Syllabus MATH 4/5779: Math Clinic

Last update
10/20/2013
1
SYLLABUS
MATH 4/5779
–
Math Clinic
Medical Image Analysi
s
Using Artificial Neural Nets
in Support of Detection,
Diagnosis
, and
Prognosis
Sponsor:
University of Colorado
Department of Radiation Oncology
Spring Semester

2010
Instructors: Weldon A.
Lodwick and Francis Newman
Resea
rch Assistant:
Shoshona Rosskamm
Office:
Weldon Lodwick
,
U
C

Denver Building
,
Room 643
Francis Newman
, UC

Denver Building
,
Room 609
Shoshona Rosskamm,
UC

Denver Building,
Room 609
Telephone:
303.556
.8462 (office), 303.556.
8442 (sec
retary), 303.556.
8550 (fax)
AMC, Francis
720.848.0134
E

Mail:
UCD

DDC,
Weldon Lodwick
weldon.lodwick@ucdenver.edu
UCD

AMC, Francis Newman
francis.newman@ucdenver.edu
UCD

DDC, Shoshana Rosskamm
shoshana.rosskamm
@email.ucdenver.edu
Web Site:
Instructors’ website
http://www

math.ucd
enver.edu/~wlodwick
Clinic website
http://www

math.cu
denver.edu/~clinic
/5779/
Office Hours:
Mondays/Wednesdays 4:25pm
–
5:25p
m
Tuesdays
11:00am
–
12:3
0pm
Other times by arrangement
Text:
Readings in neural
networks
–
general and specific neural networks (ACM,
Auto CM, and J

Net) to be handed out
Neural Network Design
by Martin T. Hagan, Howard B. Demuth, and Mark
Beale, PWS Publishing Company, 1996
(optional
–
selected chapters can be
made
available, the fir
st four chapters can be
downloaded from
http://hagan.ecen.ceat.okstate.edu/nnd.html
... thanks Ed
Gard
)
.
Students with Disabilities:
If you have a disability that requires accommodation
in this course, please see me as soon as possible.
We are
happy to make
appropriate accommodations, provided timely notice is received.
Cell Phones:
You are to turn off your cell phones prior to enter
ing class.
Objective
of this Mathematics Clinic:
The clinic is primarily a pedagogical tool
where one learns applied mathematics by solving problems faced by the
Department of Radiation Oncology
. Working in research teams to develop results
associated wi
th a project (solving a set of problems and presenting the results) is
an integral part of every clinic. Thus, we will try to solve problems that are of
current concern. In particular, for this semester,
our
objectives will be:
To develop a software syst
em utilizing artificial neural networks
,
and/or others that we may uncover over the course of the semester
for
Syllabus MATH 4/5779: Math Clinic

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computer assisted
detection of structures of interest,
diagnosis
, and
prognosis
.
T
herefore, upon completion the student should have a go
od
foundation in the
mathematics of artificial neural netwo
rks,
and how to apply them to medical
images.
The
“deliverable” to our sponsor is
MATLAB co
de that
(or makes
good progress such that it)
performs
:
1.
Computer Assisted Prognosis: Non

small cell lung can
cer (NSCL) and
limited small cell lung cancer (LSCLC) patients respond, do not respond,
or remain unchanged upon receiving chemotherapy given to reduce the
size of the tumor. We will apply artificial neural networks (ANN’s),
specifically J

Net (and other
architectures) to computed tomography (CT)
images from the NSCL and LSCLC patients before and after
chemotherapy to determine if responders, non

responders, and unchanged
patients can be predicted from the ANN image analysis. J

Net has shown
that it can f
ind “harmonics” in images that are not responses to
chemotherapy and the question is, “Can ANN’s be trained to predict
responses from patients whose images are not in the training set?”
2.
Computer Assisted Detection and Diagnosis: It has been shown that one
can train ANN’s to differentiate between normal versus abnormal lungs
and between different lung pathologies in CT chest images. The goal is to
train ANN’s on CT’s to determine the effectiveness of differential
diagnosis of these conditions. Can the ANN’
s achieve better than 90%
success rate in the differential diagnosis? What does the confusion matrix
look like?
3.
Computer Assisted
Brain Morphology and IQ
Analysis
in Pediatric
Patients after Radiation Treatment of Brain Tumors: After cancer
treatment to t
he central nervous system, pediatric patients may undergo
noticeable changes in bran morphology. Multiple magnetic resonance
images (MRI’s) are taken of pediatric cancer patients after their treatment
to monitor changes. An IQ test may be administered po
st

