It is strongly advised to have completed Calculus I and II, Physics I and II. It is also very beneficial, but not compulsory, if Differential equations, Biomechanics of Continuum Media II (fluids) and Numerical Methods in Biomedicine have been completed.

Within this course students will be provided with a foundation in understanding and solving problems related to biomedical engineering applications of momentum, heat, and mass transport phenomena. At the end of the course, each student will be able to: - Formulate differential equations that represent the physical situation of biomedical problems involving mass, momentum, or heat transfer (or combinations of these) and determine appropriate boundary conditions. - Apply conservation laws of fluid flow to describe the system for various geometries, particularly for flow through a conduit. - Distinguish between modes of heat transfer or mass transfer, explain analogies between heat and mass transfer and apply the correct equations to describe each mode. - Determine convective mass transfer coefficients using appropriate analogies for the geometric situation. - Use modeling software (Matlab) to model mass transport problems and analyze experimental data.

RA3: Be able to carry out conceptual designs for bioengineering applications according to their level of knowledge and understanding, working in a team. Design encompasses devices, processes, protocols, strategies, objects and specifications broader than strictly technical, including social awareness, health and safety, environmental and commercial considerations. RA4: Be able to use appropriate methods to carry out studies and solve problems in the biomedical field, commensurate with their level of knowledge. Research involves conducting literature searches, designing and carrying out experimental practices, interpreting data, selecting the best approach and communicating knowledge, ideas and solutions within their field of study. May require consultation of databases, safety standards and procedures. CB1: Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study. CB2: Students are able to apply their knowledge to their work or vocation in a professional manner and possess the competences usually demonstrated through the development and defence of arguments and problem solving within their field of study. CB3: Students have the ability to gather and interpret relevant data (usually within their field of study) in order to make judgements which include reflection on relevant social, scientific or ethical issues. CB4: Students should be able to communicate information, ideas, problems and solutions to both specialist and non-specialist audiences. CG2: Ability to design, draft and develop scientific-technical projects in the field of biomedical engineering. CG4: Ability to solve problems with initiative, decision-making, creativity, and to communicate and transmit knowledge, skills and abilities, understanding the ethical, social and professional responsibility of the biomedical engineer's activity. Capacity for leadership, innovation and entrepreneurial spirit. CG7: Drafting, representing and interpreting scientific-technical documentation. ECRT30: Acquire the basis for solving problems related to biomedical engineering applications concerning the transport of momentum, heat and mass. Students will be able to formulate the differential equations that represent the physical problem being studied, will be able to apply mass conservation equations and determine flows in various geometries, and distinguish between forms of transport whether convection, diffusion, or a combination of both. CT1: Ability to communicate knowledge orally and in writing to both specialised and non-specialised audiences. CT2: Ability to establish good interpersonal communication and to work in multidisciplinary and international teams. CT3: Ability to organise and plan their work, making the right decisions based on the information available, gathering and interpreting relevant data in order to make judgements within their area of study.

