Problem 33
Consider a 1D model of transport in pulmonary airways
(a) Start with a 1D mass transport equation for the gas mixture:
[ PA ] [ PQ ]
+
=J S L , 0< z< L
t
z
Note that the crosssectional area and surface area/length of the airways change with
EBME 202, Spring 2016 Exam 1 Study guide
Disclaimers: This list is not all inclusive and is intended to serve as a guide only. Relative importance, headings
and amount of text between sections is not necessarily constant. All concepts are not necessarily
9. a) Explain the mathematical development that shows a series of perfectly mixed compartments can
approximate a time delay.
b) Explain how you can find the characteristic time scale (i.e., time constant) for a firstorder, linear, timeinvariant system.
l
Name _
EBME 309 Quiz (q) (1/12/16)
T
F
1. The simple models of drug absorption, epidemics, and stem cell differentiation
are structured as compartments in series.
X
_
2. If all the terms in an initialvalue problem involve dependent variable(s),
then the
EBME 309 BIOMECHANICAL MODELING
HOMEWORK NO. 2
1. In an experiment, a transfemoral amputee (left leg amputated above the knee)
stood with the right leg on a force platform that measures the ground reaction forces
as shown in Figure Q.1.a. The purpose of
Name _
EBME 309 quiz (q) (1/26/16)
T
F
1. For the multipool model of glucose metabolism, the C14 tag on the input glucose
is measured in the blood glucose and expired CO2.
X
_
2. In general, each compartment of the multipool model of glucose metabolism
Name _
EBME 309 Quiz (Q) I.1 (1/14/16)
T
F
1. In a model of solute concentration dynamics, different initial and input solute
concentrations can be incorporated.
_
_
2. A model of concentration dynamics for two perfectly mixed compartments
in series with
Name _
EBME 309 quiz (q) (1/19/16)
T
F
1. The diffusive transport rate of a nonreacting solute across a homogeneous
membrane is proportional to its surface area and membrane permeability coefficient. X
_
2. If a Laplace transform with respect to time is
Name _
EBME 309 Quiz I.2 (Q) (1/21/16)
T
F
1. For appropriately scaled impulse and step responses of a linear compartment
model of chemical species concentration dynamics, the step response is the
derivative of the impulse response.
_
2. A flowthrough tr
Name _
EBME 309 quiz (q) (2/2/16)
T
F
1. A simple model of cell proliferation assuming contact inhibition describes the net rate
of population change produced by linear cell division and quadratic cell death.
X
_
2. The model of endothelial cell migration
EBME 309: ASSIGNMENT 3 (due 2/2/16)
(These problems will be done in teams. Each team will submit as a PDF file one set of answers
including MATLAB codes . Use MathType for symbols and equations.)
1. Drug delivery from a medium on skin has the following ch
Bioelectrics Homework 1 Rubric
General Matlab Code (10 pts)
Uses a loop to search for threshold values
ode15s function calculations: derivatives, currents, second spatial
difference
Code correctly identifies propagation of an action potential
Correctly re
EBME 309: ASSIGNMENT 1 (due 1/19/16)
(These problems will be done in teams. Each team will submit one set of answers as a PDF file
including MATLAB codes . Use MathType for symbols and equations.)
1. Characterize the following differential equations (in w
EBME 309: ASSIGNMENT 2 (due 1/26/16)
(These problems will be done in teams. Each team will submit one set of answers as a PDF file
including MATLAB codes . Use MathType for symbols and equations.)
1. Consider a 3phase tissue system consists of capillary
Bioelectrics Homework 2 Solutions
Problem 1
The relationship between fiber diameter and threshold most resembles a decaying exponential (or
another reasonable fit) as the fiber diameter increases, the minimum threshold required to stimulate the
fiber decr
Name _
EBME 309 quiz (Q) (1/28/16)
T
F
1. Only two species mass balances are needed to determine the species concentration
output of a system of two compartments in parallel without any direct interaction.