treatment as
well. A semi

automatic segmentation routine has been employed on the
post

treatment MRI’s to measure brain morphology. That is, volumes of
certain brain regions such as the right cerebral cortex are measured (albeit
imperfectly because of
motion artifacts common in pediatric patients).
Can one determine a correspondence between the changes in brain
morphology and IQ?
4.
Computer Assisted Brain Lesion Detectors: Find all lesions and/or MS
scabs in an MRI or CT.
To accomplish these
objectives, the clinic w
ill split up into several teams
to work
on a semester project.
Each individual
will be working on subtasks le
ading to the
completion of the team
p
roject and each team will have a team leader to
coordinate the tasks.
Software develop
ment involves research to create
, to test,
to
Syllabus MATH 4/5779: Math Clinic

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3
analyze, and to document (
the software
)
.
Prerequisites
Linear algebra, advanced calculus or junior level engineering mathematics or
mathematical physics. The student should have some familiarity with M
ATLAB
o
r be ready to learn quickly.
Assignments
There are three
problem sets which will be questions and calculations associated
with the readings.
These are to be done individually.
Implementation
Each our four
teams will implement one of the following systems either by
writing their own MATLAB application or by using Semeion software: J

Net,
Auto CM, ACM
, and probabilistic (Bayesian) ANNs
.
PROPOSED COURSE OUTLINE
The proposed outline is the initial guess of th
e topics that will be fruitful to
investigate. Research is a process of discovery when one does not know, so the
rule is that we will modify our topics during the semester. Thus the proposed
outline will undoubtedly change as we learn more during the sem
ester.
The tentative topics we will cover are:
I.
Introduction
A.
Conduct of the course, expectations, assignments, projects
B.
Problem statement for this semester’s Math Clinic
II.
Artificial Neural Networks
(from
Neural Network Design
)
A.
Example problems and
architectures (Chapters 2/3)
B.
Perceptron (Chapter 4)
C.
Hebbian Learning (Chapter 7)
D.
Backpropagation (Chapter 11)
E.
Associative Learning (Chapter 13)
III.
Specialized Neural Networks
(from articles handed out)
A.
Bayesian Neural Networks, Probabilistic Neural Networks
B.
J

Net
C.
ACM
D.
Auto CM
E.
Adaptive Resonance Theory (Chapter 16)
IV.
Other Approaches (it will depend on what is uncovered during the
course of the semester)
Important Dates/Tentative Schedule
Week of:
Topics Covered
January 20

February 20
Introduction to the tec
hnical aspects of the clinic
.
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February 12
Problem Set 1 due
(5pm)
February 19
Draft Project Proposal
February 26
Written
Project proposal due
methods, materials,
schedule, di
vision of labor (5pm)
March 12
Problem Set 2 due (5pm)
March 17
Progress report
and
annotated bibliography
–
Written paper and a
15
m
inu
te oral presentation
by
each
team
April 9
, 12, 16, 19, 23, 26
Implementations
April 16
Problem Set 3
due
(5pm)
May 7
Fina
l written reports
(with software)
due
(5
pm
)
M
ay 10 or 12
Presentations
,
30 minutes/group
Projects
You are
, in conjunction with us,
to choose projects from the following list
.
P
rojects could evolve
, be added,
subtracted or
modified during the course

not
arbitrarily but as a result of
circumstances.
Project 1:
Develop a computer assisted prognosis system in MATLAB that
applies artificial neural networks (ANN’s), specifically J

Net (and other
architectures) to computed tomography (CT) images from the NSCL and LSCLC
patients before and
after chemotherapy to determine if responders, non

responders, and unchanged patients can be predicted from the ANN image
analysis.
Project 2:
Develop a computer assisted detection and diagnosis
system in
MATLAB that applies artificial neural networks (AN
N’s)
that one can train
ANN’s to differentiate between normal versus abnormal lungs and between
different lung pathologies in CT chest images. The goal is to train ANN’s on
CT’s to determine the effectiveness of differential diagnosis of these conditions.
Part of the project will be devoted to looking at the applicability of Bayesian
decision networks (probabilistic neural networks).
Project 3:
Develop a MATLAB system to assist in brain morphology and IQ
analysis for pediatric patients who have undergone
radiation treatment of brain
tumors to determine a correspondence between the changes in brain morphology
and IQ.
The techniques that are best suited for this project are one of the things
that the project will investigate. Auto CM would be one that sho
uld be relevant.
Syllabus MATH 4/5779: Math Clinic

