this course, students will understand all aspects of medical device design, innovation, and entrepreneurship, including the importance of a clear problem definition and stakeholder input, an introduction to engineering design principles, and how to navigate the complex pathway by which these products reach patients. The end point of the semester is a final pitch (outlining the need, the solution, and the business opportunity) and a functional prototype with initial proof of concept data. The course is open to all graduate and senior undergraduate students (pre- application required).

• Taught by: Katherine Reuther
• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 5290 Applied Medical Innovation II

Applied Medical Innovation II: Bench to Bedside is a hands-on, interdisciplinary, project experience for graduate students, offered in partnership with the Center for Health, Devices, and Technology (Penn Health Tech). The course acts as device ACCELERATOR for projects originating from Applied Medical Innovation I and Penn Health Tech. Students partner with experienced technical teams (clinicians + engineers) to create a commercialization plan for real-world, cutting-edge medical technologies under development at Penn. Students work closely with their interdisciplinary team to identify and validate the clinical need, stakeholder requirements, and business case in order to de-risk the technology, increase commercial potential, and package the idea for follow-on investment. In the second half of the course, students will also gain exposure to medical technology entrepreneurship and investing. The course is open to all graduate and senior undergraduate students (pre-application required).

• Taught by: Katherine Reuther
• Activity: Lecture
• 1.0 Course Unit

BE 5300 Theoretical Neuroscience

This course will develop theoretical and computational approaches to structural and functional organization in the brain. The course will cover: (i) the basic biophysics of neural responses, (ii) neural coding and decoding with an emphasis on sensory systems, (iii) approaches to the study of networks of neurons, (iv) models of adaptation, learning and memory, (v) models of decision making, and (vi) ideas that address why the brain is organized the way that it is. The course will be appropriate for advanced undergraduates and beginning graduate students.

Knowledge of multivariable calculus, linear algebra and differential equations is required (except by permission of the instructor). Prior exposure to neuroscience and/or Matlab programming will be helpful.

• For BA Students: Natural Science and Math Sector
• Taught by: Vijay Balasubramanian
• Course usually offered in spring term
• Also Offered As: BIBB 585, NGG 594, PHYS 585, PSYC 539
• Activity: Lecture
• 1.0 Course Unit

BE 5370 Biomedical Image Analysis

This course covers the fundamentals of advanced quantitative image analysis that apply to all of the major and emerging modalities in biological/biomaterials imaging and in vivo biomedical imaging. While traditional image processing techniques will be discussed to provide context, the emphasis will be on cutting edge aspects of all areas of image analysis (including registration, segmentation, and high-dimensional statistical analysis). Significant coverage of state-of-the-art biomedical research and clinical applications will be incorporated to reinforce the theoretical basis of the analysis methods. Prerequisite: Mathmatics through multivariate calculus (MATH 241), programming experience, as well as some familiarity with linear algebra, basic physics, and statistics.

• Taught by: Paul Yushkevich
• One-term course offered either term
• Also Offered As: CIS 537, MPHY 609
• Activity: Lecture
• 1.0 Course Unit

BE 5400 Biomolecular and Cellular Engineering

This course will introduce concepts and methods for the quantitative understanding of molecular and cellular phenomena. Topics include molecular recognition, receptor-ligand binding, viral infection, signal transduction, cell adhesion, motility, and cytoskeletal dynamics. The course requires mathematics at the level of differential equations, and some knowledge of Matlab programming. A basic knowledge of cell biology is suggested, although not required.

• One-term course offered either term
• Also Offered As: CBE 540
• Activity: Lecture
• 1.0 Course Unit

BE 5410 Engineering and Biological Principles in Cancer

This course provides an integrative framework and provides a quantitative foundation for understanding molecular and cellular mechanisms in cancer. The topics are divided into three classes: (1) the biological basis of cancer; (2) cancer systems biology; and (3) multiscale cancer modeling. Emphasis is placed on quantitative models and paradigms and on integrating bioengineering principles with cancer biology. Prerequisite: Seniors in BE or permission of the instructor.

