0540.6445 ביומכאניקה של עצמות ועורקים

Biomechanics of bones and arteries

קורסי קדם: מכניקת מוצקים I

קורסי קדם מומלצים: מבוא לתורת האלסטיות , מבוא לאלמנטים סופיים

סילבוס: חזרה על תורת האלסטיות הלינארית בגופים תלת ממדיים. מערכת השלד והמבנה רב הסקאלות של רקמת העצם. אנאיזוטרופיית העצם והטנזור הבדי. קביעת התכונות המכאניות האיזוטרופיות והטרנסוורסלי-איזוטרופיות של רקמת העצם מנתוני סיטי. עומסים פיזיולוגיים ותנאי שפה על עצם הירך, עצם ההומרוס ועל חוליות עמוד שדרה. מקרים פתולוגיים שנבדקו באנליזות אלמנטים סופיים: החלפת מפרק ירך, סכנת שבר בעצמות אוסטאופורוטיות ועצמות ירך עם גרורות סרטניות, אנליזות לשברים בדחיסה בהומרוס, ותיקון Halux Valgus בעצמות כף הרגל.

מבוא לעורקים: אנטומיה של עורק והמבנה המורכב. מבוא למכניקת הרצף. חוקים קונסטיטוטיביים היפראלסטיים. התגובה האקטיבית של עורקים וכמעט בלתי-דחיסות. ניתוחים בהם התגובה המכנית של העורק מכרעת.

Grade: Final exam 90%, 5 Homework assignments 10%.

Suggested Prerequisites: Intro to Elasticity, Intro to finite element analysis

Detailed Weekly Syllabus

Lecture 1: Introduction to the theory of linear elasticity in 3-D: ([IS] chapters 1,2,3)

1. The syllabus, grade structure and global aims and scopes of the course
2. Displacements, strains and stresses.
3. Kinematic relations and the Hooke’s law for an isotropic material, equilibrium equations.
4. Hooke’s law for a transversely isotropic and orthotropic material.

Lecture 2: Intro to linear elasticity (continuation)

1. Trajectories in a transversely isotropic material and transformation of stress and strain tensors due to transformation of coordinate system.
2. Invariants of strain and stress tensors
3. Principal strains and stresses.

Lecture 3: Introduction to the skeleton system and the multi-level structure of bone ([DB] chapters 1,3)

1. General data on bones in human body, role and types.
2. The components of bone – from nano to macro scales.
3. Classification of bone into cortical and trabecular bone at the macro scale.
4. Bone pathologies (osteoporosis, fracture, stress fracture).
5. The different density measures – wet density, dry density, ash density, EQM density, BV/TV, BMD.
6. Micro indentation and the determination of material properties.

Lecture 4: Bone anisotropy and the related fabric tensor. (Cowin&Zysset papers and others)

1. The micro structure of the trabecular bone.
2. The fabric tensor and different methods for its determination from QCT data.

Lecture 5: Determination of isotropic and transversely isotropic material properties from CT and micro-CT scans. (E(rho) – [ZY,NT], Schileo papers)

1. Clinical CT and micro-CT scans – what data do they provide on bone densities.
2. Various relations between Young moduli and densities, and yield and ultimate strains and stresses.
3. Homogenized material properties and their relation to density measures.

Lecture 6: Physiological load boundary conditions on femurs, humeri and vertebrae. (Bergman in-vivo studies, kinematic analysis, Wille&Yosibash papers)

1. The telemetric implanted femurs, humeri and vertebrae and the measured loads – videos of OrthoLoad and Hip98.
2. Muscle locations and direction of applied forces.
3. Load histories and patient variations.
4. Kinematic means to evaluate loads during motion by analysis (Anybody code, etc).