Intro. Introduction to Transport in Biological Systems: 1. Introduction, - 1.1. The Role of Transport Processes in Biological Systems, - 1.2. Definition of Transport Processes (Diffusion, Convection, Transport by Binding Interactions) - 1.3. Relative Importance of Convection and Diffusion, - 1.4. Transport Within Cells (Transport Across the Cell Membrane, Transport Within the Cell, - 1.5. Transcellular Transport (Junctions Between Cells, Epithelial Cells, Endothelial Cells) - 1.6. Physiological Transport Systems (Cardiovascular System, Respiratory System, Gastrointestinal Tract, Liver, Kidneys, Integrated Organ Function) - 1.7. Application of Transport Processes in Disease Pathology, Treatment, and Device Development (Transport Processes and Atherosclerosis, Transport Processes, Artificial Organs, and Tissue Engineering) - 1.8. Relative Importance of Transport and Reaction Processes Part I. Introduction to Physiological Fluid Mechanics: 2. Conservation Relations and Momentum Balances: - 2.1. Introduction, - 2.2. Fluid Kinematics (Control Volumes, Velocity Field, Flow Rate, Acceleration, Fluid Streamlines, - 2.3. Conservation Relations and Boundary Conditions (Conservation of Mass, Momentum Balances, Forces, Boundary Conditions) - 2.4. Fluid Statics (Static Equilibrium, Surface Tension, Membrane and Cortical Tension) - 2.5. Constitutive Relations (Newton's Law of Viscosity, Non-Newtonian Rheology, Time-Dependent Viscoelastic Behavior) - 2.6. Laminar and Turbulent Flow - 2.7. Application of Momentum Balances (Flow Induced by a Sliding Plate, Pressure-Driven Flow Through a Narrow Rectangular Channel, Pressure-Driven Flow Through a Cylindrical Tube, Pressure-Driven Flow of a Power Law Fluid in a Cylindrical Tube, Flow Between Rotating Cylinders) - 2.8 Rheology and Flow of Blood 3. Conservation Relations for Fluid Transport, Dimensional Analysis, and Scaling: - 3.1. Introduction, - 3.2. Differential Form of the Equation of Conservation of Mass in Three Dimensions (General Form of the Equation of Conservation of Mass, Conservation of Mass for Incompressible Fluids) - 3.3. Differential Form of the Conservation of Linear Momentum and the Navier-Stokes Equations in Three Dimensions (General Form of the Equation of Conservation of Linear Momentum, The Navier-Stokes Equation) 4. Approximate Methods for the Analysis of Complex Physiological Flow: - 4.1. Introduction, - 4.2. Integral Form of the Equation of Conservation of Mass, - 4.3. Integral Form of the Equation of Conservation of Linear Momentum Part II. Fundamentals and Applications of Mass Transport in Biological Systems: 5. Mass Transport in Biological Systems: - 5.1. Introduction - 5.2. Solute Fluxes in Mixtures (The Dilute-Solution Assumption) - 5.3. Conservation Relations (Equation of Conservation of Mass for a Mixture, Boundary Conditions) - 5.4. Constitutive Relations (Fick's Law of Diffusion for Dilute Solutions, Diffusion in Concentrated Solutions) - 5.5. Diffusion as a Random Walk - 5.6. Estimation of Diffusion Coefficients in Solution (Transport Properties of Proteins, The Stokes-Einstein Equation, Estimation of Frictional Drag Coefficients, The Effects of Actual Surface Shape and Hydration, Correlations) - 5.7. Steady-State Diffusion in One Dimension (Diffusion in Rectangular Coordinates, Radial Diffusion in Cylindrical Coordinates, Radial Diffusion in Spherical Coordinates) - 5.8. Unsteady Diffusion in One Dimension (One-Dimensional Diffusion in a Semi-Infinite Medium, One-Dimensional Unsteady Diffusion in a Finite Medium, Model of Diffusion of a Solute into a Sphere from a Well-Stirred Bath) 6. Diffusion with Convection or Electrical Potentials: - 6.1. Introduction - 6.2. Fick's Law of Diffusion and Solute Flux, - 6.3. Conservation of Mass for Dilute Solutions (Transport in Multicomponent Mixtures) - 6.4. Dimensional Analysis - 6.5. Diffusion and Convection (Release from the Walls of a Channel: A Short-Contact-Time Solution - 6.6. Macroscopic Form of Conservation Relations for Dilute Solutions - 6.7. Mass Transfer Coefficients - 6.8. Mass Transfer Across Membranes: Application to Hemodialysis 7. Energy and Bioheat Transfer -7.1. Introduction -7.2. First Law of Thermodynamics and Metabolism -7.3. Steady and Unsteady Heat Conduction -7.4. Convective Heat Transfer -7.5. Energy Transfer Due to Evaporation -7.6. Metabolism and Regulation of Body Temperature

LECTURES: Due to the large amount of topics covered and their multidisciplinary nature, it is important that the student does some research on the topic before the class. 1) Lectures: During the lectures the proposed topic will be presented, always encouraging discussion. 2) Discussion Sessions: When the topic allows it, discussion sessions will take place to solve particular problems related to the current topic with the main idea of understanding the system and developing different strategies to solve it, underlining the fact that there are almost always different approaches to the same problem. 3) Oral Presentations: At least once during the course each student will have the chance to do a short oral presentation on a topic related to the course within their "Team". These oral presentations will be prepared online by groups of between 4 and 6 students ("Teams") and have a duration of approx. 10 minutes per student. The students will prepare a video with their material which will be projected to the rest of the class during the last days of the course. TEAM PRESENTATIONS: When divided in the reduced groups, there will be several days dedicated to group research, being the class divided into 5 teams: TEAM Cardio TEAM Vascular TEAM Hemoglobin TEAM Gastro TEAM Glomerulus TEAM Joints Each team will have approximately 7 members, ensuring that each team is balanced. The role of these teams is to prepare a 50 minute class, to be presented in video format, that will be presented in VIDEO format at the end of the course on their particular topic, covering: Biology, Physics, and Artificial Organs related to their particular organ or system, One Problem to be solved by the class, and Two multiple Choice questions HOMEWORK: Homework will be assigned frequently during the course. Homework is intended to help each student practice setting up and solving momentum, heat, and mass transfer problems. For each assignment, all homework problems are required to be solved. All problems will be checked for effort. Credit will be given only for problems for which the student has made a clear attempt to solve the problem correctly. All assignments are due at the beginning of class on the due date. No late assignments will be accepted. MULTIPLE CHOICE QUIZ: During the classes multiple choice questions will be shown that are to be answered by each student individually using their mobile phone or an iPad/tablet. LABORATORY SESSIONS: These sessions are individual, and the class will be divided into its reduced groups. Each experiment will be performed individually groups. During these sessions simple experiments will be done to understand the basics of transport and flow. The main goal during these sessions is to understand the physics behind the experiment and how it relates to the theory we presented during the lectures, to obtain rigorous experimental data, to analyze this data, and finally to present this data as a scientific report. Matlab will be used to analyze the data. Students may form groups of up to 3 students to upload the report. IMPORTANT: laboratory sessions will take place during the first two weeks of the course. Attendance is mandatory.