University of California San Diego

The problem solving sessions offer an exercise in bioengineering problem formulation and solving, demonstrating creative thinking, effective teamwork, and clear presentation skills. In groups of nominally three students you will:

- Formulate a problem in bioengineering in quantitative mathematical terms
- Simplify the problem to arrive at an analytical solution, and interpret the solution in terms of the dependence on the parameters;
- Use numerical methods to arrive at an approximate solution to the full problem, and interpret any discrepancies between the numerical solution and the simplified analytical solution;
- Present the problem and solutions during one of the presentation sessions, and answer questions from peer students;
- Write and submit a report, presenting and documenting the problem and solutions.

Group assignments, and the scheduling of presentations, are made during the first week of classes. Each group presents once, with two group presentations each meeting time. Time your presentations not to exceed a total of 20 minutes, not including questions. Use the whiteboard and/or your computer with provided projector for your presentations. There will be 5-10 minutes for questions, and you can use the whiteboard to answer questions. The report is due one week after your presentation, and should include title, presenters' names, problem statement, simplified solution, numerical validation, conclusion, and references/credits. Use diagrams and graphs to document the problem and the solutions. The report should be submitted over TritonEd, in PDF format. Revised submissions in response to feedback are welcome (and encouraged) through the end of finals week. Final versions of reports will be posted on the class web page as a service to future students taking the class searching for ideas and inspiration.

You may consult anyone on your problem statement and methods, but you must do the problem solving yourselves, working with your group companion. You must also give credit to all sources where these guided your problem statement or solutions. Where these sources are in the open literature, you must cite the publications in print or on-line.

Success, and enjoy!

Mathematical Model for the Determination of Oxygen Spatial Maps in Microcirculatory Networks

Modeling Doxorubicin Delivery in Tumor Cells

Modeling the Propagation of Inflammation in Atherosclerosis

Numerical Modeling of Drug Delivery in Solid Tumor Microvasculature

Building and Understanding Repressilators and Synchrony Three Cells in a Bubble Bath [ Report | Slides ]

Comparison of Intravenous Bolus vs. Infusion of Heparin Diffusion through Cubital Vein

Diffusion of dexamethasone from a PLGA-wrapped suture

Kinetic Modeling for Vesicle Drug Delivery to the Liver

Microneedle Mediated Transdermal Vaccine Delivery

Modeling EDTA Diffusion into Bone for Demineralization

Modeling of Intrathecal Drug Delivery

Modeling the Effects of Brain Cooling on Neuronal Inactivation

Models of Human Normal Vocal Fold and Vocal Cord Nodule during Phonation

Nutrient Diffusion through a 3-D Bio-printed Cellular Matrix

Thermal Modeling of Microwave Percutaneous Hepatic Tumor Ablation

Minimal Cascade Model for Mitotic Oscillator

Modeling Transdermal Delivery of Contraceptive Hormones

Mathematical Evaluation of Body Cooling Using Heat Equation

Microneedle Delivery of Ophthalmic Macromolecules

Mathematical Model for Carbon Monoxide Diffusion in Man

Mathematical Model for Protein Diffusion through Biodegradable Polymer

Hollywood vs Reality - Examining Diffusion of Etorphine Following Direct Injection

Diffusion of Acetylcholine in the Synapse

Modeling Electro-Mechanical Transduction

Diffusion of Gadolinium Contrast Agent through Patellar Cartilage

Optimizing a PID Controller for Simulated Single-Joint Arm Dynamics

Insulin-Mediated Blood Glucose

A Mathematical Model of a Synthetically Constructed Genetic Toggle Switch

1-Dimensional Model for Vocal Fold Vibration Analysis

Modeling 1-Dimensional Diffusion of TDF via an Intravaginal Ring

Modeling Oxygen Diffusion and Consumption in a Skin Graft

Modeling the Spread of Frostbite

Modeling of O2 Concentration in a Cellular Parallel-Plate Flow Bioreactor

Model of Radial Diffusion of the Drug Phenylephrine following Vein Injection

Hyperthermia Cancer Therapy by Magnetic Nanoparticles

Oxygen Diffusion in Wound Healing

Modelling Diffusion Process of Neurotransmitter Across Synapse

Modeling First-Pass Ethanol Metabolism in the Human Hepatic Lobule

Modeling Receptor Protein Regulation and Enzyme Cascades

Model of Aortic Blood Flow Using the Windkessel Effect

A Mathematical Model for an Intravenous Bolus Injection

Modeling Temperature in a Breast Cancer Tumor for Ultrasound-Based Hyperthermia Treatment

Modeling Diffusion in the Small Intestines

Modeling of Neuron Signaling from Dendrite to Axon Hillock

Modeling Bone Morphogenetic Protein Diffusion of Infuse^{®} Bone Graft

Mathematical Model for Leukocyte Migration in Prosthetic Materials

Hydrogel Drug Delivery: Diffusion Models

Keller-Segel?Models for Chemotaxis

Computational Analysis of Coffee Burns: 1-D Heat Transfer in the Skin

Modeling the BP Oil Spill of 2010: A Simplified Model of Oil Diffusion in Water

Modeling the Competitive Growth of *Saccharomyces Cerevisiae* and *Schizosaccharomyces Kefir*

Modeling the Absorption, Circulation, and Metabolism of Tirapazamine

Diffusion of Lidocaine Across Skin

Protein Diffusion in a Lipid Bilayer

Scopolamine Delivery to the Skin Using a Transdermal Patch

Spatial Distribution of Protein Concentration Can Control Cellular Pathway Fluxes

Glossal Immobilization to Metallic Beam at Hyperborean Temperatures

Modeling the Diffusion of TGF-β1 from a Fibrin Scaffold through Alveolar Bone

Two Models Simulating Focal Cerebral Cooling as a Therapy for Epilepsy

Mathematical Modeling of Heat Distribution during Cryosurgery

Modeling Drug Elution in Stents

Insulin Diffusion from a Pancreatic Islet

The Minimum-Jerk Trajectory for n-DOF Reaching Movements via Calculus of Variations

Diffusion of Acetylcholine in the Synaptic Cleft

Alcohol Diffusion in the Stomach Lining

Simulation of Glucose Diffusion in a Cylindrical Cell

Mathematical Modeling of Action Potentials with Transmission Equations and Hodgkin-Huxley Model

Drug Diffusion Through a Coated Stent

Disinfecting Mad-Cow Diseased Beef: A Heat Transfer Approach