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A model of thyroid cancer initiation
and growth in autoimmune
thyroiditis
Stephen J. Merrill
Program in Computational Sciences
Department of MSCS
Marquette University
Milwaukee, Wisconsin USA
12/9/2010
NAMIAM 2010
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Thyroid Gland
• One of the largest endocrine gland, controlling
metabolism in the body
• Also controls how the body should react to other
hormones (such as products of the adrenal gland)
• Produces two hormones, T3, which has 3 atoms of
iodine and T4, which has 4.
• T3 is the active form, produced from T4 by one of two
deiodination enzymes.
• Hypothyroidism (low T4) is most commonly caused by
an autoimmune condition. Incidence is increasing
world-wide
• Hypothyroidism is usually treated by hormone
replacement with synthetic T4, Levothyroxine.
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Basic Idea
• Basic feedback control -- the
HPT axis.
• This control is disrupted in
autoimmune (Hashimoto’s)
thyroiditis
• As the thyroid is slowly
destroyed, the thyroid is
unable to respond
to the TSH signal
• As T4 falls -- TSH increases.
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Consequences of increasing TSH
• Areas of the thyroid are stimulated to grow,
forming “nodules” of follicular cells (the T4producing cells).
• The overall size of the thyroid can grow
dramatically, forming a temporary thyroid goiter.
• In the face of autoimmune thyroiditis, there is a
large inflammatory response and sometimes a
large short-term release of T4, Hashitoxicosis.
• For any cancers that form in a nodule, TSH acts as
a hormonal growth factor.
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Thyroid Nodules
• Found in 20-70% of the population
• About 5% (and to up to 15% in thyroiditis)
are malignant
• Main type of thyroid cancer is carcinoma,
papillary (75%), follicular (10%), other types
(15%).
• Treatment options: thyroidectomy
sometimes followed by radioactive iodine or
TSH suppression by levothyroxin (T4)
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Outline of the model
1. Due to the nature of the process, a stochastic
model (with a continuous input) is chosen.
2. In any Dt of time, a region in the thyroid may
be stimulated to begin a nodule. This rate is
determined by TSH.
3. Growth of an existing nodule is determined by
TSH.
4. Cancer development rate is determined by the
nodule growth rate. Once started, growth rate
of cancer is higher than the growth rate of
other nodules.
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How many areas get a nodule
initiation signal?
• Assuming N potential growth sites, consider
the distribution of M TSH molecules
distributed to the N sites (assuming a large
signal would mean a nodule initiation).
• Number of molecules per site follows a
binomial distribution. Counting the number
of sites that exceed a threshold given M
molecules in this case can be
4
TSH
approximated by
K  TSH 4
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Number of Nodules
As TSH changes, the number of nodules increases (100 paths at each TSH level)
35
mean number of nodules
30
25
20
15
10
5
0
0
0.5
1
1.5
2
2.5
TSH
3
3.5
4
4.5
5
Over 30 years, effect of elevated TSH.
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Largest Nodule increases with TSH
100 simulations -- TSH=1
100 simulations -- TSH=5
100
60
90
50
80
40
60
frequency
frequency
70
50
30
40
20
30
20
10
10
0
0
0.2
0.4
0.6
0.8
largest nodule size (in cm)
1
1.2
1.4
0
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
largest nodule size (in cm)
4.8
5
5.2
Frequency of large, 4 cm nodules increases if TSH increases.
Half of these may be cancerous in autoimmune thyroiditis.
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The connection to autoimmune
thyroiditis
• There can be a long period of asymptomatic
hypothyroidism (T4 normal or low, TSH
increasing).
• Treatment (with levothyroxin) is often started
when TSH is beyond normal reference (4-5
mU/mL) .
• This can result in a long (several year) period
where TSH is high and nodule formation is
encouraged.
• In undiagnosed conditions, TSH can reach very
high levels, raising the risk of cancer.
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Question of Interest
• What is the cost (in terms of increased
thyroid cancer) for late treatment of
hypothyroidism?
Approach is to compare the untreated and
treated simulated populations and to
compare cancer incidence.
Need to find a way to mimic the natural
changes in TSH in this disease.
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Model of Autoimmune Thyroiditis
• The work of a doctoral student, Bala Pandiyan,
along with Dr. Salvatore Benvenga, University of
Messina in Sicily and an undergraduate McNair
Fellow, Mike Castillo (Marian University)
• Based on data from Benvenga’s clinic of
hundreds of thyroiditis patients.
• Describes the disruption of the feedback system
as a result of the disease.
• Takes the form of a nonlinear system of
differential equations.
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Pandiyan’s Model
• T is the functional
(active) size of the
thyroid
• Ab is the level of
antithyroid
antibodies
(TPOAb) and TgAb
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k1T 4
d (TSH )
 k1 
 k2TSH
dt
ka  T 4
d (T 4) k3T (TSH )

 k4T 4
dt
kd T  TSH
dT
 TSH

 k5 
 N   k6 ( Ab)T
dt
 T

d ( Ab)
 k7 ( Ab)T  k8 Ab
dt
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Parameters
Free T4
• Determined by
the literature, data,
and equilibrium
arguments, and
simulation.
• For this talk, using
a simplified model,
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
T 4(t )  1.8e .12t
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10
15
time(years)
20
25
30
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TSH increases over time
16
14
12
TSH
10
8
6
4
2
0
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0
5
10
15
time (years)
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20
25
30
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Disease Progression
16
14
12
TSH
10
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
T4
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Untreated
40
35
30
frequency
25
20
15
10
5
0
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0
10
20
30
40
50
60
largest nodule size (cm)
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70
80
90
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With Treatment
TSH returns
To normal
levels
Treatment beginning at t=15
4.5
4
TSH with treatment
3.5
3
2.5
2
1.5
1
0.5
0
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10
15
time (years)
20
25
30
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Nodule sizes – with Treatment
With Treatment
80
70
60
frequency
50
40
30
20
10
0
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0
0.1
0.2
0.3
0.4
0.5
0.6
largest nodule size (cm)
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0.7
0.8
0.9
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Summary
• A dynamic model of autoimmune thyroiditis
enables one to study consequences of the
disease, such as initiation and growth of
thyroid cancer.
• Similar studies could be done to study other
treatment effects, such as side effects or
even patient satisfaction.
• Patient-specific parameters can be identified.
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Thank You!
Much of this presented work was joint with Mike Castillo (no picture available)
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