Week of 
Topic 
Instructor 
Handouts 
PDF Lecture Notes 
Interactive Video 
Mar 29 
Foundations of Biomechanics.
Introduction to Biomechanics, Deforming and Flowing Continua, Tensors and Tensor Analysis

McCulloch 
Continuum Mechanics Preliminaries
Tensor Notation
Tensor Calculus 
Introduction to Biomechanics
Deforming & Flowing Continua
Review of Matrices
Review of Vectors
Tensors
Tensor Analysis 
Introduction(YouTube)
Deforming & Flowing Continua(YouTube)
Review of Matrices(YouTube)
Review of Vectors(YouTube)
Tensors(YouTube)
Tensor Properties and Operations(YouTube) 
Apr 5 
Stress and Kinematics.
Stress, Strain and Rate of Deformation. 
McCulloch 
Kinematics Summary 
Stress
Cauchy's Formula
Stress Equilibrium
Equilibrium Derivation
Deformation Gradient
Polar Decomposition
Strain
Flow 
Stress
Cauchy's Formula
Stress Equilibrium
Equilibrium Derivation
Deformation Gradient
Polar Decomposition
Strain
Flow
Strain and Flow Examples 
Apr 12 
Governing Laws.
Conservation Laws and Constitutive Laws for Solids and Fluids. 
McCulloch 
Conservation Laws 
Conservation of Mass
Conservation of Momentum
Conservation of Energy
Newtonian Viscous Fluids
Hookean Elastic Solids 
Conservation of Mass
Conservation of Momentum
Conservation of Energy
Newtonian Viscous Fluids
Hookean Elastic Solids 
Apr 19 
Analysis of Blood Flow.
NavierStokes equation, Poiseuille flow, Flow in elastic vessels, Pulsatile flow 
McCulloch 
Handout 
NavierStokes equations
Arterial Blood flow
Flow in elastic vessels and Pulsatile flow 
NavierStokes equations
Arterial Blood flow
Flow in elastic vessels and Pulsatile flow 
Apr 26 
Soft Tissue Mechanics.
Finite deformations. Hyperelasticity. 
McCulloch 
Handout
Hyperelasticity Handout 
Soft Tissue Mechanics
Finite Deformation Elasticity 
Soft Tissue Mechanics
Finite Deformation Elasticity 
May 3 
Finite Element Modeling of Tissue Mechanics. Finite element approximations. Finite element basis functions. Boundary conditions. Nonhomogeneous strain analysis. 
McCulloch 

Introduction to the Finite Element Method
More on the Finite Element Method 
Introduction to the Finite Element Method 
May 10 
Nonlinear Stress Analysis
Solving nonlinear boundary value problems in soft tissue elasticity. 
McCulloch 

FE Stress Analysis
Continuity documentation/Strain tutorial 

May 17 
Growth and Remodeling
Modeling volumetric finite growth and remodeling. Residual stresses. Hypertrophy and mechanotransduction mechanisms 
McCulloch 
Rodriguez et al, 1994 
Mechanics of Growth and Remodeling 

May 24 
Muscle Mechanics
Striated muscle structure and mechanics. Excitationcontraction coupling. Molecular motors. Crossbridge models. 
McCulloch 

Muscle Mechanics
The Crossbridge model 

May 31 
Cardiac Mechanics
Cardiac muscle structure and function. Modeling cardiac excitationcontraction coupling. Ventricular pump function. 
McCulloch 

Cardiac Muscle
Ventricular Mechanics 

Jun 7th 
FINAL EXAM (Closed Book and notes)
3:006:00 pm PFBH room 161 