Handouts
1: Intro to elasticity and anisotropy
Handouts
2: Material properties of bones
Powerpoint
presentation - Anatomy of femurs, material properties. Update Jan 5, 2019
Powerpoint presentation
- Typical fractures of bones.
Handouts 3: and 4: Loads on femurs and spine
Handouts 5: Fabric tensor Update Jan 5,
2019
Handouts 6: Introduction to Continuum Mechanics 1
and 2 Update Jan 5, 2019
Powerpoint
presentation – Introduction to arteries
Powerpoint
presentation – SEDFs for arteries Update Jan 12, 2019
Homework Assignments:
Solution to Homeworks:
· Solution to HW4 (Notice that in the HW the size of the cube was changed to mm3) Update Jan 12, 2019
Example of a final exam:
· 2015 final exam Update Jan 12, 2019
· Further examples of test questions
Lectures schedule:
· Week 1:
a. The syllabus, grade structure and global aims and scopes of the course.
b. Introduction and example of bone and artery mechanical response.
c. Displacements, strains and stresses.
d. Kinematic relations and the Hooke’s law for an isotropic material, equilibrium equations.
· Week 2:
a. Hooke’s law for a transversely isotropic and orthotropic material.
b. Trajectories in a transversely isotropic material and transformation of stress and strain tensors due to transformation of coordinate system.
c. Principal strains and stresses.
d. The components of bone – from nano to macro scales (pptx presentation).
e. Classification of bone into cortical and trabecular bone at the macro scale (pptx presentation).
· Week 3:
a.
Bone pathologies (osteoporosis,
fracture, stress fracture), (pptx presentation).
b. General data on bones in human body, role and types.
c. The different density measures – wet density, dry density, ash density, EQM density, BV/TV, BMD.
d.
Homogenized material
properties and their relation to density measures.
· Week 4:
a. Various relations between Young moduli and densities.
b. Clinical CTs – CT#, HU, QCT and what data does CT provide on bone densities.
· Week 5:
a. 1-D yield and ultimate strains and stresses.
b. Transversely isotropic material properties – Wirtz and Rho relations between trans.isot. material properties and densities.
· Week 6:
a. Physiological load boundary conditions on femurs and vertebrae.
b. The telemetric implanted femurs and vertebrae and the measured loads – videos of OrthoLoad and Hip98.
c. Load histories and patient variations.
d. The micro structure of the trabecular bone.
· Week 7:
a. The fabric tensor and different methods for its determination from micro-CT scans.
b. The stiffness tensor computed by the fabric tensor.
· Week 8:
a. CT-based finite element methods for the analysis of bones.
b. Pathological cases examined by the FE method: Total hip arthoplasty, risk of fracture in osteoporotic bones and femurs with metastatic tumors, analysis of compacted fractures in the humerii, fixation of Hallux Valgus in the second metatarsals. Fixation of GCT by plates.
· Week 9: Please see book of Jay Humphrey – chapters 7-8
a. The blood vessel tree, types of arteries and classification into veins and artery. Classification of arteries.
b. Structure of an artery and mechanical response. Collagen fibers distribution and their direction distribution. The elastin matrix.
c. Pathologies of arteries – atherosclerosis and aneurysm.
d. Characteristics of an elastic artery – multi-structured, composite, soft tissue, anisotropic, large deformations, residual strains.
e. Kinematic relations for large deformations, the deformation gradient, notions of strains.
· Week 10:
a. Kinematic relations for large deformations, the deformation gradient, notions of strains, invariants of the Cauchy-Green tensors, notion of stresses.
· Week 11: [JH] chapters 3,4, [GH] chapter 2
a. Definition of a strain energy density function and constitutive laws for hyperelastic materials.
b. A hperelastic material with two families of enforcing fibers (Holzapfel’s model) – the SEDF.
· Week 12:
· The smooth muscle cells, and their contribution.
· The SEDF for the active response part.
· Aneurysm of the proximal aorta and the abdominal aorta.
· Atherosclerosis of the carotid and coronary arteries
· Week 13:
· Solution of three problems as an example typical to exam questions.
Topics for future consideration.
a. micro-CT scans – what data do they provide on bone densities.
b. Kinematic means to evaluate loads during motion by analysis (Anybody code, etc).
Lecture: Nano-indentation tests and micromechanical models to evaluate homogenized material properties. ([AR], Hellmich papers)
a. Nano-indentation for the evaluation of material properties at the micro scale.
b. Hellmich’s micromechanical models to determine homogenized material properties.
Lecture : Hyperelastic constitutive equations ([GH] chapters 3 and 6)
a. Dispersion of fiber’s direction.
b. Determination of material parameters by experimentation ([JH] chapter 5).
Lecture : The active response of the artery and almost incompressibility
a. Various vasoconstrictors and vasodilators and their influence on the active response.
c. Experiments for the determination of the active response and incompressibility of arteries (ZY paper on new exp device,[JH] chapter 5).
Lecture : Surgeries in which the artery response plays important roles.
a. The coronary artery bypass grafts