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10/20/2013
5
Project 4
:
Computer assisted detection, CADe, of brain lesions
, t
his project will
employ ANNs (novel or traditional) to find lesions in MRIs but perhaps in CTs as
well. A substantial database of MRIs with multiple sclerosis (MS) plaques exists
and it is of diagnostic significance to be able to locate all lesions. Some m
ay be
quite small and difficult to find. Likewise we will employ brain MRIs and CTs to
locate small tumors (usually metastatic lesions) that are also difficult to find.
Small tumors may become large tumors and it is therapeutically important to find
the le
sions when they are still small.
OUR APPROACH
We
believe that teaching is a process that inv
olves an active partnership. Our
role
is that of a guide to your learning. Therefore,
we are
responsible to open the way,
to encourage, and to nudge you towar
d your own learning. In t
he context of the
math clinic, we
will try to model the process of applying mathematics to the
medical image analysis. We
will help guide you toward this learning by providing
mathematics
for you to experience. It is our
aim to c
ommunicate mathematics in
a way that is supportive and nurturing of your efforts. Your role is to find a way to
experience and articulate the mathematics that is pres
ented and that you
encounter. We
believe that it
is your responsibility to let us
know wh
en you find
yourself not understanding mathematical concepts that are presented in class.
Once you make this known, it is our responsibility to work
on trying to attain
clarity. We
will try to
be as proactive as possible. We
believe that results on
proj
ects give us the opportunity to clearly see where the areas of mathematical
understanding are and what areas need more attention.
OUTCOMES
By the end of the semester you should be able to read, understand
,
and apply
appropriate methods associated with asp
ects of medical image
analysis
we’ve
stu
died this semester to
model
correctly
and
to
solve associated probl
ems.
Secondly, given a
medical image
analysis
problem
, you should be able to: (i)
translate the description of the problem into an algorithm, (ii) choose and apply
the appropriate software method(s), (iii) obtain the
an appropriate
solution(s), and
(iv) (correctly) interpret and display results. Lastly, by
the end of the semester
you should be able to judge, for yourself, the veracity of statements made in the
areas of our study.
EVALUATION
Each person on a team will execute a project (identify a set of problems, find
solution methods, present the results
and write

up the results).
Individualization
of grades are based on the adequacy of fulfillment of the division of labor
associated with your team’s project proposal.
In particular, the following are
components that will be evaluated.
1.
Participation
–
att
endance and contributi
ng to class interactions and
discussio
ns (10
%)
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2.
Annotate
d bibliography
–
Included in
the Progress
R
eport
(5
%)
3.
Progress
Report
(10%
)
a.
Write

up (5%
)
b.
Presentation (
5
%)
4.
Final Presentation (10%)
5.
Final written report (20%)
6.
Final software (1
5
%)
7.
Assignments
(2
0
% total)
8.
Implementation (10%)
** Graduate students will have extended content and be held to higher standards.
The grade assignments are on the 10 percent scale (A = 90%

100%, B = 80%

89%, C = 70%

79%, D = 60

69%).
General advice:
Kee
p all materials that
we
turn back in case you think
we
have
not credited you with the points you earned.
we
can only correct your score if
you have what
we
have turned back to you. It is a good idea to xerox anything
that you turn in just in case
we
lose
what you turn in. Please check to make sure
that the points you earned are the points
we
have recorded. Note: The statistics
that
we
have read about correctness of professors in recording grades state that
there is a 6% error rate in our recording of you
r grades. Please make sure that
we
have correctly recorded your points.
POLICIES
Legitimate Excuses:
Legitimate excuses are for reasons that are beyond your
control. You may be required to produce an official, signed excuse. If you are
needed in a wedding,
for example, you must talk to us
prior
to the (blessed)
event. If you are legally arrested, then
this is not a legitimate excuse. For matters
that are within your control, the general rule is that it is n
ot excused. However,
talk to us
prior
to the event
or arrest
or departure
.
ANNOTATED BIBLIOGRAPHY
An annotated bibliography is
a
full bibliograph
ical
list of
citation
s
of the materials
you have read and consulted with notes. The notes you write are more or less
notes to yourself or to someone next semester that may take up your project. In
general you should have at least five citations and the a
nnotation should state
whether or not you found it useful to your project and why.
INSTRUCTIONS FOR PROJECTS
A project consists of:
1.
Proposal
–
Depending on the size of the class, projects may be coalesced
or deleted. Each
proposed
project
will be divided into tasks and assigned
to each group so that the assignment is equitable. These tasks and
assignments need to b
e written up and submitted to us
.
Once the tasks
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have been identified, assigned
,
and approved, a division of labor is written
by each of the groups.
2.
Division of labor
–
Each group must take their tasks and subdivide them
into subtasks that are assigned to individuals in the group with an
associated due

