Homework #6 KEY Systems Bioengineering I, Fall 2013, page 1 of 10
Homework 6: Computational Models of the Myocyte
(100 points in total)
As per HW policy, ALL MATLAB code must be turned in along with
your solutions.
Suppose the transport of K+ ions across
Homework #4 KEY Systems Bioengineering I, Fall 2013, page 1 of 9
Homework 4: Contractile Mechanisms I
(70 points in total)
1. (30 points total) CLASSICAL LUMPED PARAMETER MODELS
FPE
kPE
FAct
FTot
kSE
FSE
T0
B
FDash
x1
x2
Consider the classical lumped para
Homework #1 KEY Systems Bioengineering I, Fall 2013, page 1 of 8
Homework 1: Ion-channel permeation
(100 points in total)
1. (40 pts) Review of circuit analysis.
A. Consider the battery connected to an infinite chain of resistors as drawn immediately belo
Homework #1 Systems Bioengineering I, Fall 2013, page 1 of 8
Homework 1: Ion-channel permeation
(100 points in total)
1. (40 pts) Review of circuit analysis.
A. Consider the battery connected to an infinite chain of resistors as drawn immediately below.
I
Homework #5 KEY Systems Bioengineering I, Fall 2013, page 1 of 12
Homework 5: Contractile Mechanisms Part II: Huxley 57 Derivation and
Simulation, Types of Muscle, and Excel-baed Monte Carlo Simulation
(90 points in total)
1. (10 points) HUXLEY 57 MODEL D
Homework #2 KEY Systems Bioengineering I, Fall 2013, page 1 of 10
Homework 2 KEY: Ion-channel gating (100 points in total)
1. (40 pts) Consider a simple human voltage-activated K channel with a single n gate, whose
properties are given by the Eyring-rate-
Homework #11 Systems Bioengineering I, Fall 2013
Page 1 of 11
Homework 11:
Electrical Model of the circulation, Baroreceptor Reflex, Hemorrhage
(70 points total, will be scaled up to 100 points)
Electrical Model of the Circulation
The four-quadrant model
Systems Bioengineering I HW VII Fall 2013
Page 1 of 10
Homework VII
Basic circulatory hydraulics and heart as a pump
(65 points total - will be scaled to 100 points)
Pressure Background
The cardiovascular system is designed to be a transport system. The r
Homework #10 Systems Bioengineering I, Fall 2013
Page 1 of 11
Homework 8:
Application of Poiseuilles Law, Compliance, and Starlings Filtration Hypothesis
(43 points total will be scaled to 100 points)
Background on Poiseuilles Law
Poiseuilles Law gives th
Homework #9 KEY Systems Bioengineering I, Fall 2013
Page 1 of 12
Homework 9:
Basic circulatory hydraulics and heart as a pump
(65 points total - will be scaled to 100 points)
Pressure Background
The cardiovascular system is designed to be a transport syst
Homework #3 KEY Systems Bioengineering I, Fall 2012, page 1 of 7
Homework 3: More gating and action-potential generation KEY
(100 points in total)
1. (80 points total) ION-CHANNEL GATING (Shaker K channels). Consider the whole-cell
current trace carried b
Homework #2: Systems Bioengineering I, Fall 2013, page 1 of 10
Homework 2: Ion-channel gating (100 points in total)
1. (40 pts) Consider a simple human voltage-activated K channel with a single n gate, whose
properties are given by the Eyring-rate-theory
Homework #3 Systems Bioengineering I, Fall 2012, page 1 of 7
Homework 3: More gating and action-potential generation
(100 points in total)
1. (80 points total) ION-CHANNEL GATING (Shaker K channels). Consider the whole-cell
current trace carried by Shaker
Homework #5 Systems Bioengineering I, Fall 2013, page 1 of 9
Homework 5: Contractile Mechanisms Part II: Huxley 57 Derivation and
Simulation, Types of Muscle, and Excel-baed Monte Carlo Simulation
(90 points in total)
1. (10 points) HUXLEY 57 MODEL DERIVA
Homework #6 Systems Bioengineering I, Fall 2013, page 1 of 4
Homework 6: Computational Models of the Myocyte
(100 points in total)
As per HW policy, ALL MATLAB code must be turned in along with
your solutions. Comment your code!
Suppose the transport of K
1
Homework Assignment: Propagating Action
Potentials
To simulate the propagating action potential along a ber of length l (from
left to right), Vm (x, t) has to be determined as the solution to the following
PDE
a
2 Vm
Vm
= Cm
+ Iion
2
2(i + e ) x
t
wher
1
Homework Assignment: Propagating Action
Potentials: Key
We need to solve the equation
a 2 Vm
Vm
= Cm
+ Iion
2
2i x
t
together with
Iion = Gk (Vm Ek ) + GN a (Vm EN a )
and the ODEs for the gating variables n, m, h, nd Vm (x, t) over the length
of a one-
Set Initial
Conditions
Vm(n,0)=Vrest
m(n,0)=m(Vrest)
h(n,0)=h(Vrest)
n(n,0)=n(Vrest)
Set Boundary
Conditions
Vm(0,t)=V(2,t)
Vm(N-1,t)=V(N+1,t)
for t=0 to
t=timesteps*t
while 0<t<T
|ion=NNa*m4h*gNa*(Vm-ENa)
+NK*n4*gK*(Vm-EK)
+Istim
while t>T
while |ion=NNa
Homework #8 Systems Bioengineering I, Fall 2013, page 1 of 3
Homework 8: Electrocardiography
(100 points in total)
1. (30 pts)
At rest, the heart rate of an individual is 60 beats/min. Under these conditions, the
dominant pacemaker cells in the individual