1 Age Specific Cancer Incidence for Two Major Historical Models, Compared to the Beta Model and SEER...
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1 Age Specific Cancer Incidence for Two Major Historical Models, Compared to the Beta Model and SEER Data 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 20 40 60 80 100 120 A ge Age-SpecificIncidence(per100,000) A -D pow erlaw M V K clonalexpansion Beta m odel SEER (allsitesM ,F) I(t)=(t) k-1 (1-t I(t)=at k-1 I(t) 1 2 N(s)exp[( 2 - 2 )(t -s)]ds
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Transcript of 1 Age Specific Cancer Incidence for Two Major Historical Models, Compared to the Beta Model and SEER...
1
Age Specific Cancer Incidence for Two Major Historical Models, Compared to
the Beta Model and SEER Data
0
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0 20 40 60 80 100 120
Age
Age
-Spe
cific
Inc
iden
ce (p
er 1
00,0
00)
A-D power law
MVK clonal expansion
Beta model
SEER (all sites M, F)
I(t)=(t) k-1(1-t
I(t)=at k-1
I(t) 12 N(s)exp[(2 -2 )(t -s)]ds
2
Beta Fit to SEER DataAge-specific incidence per 100,000
0
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0 20 40 60 80 100
Colon rectum
Male Female = 0.00732 0.00717 = 0.01003 0.00995k-1 = 7 7.3Fit = 1.00 1.00
b
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0 20 40 60 80 100
Lung and bronchus
Male Female = 0.00755 0.007 = 0.0105 0.0108k-1 = 6.6 6.5Fit = 0.99 0.98
a
0
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150
200
250
300
350
0 20 40 60 80 100
Urinary bladder
Male Female = 0.00688 0.00525 = 0.01007 0.0098k-1 = 7.2 6.7Fit = 1.00 1.00
c
0
20
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60
80
100
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140
0 20 40 60 80 100
Non-Hodgkins lymphoma
Male Female
a = 0.00509 0.00481
b = 0.00997 0.0101k-1 = 5.7 5.7Fit = 0.99 1.00
d
3
Beta Fit to SEER DataAge-specific incidence per 100,000
0
20
40
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140
0 20 40 60 80 100 120
Leukemias
Male Female = 0.0048 0.0043 = 0.00925 0.009k-1 = 5.9 5.9Fit = 0.99 0.99
e
0
20
40
60
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0 20 40 60 80 100
Melanomas
Male Female = 0.0023 0.00034 = 0.0089 0.007k-1 = 3.5 2Fit = 1.00 0.98
f
0
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60
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100
120
0 20 40 60 80 100
Oral cavity and pharynx
Male Female = 0.0038 0.00305 = 0.01015 0.00985k-1 = 4.6 4.6Fit = 0.99 0.99
h
0
20
40
60
80
100
120
140
0 20 40 60 80 100
Stomach
Male Female = 0.00542 0.00475 = 0.00952 0.00925k-1 = 6.7 6.7Fit = 1.00 1.00
g
4
Beta Fit to SEER DataAge-specific incidence per 100,000
0
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0 20 40 60 80 100
Kidney and renal pelvis
Male Female = 0.00435 0.0038 = 0.0102 0.0102k-1 = 5.2 5.2Fit = 0.99 1.00
a
j
0
20
40
60
80
100
120
0 20 40 60 80 100
Pancreas
Male Female = 0.00545 0.00515 = 0.00995 0.0095k-1 = 6.6 6.6Fit = 1.00 1.00
i
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100
Esophagus
Male Female = 0.00464 0.00363 = 0.01035 0.0097k-1 = 6 6Fit = 0.98 0.98
l
0
10
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30
40
50
60
70
80
0 20 40 60 80 100
Multiple myelomas
Male Female = 0.00493 0.00463 = 0.00998 0.01015k-1 = 6.5 6.5Fit = 1.00 1.00
k
5
Beta Fit to SEER DataAge-specific incidence per 100,000
0
5
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15
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35
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45
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0 20 40 60 80 100
Larynx
Male Female = 0.0047 0.0031 = 0.0108 0.0108k-1 = 5.9 5.4Fit = 0.96 0.93
n
0
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30
40
50
60
0 20 40 60 80 100
Liver and bile duct
Male Female = 0.00439 0.00411 = 0.01025 0.01k-1 = 5.8 6.3Fit = 0.99 1.0
m
0
5
10
15
20
25
0 20 40 60 80 100
Thyroid
Male Female = 0.0002 0.00025 = 0.009 0.0102k-1 = 2 1.9Fit = 0.96 0.71
p
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100
Brain and other nervous
Male Female = 0.00295 0.002655 = 0.0102 0.0102k-1 = 4.5 4.5Fit = 0.94 0.94
o
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500
1000
1500
2000
2500
3000
0 20 40 60 80 100
6
Beta Fit to SEER DataAge-specific incidence per 100,000
0
2
4
6
8
10
12
0 20 40 60 80 100
Hodgkins disease
Male Female = 0.000008 0.0000013 = 0.0098 0.0098k-1 = 1.2 1Fit = 0.27 0.01
q
0
500
1000
1500
2000
2500
3000
0 20 40 60 80 100
Total non-sex sites
Age-specific cancer incidences for all 17 non-sex sites summed for each age interval, for both SEER data and Beta fits.
