BME 503
Spring 2016
Professor Nicoll
Due Date: 3/15/16
Homework Assignment #1 Solutions
1. Materials with a bcc metal structure have atom contact along the body diagonal.
(a) Show that the lattice constant, a, for a bcc metal is
4R
where R is the atomic r
Chapter 4: The Circulatory System Question 4.8
A Wain/Med aviary will resist; exfmsm / on! Se due;
to the, em- warbseri 0d"? fresSWQ Move e; Axel]
than 16k, W an? Mrre; m Mvdmacl arm/17
will cilia/L at A hi (or assure, Mum/L 12M, [EL assure.
"(s rewvale
Examples of full electronic texts available via CCNY library
Found via a WorldCat search
Engineering Materials for
Biomedical Applications, 2004
Principles of Biomedical
Engineering, 2010
The Biomedical Engineering Handbook,
4th edition, 4 volume set, 201
Stress and Strain
Axial Loading
Review of Chapter 2 from
Mechanics of Materials, Beer, Johnston & DeWolf, McGrawHill, third edition, 2001
All Figures taken from the text (second edition)
Purpose of chapter: To introduce the concept of strain,
to discuss
Name:
_
BME 50100 Cell and Tissue Mechanics
Homework #7 Due 4/7/16
Using the two-link spinal model presented in class with a load of 200 N and the following parameters
(and using the diagram below and the class slides)
h = 50 cm
H = 60
E = 5 cm
b = 30 cm
Types of muscle
?
specialized for heart contraction
only voluntary muscle
lines internal organs, found in
some blood vessels
Skeletal muscle
Most abundant tissue in the body: ~40-45% of total weight
> 400 skeletal muscles (found in pairs); usually act in
Knee joint
Largest joint
Two-joint structure:
Articular
cartilage
tibiofemoral joint
patellofemoral joint
http:/www.medicinenet.com/image-collection/knee_joint_picture/picture.htm
Situated between two longest
lever arms in the body:
susceptible to injur
BME 501 Cell and Tissue Mechanics
Prof. Susannah Fritton
Department of Biomedical Engineering
Spring 2016
Course topics
Introduction
Mechanics review
Bone
Cartilage, ligament, tendon, viscoelasticity
Skeletal muscle
Joint force calculations
Knee joint
Sep
The Spine
Forms supporting backbone of
the skeleton
Protects spinal cord
Spine mechanics
Facet joints allow motion
Ligaments stabilize spinal column
http:/static.spineuniverse.com/
Intervertebral disks provide
stability & distribute loads
Intervertebral d
Calculating joint forces
Important when restoring function (e.g., with an implant) or for rehab
Human body
Rigid: can maintain posture
Flexible: can move because of joints
Forces on the human body
cnx.org
Internal: forces associated with muscles, ligament
Hip joint
One of the most stable joints in the body; stability provided by ball & socket
Has lots of mobility
acetabulum
http:/72.32.38.129/hip/hipanatomy/images/Normal_hip.gif
http:/www.reshealth.org/images/greystone/em_0244.gif
Hip kinematics, range o
The heart: an efficient pump
http:/www.humananatomyorgans.com
3 major types:
Blood vessels
Arteries/arterioles: carry blood away from heart
Capillaries: enable gaseous exchange between blood
and tissues
Veins/venules: return blood to heart
The circulatory
Articular Cartilage
Covers the ends of long bones;
provides articulating surface
No blood vessels
No nerves
Not many cells (chondrocytes)
Mechanical functions:
Distribute joint load over a wide
area ( joint stresses)
Allow joint movement with
minima
Bone mechanics
Borelli (1608 - 1679)
Bone functions
1.
2.
3.
4.
5.
Provides mechanical support
Allows movement via attachment to muscles
Protects internal organs
Produces blood cells in marrow
Aids mineral ion balance (especially calcium &
phosphorus)
htt
BME 50100 Cell and Tissue Mechanics
Solutions for Homework #4 (3/14/2016)
In order to calculate material properties (not depending on geometry) a stress/strain curve is needed.
Stress and strain are calculated from displacement and load data normalized by
Bone mechanical properties
http:/www.pt.ntu.edu.tw/hmchai/biomechanics/bmmaterial/bmbone.htm
Bone mechanical properties arise from the tissue
materials and their architectural arrangement
Two-phase (biphasic) composite material: mineral (strong, brittle)
Lecture'10*
Concept'Question*
You can work with a partner. Write down your
answer.
If we use 5% of the oxygen in our blood, can we
survive in an atmosphere with 15, 10 or 5% oxygen?
Why or why not?
Use a model to support your answer.
Variation of Para
Lecture 9
Systems of DE
We will study systems of first order DE that are sp
ecial cases of systems that have the normal for
m
dx1
g1 t , x1 , x2 ,.xn
dt
dx2
g 2 t , x1 , x2 ,.xn
dt
dx3
g 3 t , x1 , x2 ,.xn
dt
Such a system is called a system of firs
Lecture'5)
Heart and Circulation 4
Mass'balance)
Net Accumulation =
Transport in transport out + generation consumption
THIS APPLIES TO EVERYTHING
How do we account for generation and consumption?
Reaction'rate'equations'for'
generation'and'consumption)
W
Lecture 6
Heart and Circulation 5
Quiz 1
Consider the mass balance over a differential volume in
the x direction. Write an equation for
x/L = f(CA, CA1, CA2)
Ficks law:
dC
jA = DAB
dx
What are the BC at x=0, x=L?
SA1
L
Quiz 2
Write an equation f
Lecture 2
Heart and Circulation 1
How does pressure relate
to volume?
PV=nRT
Differentiate with respect to time
! nRT $
d#
&
! 1 $ dV
dP
" V %
=
= nRT # 2 &
" V % dt
dt
dt
V(t)? Lets assume a linear relationship such that:
V (t) = V0 + at
dV
=a
dt
How
Review
This review will cover
Solving 1st order ODEs
o Integrating Factors
o Separation by Variables
o Homogeneous and Nonhomogeneous ODEs
Solving 2nd order ODEs
o Reduction of Order
o Variation of Parameters
o Undetermined Coefficients
Systems of Eq
Dynamical systems and modeling
BME 30500
Introduction to
Mathematical Modeling
Differential Equations (DE) and
Initial Value Problems
What equations do you know?
Mathematical Modeling
Models are conceptual constructions that allow
formulation and testing
Lecture 14
Inhala/on anthrax
Disease spread
We seek to model the transmission of a disease through a popula/on. Such modeling is very
important to the study of epidemiology and the prac/ce of medicine, since examining
Lecture 3
Heart and Circulation 2
Concept Questions
1. How long does it take a single blood cell to
circulate once around the body?
2. What happens to the flow rate if the viscosity goes
up by a factor of 20%, keeping the radius
constant?
3. What happen