Lecture 7: Pathological cases examined by the Finite element method

1. 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 ([DB] chapters 7-9, Yosibash papers)

Lecture 8: Introduction to arteries: The anatomy of an artery and the complex structure and deformation ([JH] chapters 7 and 8)

1. The blood vessel tree, types of arteries and classification into veins and artery. Classification of arteries.
2. Structure of an artery and mechanical response. Collagen fibers distribution and their direction distribution. The elastin matrix.
3. Pathologies of arteries – atherosclerosis and aneurysm.
4. Characteristics of an elastic artery – multi-structured, composite, soft tissue, anisotropic, large deformations, residual strains.

Lecture 9: Introduction to the theory of continuum mechanics ([JH] chapters 3,4, [GH] chapter 2)

1. Kinematic relations for large deformations, the deformation gradient, notions of strains, invariants of the Cauchy-Green tensors, notion of stresses.
2. Definition of a strain energy density function and constitutive laws for hyperelastic materials.

Lecture 10: Hyperelastic constitutive equations ([GH] chapters 3 and 6)

1. A hperelastic material with two families of enforcing fibers (Holzapfel’s model) – the SEDF.
2. Dispersion of fiber’s direction.
3. Determination of material parameters by experimentation ([JH] chapter 5).

Lecture 11: The active response of the artery and almost incompressibility

1. The smooth muscle cells, and their contribution.
2. The SEDF for the active response part.
3. Various vasoconstrictors and vasodilators and their influence on the active response.
4. Experiments for the determination of the active response and incompressibility of arteries (ZY paper on new exp devices,[JH] chapter 5).

Lecture 12: Surgeries in which the artery response plays important roles.

1. The coronary artery bypass grafts
2. Aneurysm of the proximal aorta and the abdominal aorta.
3. Atherosclerosis of the carotid and coronary arteries.

Lecture 13: Summary of the course and preparation for the final exam.

Textbook:

Handouts provided by the lecturer

Helpful other textbooks & papers:

[JH] Jay D. Humphrey, Cardiovascular solid mechanics, Cells, Tissues, Organs, Springer 2002

[GH] Gerhard A. Holzapfel, Nonlinear solid mechanics, A continuum approach for engineering, Wiley, 2001

[IS] I.S. Sokolnikoff, Mathematical Theory of Elasticity, McGraw-Hill, 1956

[DB] Donald L. Bartel, Dwight T. Davy and Tony M. Keaveny, Orthopaedic biomechanics, Mechanics and design in musculoskeletal systems, Pearson Prentice Hall, 2006

[AR] Andreas G. Reisinger, Dieter H. Pahr, Philippe K. Zysset , “Principal stiffness orientation and degree of anisotropy of human osteons based on nanoindentation in three

distinct planes”, J of the Mechanical Behaviour of Biomedical Materials, 24, 2113-2127, (2011).

[ZY] Yosibash Z, Trabelsi N. and Milgrom, C., "Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations", Journal of Biomechanics, 40, 3688-3699, (2007).

[NT] Trabelsi N. and Yosibash Z., "Patient-specific FE analyses of the proximal femur with orthotropic material properties validated by experiments", ASME Journal of Biomechanical Engineering, 133 (6), pp. 061101-1-11, (2011).

Grading:

10% Home assignments

90% Final exam

Similar courses at universities worldwide:

Bones:

Boston University, USA: ME/BE/MS 524: Skeletal Tissue Mechanics (E. Morgan)

UC Berkeley, USA: ME C210 /Bio Eng C209: Advanced Orthopedic Biomechanics

Univ. of Oregon, USA    ME 753: Bone Biomechanics

Washington Univ, USA  BIOEN 520 | ME 527 MUSCULOSKELETAL BIOMECHANICS

TAU – Biomedical Eng   0553.5360 Bone Biomechanics

Arteries:

EPFL, Switzerland: ME-481 Biomechanics of the cardiovascular system

Washington Univ, USA: BIOEN326 Blood vessel mechanics

Technical Univ Eindhoven, Holland, : 8QA03 - Mechanics of a Blood Vessel