r
7
Beta Fit to SEER DataAge-specific incidence per 100,000
0
100
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300
400
500
600
0 20 40 60 80 100
Breast (F)
= 0.00375 = 0.0115 k-1 = 2.8 Fit = 1.00
b
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100
Prostate
= 0.0085 = 0.0122 k-1 = 4.8 Fit = 0.96
a
For the 6 gender-specific sites the fits are performed with t
= (age-15) 0, as suggested by Armitage and Doll (1954).
0
20
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60
80
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120
140
0 20 40 60 80 100
Corpus Uteri
= 0.0038 = 0.0124 k-1 = 3.7 Fit = 0.98
c
0
10
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30
40
50
60
70
80
0 20 40 60 80 100
Ovary
= 0.00142 = 0.0108 k-1 = 2.6 Fit = 1.00
d
8
Beta Fit to SEER DataAge-specific incidence per 100,000 (Ries et al 2000)
0
20
40
60
80
100
120
140
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
0 20 40 60 80 100
0
5
10
15
20
25
0 20 40 60 80 100
Cervix Uteri
= 0.0000065 = 0.01 k-1 = 1 Fit = 0.91
e
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100
Testis
= 0.000035 = 0.029 k-1 = 1.1 Fit = 0.87
f
9
Beta Fit to California DataAge-specific incidence per 100,000 (Saltzstein et al 1998)
0
100
200
300
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500
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0 20 40 60 80 100
California (M)
Model Fit to SEER (M)
California (F)
Model Fit to SEER (F)
aColorectal
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100
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600
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800
0 20 40 60 80 100
bBronchus, lung
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1400
0 20 40 60 80 100
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200
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800
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1200
1400
0 20 40 60 80 100
cProstate
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600
0 20 40 60 80 100
dBreast
10
Beta Fit to Dutch DataAge-specific incidence per 100,000 (de Rijke et al 2000),
error bars ±2 SEM
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200
300
400
500
600
700
800
0 20 40 60 80 100
Male (Rijke 2000)
Male (Model Fit to SEER)Female (Rijke 2000)
Female (Model Fit to SEER)
Colorectal a
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100
200
300
400
500
600
700
800
900
1000
0 20 40 60 80 100
Lung b
0
200
400
600
800
1000
1200
1400
0 20 40 60 80 100
Prostatec
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50
100
150
200
250
0 20 40 60 80 100
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100
e
0
100
200
300
400
500
600
0 20 40 60 80 100
Breastd
11
Beta Fit to Dutch DataAge-specific incidence per 100,000 (de Rijke et al 2000),
error bars ±2 SEM
0
50
100
150
200
250
0 20 40 60 80 100
Stomach f
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100
Bladder e
12
Age-Specific Incidence Normalized to the Peak Value
for Each Cancer. All Male Sites Except Childhood Cancers (Hodgkins, Thyroid, Testes).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100Age
Age
-Spe
cific
Can
cer
Inci
denc
e N
orm
aliz
ed to
Pea
k
Brain (M)
Colo-rectal (M)
Esophagus (M)
Kidney (M)
Larynx (M)
Leukemias (M)
Liver (M)
Lung (M)
Melanomas (M)
Myelomas (M)
Lymphoma (M)
Oral (M)
Pancreas (M)
Stomach (M)
Bladder (M)
Prostate
Mean (SEER-M)
Beta model of SEER
Colorectal (Dutch)
Lung (Dutch)
Prostate (Dutch)
Stomach (Dutch)
Lymphoma (Dutch)
Bladder (Dutch)
Esophagus (HK)
Stomach (HK)
Colorectal (HK)
Lung (HK)
Prostate (HK)
Bladder (HK)
Colorectal (Calif)
Lung (Calif)
Prostate (Calif)
eta parameters
k
13
Liver Tumor Rates Vs. Age for NTP (TDMS) Mice Controls Removed for
Natural Death or MorbidityLiver Hepatocellular Carcinoma Rate
in B6C3F1 Mice Controls: Natural Death or Moribund Sacrifice
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000
Age at Death
Perc
ent w
ith T
umor
All TDMS (Ad Libitum) Controls
Dietary Restricted (Scopolamine study)
3rd order polynomial fit to data points
Liver Hepatocellular Adenoma Rate in B6C3F1 Mice Controls:
Natural Death or Moribund Sacrifice
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000
Age at Death
Perc
ent w
ith T
umor
All TDMS (Ad Libitum) Controls
Dietary Restricted (Scopolamine study)
3rd order polynomial fit to data points
Error bars = ±1 SEM
14
ED01 Control Mice Age-Specific Mortality With Beta Function Fit.