• Course usually offered in spring term
• Also Offered As: CBE 541
• Activity: Lecture
• 1.0 Course Unit

BE 5460 Fundamental Techniques of Imaging I

This course covers the fundamentals of modern techniques in biological and in vivo biomedical imaging. This practical course consists of a series of hands-on lab exercises, covering major imaging modalities, but also extends to non-radiology modalities of interest in biological, pathological or animal imaging (e.g., optical imaging). Topics include x-ray, mammography, CT, proton therapy, radiation safety and brachytherapy. The emphasis will be on hands-on aspects of all areas of imaging and imaging analysis. Small groups of students will be led by a faculty member with technical assistance as appropriate. Graduate students or permission of the instructor.

• Course usually offered in spring term
• Activity: Lecture
• 1.0 Course Unit

BE 5470 Fundamental Techniques of Imaging 2 (BE 483/583 or MMP 507 preferred).

This laboratory course covers the fundamentals of modern medical imaging techniques. Students will participate in a series of hands-on exercises, covering the principals of X-ray imaging, CT imaging, photoacoustic imaging, diffusion tensor imaging, localized magnetic resonance (MR) spectroscopy, MR contrast agents, diffuse optical spectroscopy, and bioluminescence imaging. Each lab is designed to reinforce and expand upon material taught in BE483/583 Molecular Imaging and MMP507 Physics of Medical Imaging Graduate students or permission of the instructor.

• Course usually offered in spring term
• Activity: Lecture
• 1.0 Course Unit

BE 5500 Continuum Tissue Mechanics

This course introduces tensor calculus and continuum mechanics, with a focus on finite-deformation behavior of biological tissues including skin, tendon/ligament, cartilage, bone, blood vessels, nerves. Senior/Graduate Student in Bioengineering or permission of the instructor.

• Course usually offered in spring term
• Activity: Lecture
• 1.0 Course Unit

BE 5510 Biomicrofluidics

The focus of this course is on microfluidics for biomedical applications. Topics to be covered in the first half of this course include microscale phenomena, small-scale fabrication techniques, and sensing technologies that are often leveraged in the development of microfluidic systems for the study of biomolecules, cells, tissues, and organs in living biological systems. In the second half of this course, strong emphasis will be placed on the application of microfluidics in cell biology, bioanalytical chemistry, molecular biology, tissue engineering, and drug discovery. Prereqisite: Experience with an undergraduate level fluid mechanics course is preferred. Examples of relevant SEAS courses include BE 350 (Biotransport), CBE 350 (Fuild Mechanics), and MEAM 302 Fluid Mechanics).

• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 5530 Principles, Methods, and Applications of Tissue Engineering

Tissue engineering demonstrates enormous potential for improving human health. This course explores principles of tissue engineering, drawing upon diverse fields such as developmental biology, 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. A significant component of the course will involve review of current literature within this developing field. Graduate Standing or instructor’s permission. Course usually offered in spring term

• Activity: Lecture
• 1.0 Course Unit

BE 5540 Engineering Biotechnology

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.

• Course usually offered in spring term
• Also Offered As: CBE 554
• Activity: Lecture
• 1.0 Course Unit

BE 5550 Nanoscale Systems Biology

Nano-science and engineering approaches to systems in biology are of growing importance. They extend from novel methods, especially microscopies that invite innovation to mathematical and/or computational modeling which incorporates the physics and chemistry of small scale biology. Proteins and DNA, for example, are highly specialized polymers that interact, catalyze, stretch and bend, move, and/or store information. Membranes are also used extensively by cells to isolate, adhere, deform, and regulate reactions. In this course, students will become familiar with cell & molecular biology and nano-biotechnology through an emphasis on nano- methods, membranes, molecular machines, and ‘polymers’ – from the quantitative perspectives of thermodynamics, statistical physics, and mechanics. We specifically elaborate ideas of energetics, fluctuations and noise, force, kinetics, diffusion, etc. on the nano- thru micro- scale, drawing from very recent examples in the literature.

Laboratory experiments will provide hands-on exposure to microscopies in a biological context (eg. fluorescence down to nano-scale, AFM), physical methods (eg. micromanipulation, tracking virus-scale particles or quantum dots), and numerical problems in applied biophysics, chemistry, and engineering. A key goal of the course is to familiarize students with the concepts and technology (plus their limitations) as being employed in current research problems in nanoscale systems biology, extending to nanobiotechnology. Prerequisite: Background in Biology, Physics, Chemistry or Engineering with coursework in Thermodynamics or permission of the instructor.