_
_
2. Under some conditions, the solute concentr
3. Consider the initial value problem:
d 1
= 1 [ ( ) 1 ] ; 1= , <0
d
d i
= i1 i1 i i ; i= , =0 (i=2,3)
d
The model parameters are and i, where i j (i,j = 1,2,3).
a) What is the input of this system? Impulse input =
1 ( )
What is the impulse response funct
11. Obtain the steadystate equations for G, X, and I from the following:
dG
=k 1 [G bG ( t ) ] k 4 X ( t ) G(t )
dt
dX
=k 2 [ I bI ( t ) ] k 3 X (t)
dt
Express these equations in terms of the perturbation variables:
g ( t )=G ( t )G , x ( t )=X ( t )X ,i
Problem 25
Consider a model for pulmonary ventilation, diffusion, and perfusion under steadystate conditions.
a. Draw a system diagram that describes the inputs and outputs of inert tracer gases in the dead
space, alveolar space, and the pulmonary capill
Radhika Vazirani
Problem 7:
Distinguish between the following:
(a) a boundaryvalue problem and an initialvalue problem
BoundaryValue problem: a boundary value problem specifies the conditions of the dependent
variable at 2+ points.
(ex: if z is the dep
Problem 8:
a) Find the roots and homogenous solution for [D2+2D+1]y(t) =1 with the initial conditions
t=0; Dy=1, y=0. How is the homogeneous solution related to the impulse response
function?
Roots ( ):
2
2
D + 2 D+1= +2 +1=0
( +1 ) ( +1 ) =0
=1,1
Homogen
EBME 309 Test 1 Study Guide Problem 23
23. a) We assume that the stomach acts as an unperfused variable volume compartment, empties at
a rate dependent on its volume expansion about a fasting state: Vs(t) =
V S ( t )V s and a constant
mass density.
dV s
=
6. (a) Explain how you would solve:
dy
+ty=f t 2 ; y= y 0 , t=0 ;
dt
The general solution is
t
y (t )= y 0 g ( tt 0 + x(w) g ( t w dw
t0
First we need to find the impulse response function:
t
a ( ) d
g ( t s =e
Where
s
U (ts)
a ( ) = .
Once we find th
2. Given the following problem where
0 t 1 :
df [ + ( 1 ) f ] f
=
; f =1 ; t=0
dt
[+f ]
Where
For
0< <1 . Simplify for
f
f for f
L
df [ + ( 1 ) f ] f f
=
=
=f =1; f =1 ; t=0
dt
[+f ]
For
f
df [ + ( 1 ) f ] f f 2 f 2
=
=
=1; f =1 ; t=0
dt
f
[+f ]
E1 SG Q28
a) Why must the precision of optimal parameter estimates and residuals be examined for the
validation process?
it is important to examine the precision to find the variance, if there is too large a variance value
this indicates a poor data set
b
E1 SG Q18
Given the LaPlace transform solutions from the perfusion dynamics: (reference study guide)
Obtain the limiting cases of 0 and
For 0: = 0 and for : assume all values with the exception of s are negligible
1=
( s 2+ )
(s)
2=
( s)
( s ) = 1 2
E1 SG Q13
a) Explain each term of the 1D solute transport model:
R reaction process within the system or compartment
CQ axial convection (in)
jA axial diffusion (in)
Axial convection and diffusion components enter and exit the compartment based on sign
J
Radhika Vazirani
Problem 5:
Describe whether the following differential equations in terms of Linearity, Time Variance,
and Homogeneity.
d 3 y ( ) dy 2
+c t
( t ) =0
dt
dt3
( )
a)
dy
dt
2
( )

Linear: Nonlinear because of
term

Homogeneity: Not homog
EBME 309 Test 1 Study Guide Problem 22
22. a)
b)For when there is a glucose increase:
[ ]
[ ]
fg
f h
=k 1
=k
G o
G o 4
The 1st partial derivative in this case will be negative because there is glucose loss by metabolism
due to negative feedback processes.