A Biomathematical Model for

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A Biomathematical Model for Colorectal Cancer
Georg Luebeck Fred Hutchinson Cancer Research
Center
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recent publications
Preneoplastic lesion growth driven by the death
of adjacent normal stem cells Dennis L. Chao,
J. Thomas Eck, Douglas E. Brash, Carlo C. Maley
and E. Georg Luebeck PNAS USA September 30,
2008 vol. 105, no.39.
The Age-specific Incidence of Cancer phases,
transitions and biological implications Rafael
Meza, Jihyoun Jeon, Suresh H. Moolgavkar and E.
Georg Luebeck PNAS USA October 14, 2008 vol. 105,
no.42.
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Multistage Carcinogenesis in Colon
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normal crypt renewal controlled balance of cell
birth and death (differentiation)
lumen
differentiating cells
proliferating cells
tissue stem cells
muscularis mucosae
Lgr5 (Barker, Clevers,)
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initiation of cancer disruption of the
controlled balance of cell birth and death
clonal expansion
APC loss
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initiation of cancer disruption of the
controlled balance of cell birth and death
clonal expansion
crypt bifurcation
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level
time scale
parameter
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level
time scale
parameter
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multistage-clonal expansion model for colon cancer
adenomatous polyp
crypt
TAC
DZ
SC
Cancer
X
X
malignant cell
Wnt
APC inactivation
s 2 years
t
S (sojourn time)?
time to cancer tSs
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clonal expansion (promotion) malignant
transformation
cell division
a
Ca
µ2
?
APC-/-
malignant cell
stem cell niche (crypt)
ß
death/differentiation
µ0X rate of first hit in the tissue of size X
µ1 rate of second hit
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age-specific incidence hazard function

p net cell proliferation q malignant
tramsformation
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asymptotic phase t gtgt 1/µ1

not observable (APC gene µ1 10-6 per year)
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linear phase S lt t lt 1/µ1

prob. of non-extinction of premalignant clone
mean sojourn/dwell time
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exponential phase (a-ß)-1 lt t lt S
net cell proliferation (growth) rate
Taylor series expansion in
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quadratic phase t lt (a-ß)-1
Armitage Doll approximation (power-law
behavior),
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hazard function
asymptotic value
slope
growth parameter
power-law
sojourn time of premalignant lesion
1,000,000 years
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What can be gleaned from Ca incidence data?

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Adjustment for secular trends (cohort and period)?
Age-Period-Cohort approach (age a, cal year i,
birth cohort j)
person years
expected no. of cases
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Adjustment for secular trends (cohort and period)?
Age-Period-Cohort approach (age a, cal year i,
birth cohort j)
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hazard function
asymptotic value
slope
growth parameter
power-law
decades ?
1,000,000 years
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hazard function
asymptotic value
slope
growth parameter
transient amplification
power-law
decades ?
1,000,000 years
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a-ß 0.17/yr
a-ß 0.14/yr
TS56
TS57.5
colorectal cancer (adjusted incidence)?
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a-ß 0.18/yr
a-ß 0.16/yr
TS53
TS56
pancreatic cancer adjusted incidence
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• Analysis of colorectal pancreatic Ca incidence
  yields
• slope adenoma/PanIN incidence
• transient amplification (colon)
• adenoma/PanIN growth parameter and sojourn time
• adenoma-carcinoma transition rate

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• Are our findings consistent with screening data
• for pre-malignant lesions?
• Need number and sizes to validate the model
• issues
• sensitivity and specificity of screen
• conversion of caliper size to cell numbers

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in colon adenomatous polyps (adenomas) but
what about hyperplastic polyps, serrated polyps
(sessile serrated serrated adenoma) tubular/tubu
lovillous/villous adenoma ?
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Analyze CRC incidence data from negative
screening group Kaiser-Permanente (KP) Flex-sig
study (1994-96) have 72,483 individuals in
California ages 50 and older, followed up over
7 years. have insertion length have
failure times over follow-up period and have
tumor location (proximal, distal, rectum)
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unscreened
screened/neg.
KP
scaling
scaling
SEER registry
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(No Transcript)
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• Conclusions I
• age-specific incidence exhibits 4 basic phases,
  only two of which can be observed
• age-specific incidence is essentially linear (not
  log-log linear)
• linearity due to two-hit process
  (Knudson's recessive
  oncogenesis hypothesis)

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• Conclusions II
• Premalignant lesions may sojourn in tissue for
  decades
• Growth of premalignant lesions critically
  dependent on tissue architecture and environment
  

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Reid Lab (Barrett's Esophagus)? Dennis
Chao Tom Paulson Brian Reid Luebeck Lab
(Biomathematics/Biostatistics) Rafael
Meza Jihyoun Jeon Larry Jean Bill
Hazelton Suresh Moolgavkar
Maley Lab (Computational Biology)? David
Birtwell Tom Eck Doug West
Scales of carcinogenesis cells, crypts and
cancer Georg Luebeck (PI) Carlo Maley (Co-PI)?