• Taught by: Discher
• Course usually offered in fall term
• Also Offered As: CBE 555, MEAM 555
• Activity: Lecture
• 1.0 Course Unit

BE 5580 Principles of Biological Fabrication

BE 558 introduces methodological approaches that are currently used for the de novo construction of biological molecules – primarily, nucleic acids and proteins – and how to use these molecules to engineer the properties of cells and intact tissue. By the end of the semester, students should (i) possess a molecular-scale understanding of key biological synthesis (ii) and assembly processes, (ii) gain an intuition for how to create novel (iii) methodologies based on these existing processes, and (iii) appreciate (iv) the drivers of technology adoption (e.g. cost, time, ease, and (v) reproducibility). Throughout the course, we will place the material in context of applications in bioengineering and human health, including: protein engineering, drug discovery, synthetic biology & optogenetics, bio-inspired materials, and bio-electronic devices. Graduate standing or permission of the instructor. Undergraduate level biology, physics and chemistry.

• Course offered fall; odd-numbered years
• Activity: Lecture
• 1.0 Course Unit

BE 5590 Multiscale Modeling of Chemical and Biological Systems

This course provides theoretical, conceptual, and hands-on modeling experience on three different length and time scales – (1) electronic structure (A, ps); (2) molecular mechanics (100A, ns); and (3) deterministic and stochastic approaches for microscale systems (um, sec). Students will gain hands-on experience, i.e., running codes on real applications together with the following theoretical formalisms: molecular dynamics, Monte Carlo, free energy methods, deterministic and stochastic modeling, multiscale modeling. Prerequisite: Undergraduate courses in numerical analysis and physical chemistry.

• Taught by: Ravi Radhakrishnan
• Course not offered every year
• Also Offered As: CBE 559, SCMP 559
• Activity: Lecture
• 1.0 Course Unit

BE 5610 Musculoskeletal Biology and Bioengineering

The goal of this course is to educate students in core principles and expose them to cutting-edge research in musculoskeletal biology and bioengineering through (1) lectures covering the basic engineering principles, biological fundamentals, and clinical practices involved in the function, repair, and regeneration of the musculoskeletal tissues; (2) critical review and presentation by student groups of recent and seminal publications in the field related to the basic science, translation, and clinical practice of musculoskeletal biology and bioengineering, with discussion input by faculty members with relevant expertise. This course will place an emphasis on delivering multidisciplinary knowledge of cell and molecular biology, mechanics, material science, imaging, and clinical medicine as it relates to the field of musculoskeletal bioengineering and science. Graduate student standing in Engineering and/or CAMB. Undergraduate students with permission of the instructor.

• Course offered fall; odd-numbered years
• Activity: Lecture
• 1.0 Course Unit

BE 5620 Drug Discovery and Development

Intro to Drug Discovery; Overview of Pharmaceutical Industry and Drug Development Costs, Timelines; High Throughput Screening (HTS): Assay Design and Sensitivity Solid Phase Synthesis and Combinatorial Chemistry; Enzyme Kinetics; Fluorescence, Linearity, Inner-filter effect, quenching; Time dynamics of a Michaelis- Menton Reaction; Competitive Inhibitor; FLINT, FRET, TRF, FP, SPA, alpha-screen; Enzyme HTS (protease); Cell based screening; Fura-2 ratio, loading signaling; Gfpcalmodulin-gfp integrated calcium response; Estrogen/ERE-Luc HTS; Problems with cell based screening (toxicity, permeability, nonspecificity); Instrumentation, Robotics/Automation; Z-factor; SAR, Positioning Scanning; Microarray HTS; IC50, % Conversion in HTS and IC50, Assay Optimization.

• Course usually offered in fall term
• Also Offered As: CBE 562
• Activity: Lecture
• 1.0 Course Unit

BE 5650 Developmental Engineering of Tissues

This course discusses systems biology approaches to understanding tissue development, homeostasis, and organogenesis. Emphasis is placed on modern technologies, models, and approaches to understanding collective cell behaviors that sculpt tissue form and function, placing developmental principles within an engineering framework. We will consider morphogenetic, mechanobiology, and micro-engineering/sensing analyses. Senior Standing in Bioengineering or permission of the instructor. In keeping with modern graduate-level engineering classes, this course will assume some basic knowledge of coding and/or willingness to learn coding practices. The course will not attempt to serve as a comprehensive introduction to developmental biology (CAMB 511: Principles of Development is a recommended potential companion course). However, your success in the course will not require familiarity with developmental biology.

