### Biofluid Mechanics

#### BME 44200 / 3 Cr.

BME 44200 explores fluid and solid mechanics in the context of the human circulatory system. Principal equations are derived from differential analysis of fluid flow, and models of characteristic flow conditions are fully analyzed. Vessel biomechanics, biosolid mechanics, and hemodynamic analysis of the circulation system will also be discussed.

**Available Online:** No

**Credit by Exam:** No

**Laptop Required:** No

**Prerequisites/Co-requisites:**

P: BME 35200 and BME 35400.

**Instructor: **Julie Ji, PhD.

##### Textbooks

KB Chandran, AP Yoganathan, SE Rittgers, Biofluid Mechanics: The Human Circulation, Taylor and Francis 2007

##### Goals

Upon completion of the course, students will be able to:

- Understand basic physical properties of fluids. [1]
- Evaluate force and pressure balances acting on fluid. [1]
- Derive conservation of mass and linear momentum. [1]
- Derive and apply Navier-Stokes equations. [1]
- Able to solve classic flow models. [1]
- Analytically approach and solve fluid flow problems. [6]
- Evaluate stress and strain analysis of solids. [1]
- Understand physiology of the human circulation system. [1]
- Appreciate vascular disease mechanisms (atherosclerosis). [1]
- Apply fluid mechanics to blood flow models.[1]
- Evaluate and design biofluid mechanics problems (project). [6]

##### Topics

(roughly by lectures, order may vary)

**I. Principles of fluid mechanics**- Fluid statics: pressure and force balances
- Fluid kinematics: velocity, acceleration fields
- Control volume analysis, Reynolds Transport Theorem
- Differential analysis of fluid flow – Conservation of Mass
- Stream functions – Material derivative
- Conservation of Linear Momentum (continuity, momentum equations)
- Navier-Stokes equations, Couette flow, Poiseuille flow
- Dimensional analysis – Reynolds number
- Low Reynolds – Creeping or Stokes flow
- High Reynolds number – Euler's, Bernoulli equation
- Irrotational flow, velocity potential, viscous flow in pipe
- Flow development and laminar boundary layer

**II. Biomechanics of the human circulation**- Rheology of blood - Viscometers
- Pressure-flow relationships in blood
- Rigid tube model, entrance length
- Hemodynamics of atherosclerosis

**III. Solid mechanics**- Solid mechanics – elasticity, stress and strain
- Analysis of thin and thick-walled cylindrical tube

##### Grading

- Homework (20%)
- Exam 1 (25%)
- Exam 2 (25%)
- Final Exam (30%)