date. A division of labor is a formal contract between the
members of the gro
up. Once the tasks have been approved and a written
division of labor submitted
, the group needs to schedule a meeting with us
so that we can go over the division of labor, its associated responsibilities
and expectations
.
3.
Methods and Materials
–
is a des
cription of what materials (software)
and the approach(es) (methods, algorithms)
you will use.
4.
Annotated Bibliography
5.
Software
a.
Code

the actual computer implementation of the project.
Attention must be paid to efficiency, readability
,
and portability.
b.
Input
–
the way information is passed to the software
must be
transparent and easily usable
by
the client.
c.
Execution

the algorithm as run must correctly perform what it
was designed to do.
d.
Output

relev
ant, clear display of solution(s) such as tables,
g
raphs, images, reports/lists
.
e.
Ease
–
ease of use.
f.
Documentation
–
an in

line and hardcopy of the documentation
on how to use the software needs to be written. Moreover, help
files must be part of the software.
6.
Testing and analysis
a.
Testing

this part in
the context of our clinic
consists of running
the software developed on the test problems
.
b.
Analysis

the purpose of an analysis is to get you to
critically
evaluate the results obtained from the software as it w
as run on the
test problems.
Part of an ana
lysis is a critique of the software.
* A caveat: Negative results are not prohibited. Negative results can be very
valuable. However the negative results must be robust in that it would be
novel and instructive to the expert community to avoid a particula
r pathway.
7.
Report that will be a chapter in the
Clinic Report
–
Each team will need
to be responsible for parts of the final report. This will be done in MS

Word
(needs to be translatable into PDF

Adobe)
or Latex
as lo
ng as we
can merge the files in Lat
ex or Adobe Acrobat.
The final report will
(subject to modifications we uncover) consist of:
a.
Introduction
–
clinic
instructors
b.
Project 1
i.
Theoretical foundations
–
theory, application, algorithms
ii.
Software
–
description
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8
iii.
Results
–
summary, tables, graphs, images, lists
,
distinguishing features, performance, and
limitations
iv.
Opportunities for further research
v.
Conclusions
vi.
Bibliography
vii.
Appendices
Source code
Test problems, data, example runs
Documentation
Proofs
Other
c.
Project 2
(same
as P
roject 1)
…
d.
Project N
(same as P
roject 1)
NOTE: The software from all teams needs to be burned onto one disk where each
team will have a directory into which the software is stored. At the head of each
team’s directory entry, there must be a “read

me
” file and the software system
must have a “help” command
that assists the user.
Note:
Each problem from your problems sets will be worth the same
1/22
nd
of
20% for undergrads and 1/2
9
th
of 20% for graduates
.
PROBLEM SET 1
:
Due February 12
th
at 5pm
E2.3, E2.4, E3.1,
E4.2,E4.3,E4.4,E4.7,E4.8
Graduate Students add E4.5, E4.9
PROBLEM SET 2:
Due March 12
th
at 5pm
E7.1,
E7.4,
E11.6,
E11.7,
E11.8,
E11.11,
E13.1,E13.2,
E13.6,E13.9
Graduate Students add E7.5, E7.7, E11.9
PROBLEM SET 3:
Due
April 16
th
at 5pm
E16.1, E16.2, E16.7, E16.8
Graduate Students add E16.4, E16.5
IMPLEMENTATIONS OF THE SEMEION APPROACH
:
Team 1
,
Write a MATLAB implementation
or use the Semeion software for
J

Net
.
Due April 9
th
at 5pm, class presentation April 12
th
Team
s
2
and 4
, Write a MATLAB implementation
or use the Semeion software,
Auto
CM
(half the teams), pr
obabilistic ANNs (the other half
of the teams).
Due
April 16
th
at 5pm
, class presentation April 19
th
Team 3
, Write a MATLAB implementation or u
se the Semeion softwa
re for
ACM.
Due April
23
rd
at 5pm
, class presentation April 26
th
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