• Taught by: Alex Hughes
• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 5660 Networked Neuroscience

The human brain produces complex functions using a range of system components over varying temporal and spatial scales. These components are couples together by heterogeneous interactions, forming an intricate information-processing network. In this course, we will cover the use of network science in understanding such large-scale and neuronal-level brain circuitry. Prerequisite: Graduate standing or permission of the instructor. Experience with Linear Algebra and MATLAB.

• Course usually offered in spring term
• Also Offered As: ESE 566
• Activity: Lecture
• 1.0 Course Unit

BE 5670 Mathematical Computation Methods for Modeling Biological Systems

This course will cover topics in systems biology at the molecular/cellular scale. The emphasis will be on quantitative aspects of molecular biology, with possible subjects including probabilistic aspects of DNA replication, transcription, translation, as well as gene regulatory networks and signaling. The class will involve analyzing and simulating models of biological behavior using MATLAB. Prereqisite: Graduate standing or permission of the instructor.

• One-term course offered either term
• Also Offered As: AMCS 567, GCB 567
• Activity: Lecture
• 1.0 Course Unit

BE 5680 Causality for Medicine and Biology

The goal of this course is to introduce students to the analysis of data which aims at understanding causal relations. Within biomedical research there are randomized experiments that effortlessly get at certain kinds of causality but generally only allow low-dimensional probing. There are also observational studies that generally do not meaningfully get at causality. The field of econometrics has worked out a great deal of approaches that meaningfully allow the estimation of causality without randomized experiments. This set of techniques is largely unknown in much of biology and medicine. We will thus review the econometric approaches with an eye towards applications to biology and medical problems. We will also review ways of infusing these techniques with machine learning approaches to obtain more meaningful estimates.

• One-term course offered either term
• Activity: Lecture
• 1.0 Course Unit

BE 5690 Systems Biology of Cell Signaling Behavior

This course discusses the principles of cell signaling and cell decisions. We start from a molecular description of cell signaling components. The course builds towards understanding how their interactions govern cell and tissue behavior and how these processes can breakdown in disease. We conclude with a survey of modern approaches to analyze and manipulate signaling networks to study and control biological systems. Graduate, Junior or Senior standing in Bioengineering or permission of the instructor.

• Course usually offered in spring term
• Activity: Lecture
• 1.0 Course Unit

BE 5700 Biomechatronics

Mechatronics is the combination of mechanical, electrical and computer engineering principles in the design of electromechanical systems. Biomechatronics is the application of these principles to human biology and includes orthopaedic, hearing, respiratory, vision and cardiovascular applications. In this hands-on, project-based course, these biomechatronic systems will be explored. Students will learn the basic mechanical and electrical elements needed to complete a biomechatronic design challenge including basic circuits, design considerations, material fabrication, microcontrollers and mechanisms (e.g. converting rotational motion into linear motion). Students will carry out a final design project utilizing these building blocks. A first course in programming (Matlab and/or C++ preferred), Senior standing in BE or permission of the instructor.

• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 5710 The Goals of Scientific Inquiry

A key skill needed for a successful career in engineering and applied science is the ability to capitalize on current advances in technology (e.g., big data, data science, machine learning) to solve important problems. To gain this ability a student must go beyond an understanding of the technology itself, and instead must achieve the more challenging capacity to identify tractable problems, to formulate good questions, to initiate big ideas, to guide the advancement of science. In this course, we provide a broad and rich perspective on science as a field, laying the critical groundwork for just such achievements. Prerequisites: The course is open to all graduate students. Undergraduates must have passed Math 241, ENM 375 or equivalent, CIS 120 or higher, and PHYS 141. PHIL 025 or similar is beneficial but not required.

