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  • BE 567: Mathematical Computation Methods for Modeling Biological Systems

    3.00 Credits
    University of Pennsylvania

    Prerequisite(s): BE 324 and BE 350. This is an introductory course in mathematical biology. The emphasis will be on the use of mathematical and computational tools for modeling physical phenomena which arise in the study biological systems. Possible topics include random walk models of polymers, membrane elasticity, electrodiffusion and excitable systems, single-molecule kinetics, and stochastic models of biochemical networks.
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  • BE 575: Injury Biomechanics

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 580: Medical Radiation Engineering

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 581: Techniques of Magnetic Resonance Imaging

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 583: Molecular Imaging

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 584: Mathematics of Medical Imaging and Measurements

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 591: Anatomy and Biomechanics of Synovial Joints

    3.00 Credits
    University of Pennsylvania

    Anatomy and Biomechanics of Synovial Joints in Health and Disease.
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  • BE 612: Materials Affecting Cell and Molecular Function

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 619: Statistical Mechanics

    3.00 Credits
    University of Pennsylvania

    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.
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  • BE 630: Elements of Neural Computation,Complexity and Learning

    3.00 Credits
    University of Pennsylvania

    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.
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