• Taught by: Bassett, D
• Course offered spring; even-numbered years
• Activity: Lecture
• 1.0 Course Unit

BE 5730 Special Topics in Bioengineering – 1

This special topics course will focus on emerging topics in Bioengineering at the molecular and cellular level covering genomics, epigenetics, molecular and cellular systems with focus on immunology, cancer, neuroengineering, biomechanics, and other facets of bioengineering

• Taught by: BE Staff
• Course usually offered in spring term
• Activity: Lecture
• 1.0 Course Unit

BE 5740 Special Topics in Bioengineering -2

This special topics course will focus on emerging topics in Bioengineering at the macroscale from organ to population level covering genomics, epigenetics, molecular and cellular systems with focus on immunology, cancer, neuroengineering, biomechanics, and other facets of bioengineering

• Taught by: BE Staff
• Course usually offered in spring term
• Activity: Lecture
• 1.0 Course Unit

BE 5760 The Cell as a Machine

The course is a general survey of cell mechanics, emphasizing problem-based and hypothesis-testing approaches. It is based on the concept that the cell is a complex machine, and that the cell can therefore be understood by first understanding principles of complex functions in robust machines, and then understanding the design and operation of complex functions specifically in cells. The course has been offered internationally for many years using a reverse-classroom format. Lectures, which are given primarily by Michael Sheetz, former director of the Mechanobiology Institute at the National University of Singapore, are pre-recorded and viewed independently by students, who also do outside reading and prepare questions in advance of a live, remote, 2 hour question/discussion session with Dr. Sheetz. The Penn course directors are present at all question/discussion sections, and lead tutorials on site. Homework and exams are graded, and Penn course directors will review them for consistency. Other sites that will be involved in the course in the coming year include Columbia, MIT, and Berkeley. Graduate Standing or permission of the instructor.

• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit
• Notes: Auditors not permitted

BE 5780 Principles of Controlled Release Systems

This course provides a basic understanding of the engineering of controlled release systems specifically geared towards the development of formulations for drug delivery, which stands as a 114 billion dollar industry. The course focuses on topics at the interface between engineering and medicine, such as biomaterials, pharmacokinetics, polymer chemistry, reaction kinetics, and transport phenomena. Design of controlled release systems for transdermal, aerosol, oral, gene, and targeted cellular delivery are discussed with emphasis placed on fabrication, US FDA regulatory considerations, and the relevant physiological milieu. The course comprises (1) foundational lectures that provide the basic tools for the student to elaborate a controlled delivery system, (2) an overview of key current research on biomedical controlled release systems for different pathologies and body compartments, (3) an elevator pitch competition for original ideas that use controlled release systems, and (4) a project; plan and presentation to implement the pitched controlled release; system idea to practice design and problem-solving skills and practice basic elements of business proposal. Graduate students and senior standing in Bioengineering, Chemical and Biomolecular Engineering, or permission of the instructor.

• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 5810 Techniques of Magnetic Resonance Imaging

Detailed introduction to the physics and engineering of magnetic resonance imaging as applied to medical diagnosis. Covered are magnetism spatial encoding principles, Fourier analysis, spin relaxation, imaging pulse sequences and pulse design, contrast mechanisms, chemical shift, flow encoding, diffusion and perfusion, and a discussion of the most relevant clinical applications.

• Taught by: Song and Wehrli
• Course offered spring; odd-numbered years
• Also Offered As: BMB 581
• Activity: Lecture
• 1.0 Course Unit

BE 5830 Physics of Medical / Molecular Imaging

Physical principles of diagnostic radiology, fluoroscopy, computed tomography; principles of ultrasound and magnetic resonance imaging; radioisotope production, gamma cameras, SPECT systems, PET systems; diagnostic and nuclear medicine facilities and regulations. The course includes a component emphasizing the emerging field of molecular imaging.

• Course usually offered in fall term
• Also Offered As: BE 483, MPHY 602
• Prerequisite: MATH 241 AND BIOL 215 AND BE 305
• Activity: Lecture
• 1.0 Course Unit

BE 5840 Mathematics of Medical Imaging and Measurements

In the last 25 years there 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 which is accesible is typically some collection of 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 context we cover the basic principles of mathematical analysis, the Fourier transform, interpolation and approximation of functions, sampling theory, digital filtering and noise analysis.

• Course not offered every year
• Also Offered As: AMCS 584, MATH 584
• Prerequisite: MATH 114 AND MATH 360 OR MATH 508 AND MATH 361 OR MATH 50 9
• Activity: Lecture
• 1.0 Course Unit

BE 5970 Master’s Thesis Research

For students working on an advanced research program leading to the completion of master’s thesis.

• One-term course offered either term
• Activity: Masters Thesis
• 1.0 Course Unit

BE 5990 Master’s Independent Study

The purpose of BE 599 is to allow a student to create a customized curriculum to study material beyond or outside the scope of our standard BE course offerings. Independent study is NOT a research or design project, it is a one-on-one or small- group course with a professor. The course should require an effort comparable to that of a regular course, about 10-12 hours per week. A paper or presentation is required

• One-term course offered either term
• Activity: Independent Study
• 1.0 Course Unit

BE 6080 Medical Entrepreneurship: Commercializing Translational Science

This course provides in depth insight into the process by which health technology platforms including scientific discoveries are transformed into viable commercial entities. This includes methods to evaluate market opportunities and derisk critical assumptions within the rapidly changing academic and healthcare environment.

Topics include intellectual property creation and licensing, technology transfer, regulatory pathways, raising capital/NIH SBIR/STTR grant funding, go to market strategy, market sizing, formation equity, and recruiting co-founders. The major project will involve the formation of teams that will create a defendable business plan and consummate in a presentation (pitch deck) intended to raise capital. The course will be especially valuable for students who may be considering entrepreneurial career paths including starting a company, working for an early stage venture, healthcare consulting, or assuming innovation leadership roles.

• Taught by: Nalaka Gooneratne, MD; Adam Dakin
• MBA Course usually offered in spring term
• Also Offered As: MTR 620 Activity: Lecture
• 1.0 Course Unit

BE 6400 Mechanobiology of the Cell and its Microenvironment

This course is geared towards first and second year graduate students in BGS/CAMB and SEAS/BE with an interest in the interface of extracellular matrix (ECM) cell biology and biomechanics. Students will learn about the ECM and adhesion receptors and their impact on the cytoskeleton and signaling, as well as fundamental concepts in biomechanics and engineered materials. We will discuss how these topics can inform the study of cell biology, physiology and disease. An additional objective of the course is to give students experience in leading critical discussions and writing manuscript reviews. Invited outside speakers will complement the strengths of the Penn faculty.

• Taught by: R. Mauck, R. Wells.
• Course offered spring; even-numbered years
• Also Offered As: CAMB 703
• Prerequisite: BIOM 600 Activity: Lecture
• 1.0 Course Unit

BE 6500 Advanced Biomedical Imaging Applications

The course will cover a broad range of biomedical imaging technologies including X- ray, MRI, US, molecular and optical imaging. The curriculum will focus on the design of biomedical imaging based research studies spanning from basic technology development through clinical trials. This discussion oriented course is expected prepare students for integrating imaging technology and biomedical concepts to answer biological and medical questions.

• Course usually offered in fall term
• Activity: Lecture
• 1.0 Course Unit

BE 6620 Advanced Molecular Thermodynamics

This course begins with a brief review of classical thermodynamics, including the development of Maxwell relationships and stability analysis. The remainder of the course develops the fundamental framework of statistical mechanics, then reviews various related topics including ideal and interacting gases, Einstein and Debye models of crystals, lattice models of liquids, and the basis of distribution function theory.

• Course usually offered in fall term
• Also Offered As: CBE 618, MEAM 662
• Activity: Lecture
• 1.0 Course Unit

BE 7110 Integrative plant and animal mechanobiology

This course aims to provide students with an understanding of biomechanics that spans the plant and animal kingdoms, with the goal of emphasizing principles common to both. Major concepts include 1) Plant and Animal Cell Biology; 2) Solid, Fluid, and Transport Mechanics; and 3) Integrating Biology and Mechanics – Big Questions. In addition to lectures, there will be two journal article discussion sections. Most lectures will be given by Penn faculty, although selected topics (particularly in plant biology and mechanics) will be covered by faculty at other sites through lectures broadcast remotely. The Penn director will be present at all sessions of the class. Undergraduates require special permission from the director.

• Taught by: Rebecca Wells
• Course usually offered in fall term
• Also Offered As: CAMB 711
• Activity: Lecture
• 1.0 Course Unit

BE 9900 Masters Thesis

For Master’s students who have completed the course requirements for the Master’s degree and are strictly working to complete the Master’s Thesis leading to the completion of a Master’s degree. Permission Required.

• One-term course offered either term
• Activity: Masters Thesis
• 1.0 Course Unit

BE 9990 Thesis/Dissertation Research

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

• One-term course offered either term
• Activity: Independent Study
• 1.0 Course Unit