RCSTY_B: Reticulum Cell Sarcomas
0
1
2
3
4
5
6
7
8
0 200 400 600 800 1000
Age (days)
% p
er 1
00 a
nim
al-d
ays
at r
isk
Age-specific mortality M(t)
Beta model fit to M(t)
Age-specific incidence I(t) (from Sheldon)
M(400-600) > M(200-400); p=5E-8M(600-800) > M(400-600); p<1E-10M(800-1001) < M(600-800); p<1E-10
Error bars = ±1 SEM
Lymphomas
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 200 400 600 800 1000Age (days)
% p
er 1
00 a
nim
al-d
ays
at r
isk
Age-specific mortality M(t)
Beta model fit to M(t)
Age-specific incidence I(t) (from Sheldon)
M(400-600) > M(200-400); p=0.01M(600-800) > M(400-600); p=0.0001M(800-1001) < M(600-800); p<1E-10
15
ED01 Age-specific Mortality for All Neoplasms Causes of Death vs. Dose
of 2-AAF, With Beta Function Fit.Age-Specific Mortality for Dose = 0:
Death Caused by Neoplasms
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 200 400 600 800 1000
Age (days)
Per
cen
t of
Pop
ula
tio
n a
t R
isk
(p
er 1
00
day
s)
Age-specific mortality %Beta model fit
M(400-600) > M(200-400); p=2E-5M(600-800) > M(400-600); p=1E-5M(800-1001) < M(600-800); p=4E-6
Error bars = ±1 SEM
Age-Specific Mortality for Dose = 30 ppm: Death Caused by Neoplasms
0.0
0.5
1.0
1.5
2.0
2.5
0 200 400 600 800 1000
Age (days)
Per
cen
t of
Pop
ula
tion
at
Ris
k (
per
100
day
s)
Animals Dead
Beta model fit for dose=0
M(400-600) > M(200-400); p=4E-9M(600-800) > M(400-600); p<1E-10M(800-900) < M(600-800); p=0.04
16
ED01 Age-specific Mortality for All Neoplasms Causes of Death vs. Dose
of 2-AAF, With Beta Function Fit.Age-Specific Mortality for Dose = 35 ppm:
Death Caused by Neoplasms
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 200 400 600 800 1000
Age (days)
Per
cen
t of
Pop
ula
tion
at
Ris
k (
per
100
da
ys)
Animals Dead
Beta model fit for dose=0
M(400-600) > M(200-400); p=0.006M(600-800) > M(400-600); p<1E-10M(800-900) < M(600-800); p=0.02
Error bars = ±1 SEM
Age-Specific Mortality for Dose = 45 ppm: Death Caused by Neoplasms
0.0
0.5
1.0
1.5
2.0
2.5
0 200 400 600 800 1000
Age (days)
Perc
en
t of
Pop
ula
tion
at
Ris
k (
per
100
days
Animals Dead
Beta model fit for Dose=0
M(400-600) > M(200-400); p=0.0001M(600-800) > M(400-600); p=2E-9M(800-1001) < M(600-800); p=9E-6
17
ED01 Age-specific Mortality for All Neoplasms Causes of Death vs. Dose
of 2-AAF, With Beta Function Fit.
Age-Specific Mortality for Dose = 60 ppm: Death or Moribidity Caused by Neoplasms
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600 800 1000
Age (days)
Per
cen
t of
Pop
ula
tion
at
Ris
k (
per
100
days)
Animals Dead or MoribundBeta model fit for dose=0
M(400-600) > M(200-400); p<1E-10M(600-800) > M(400-600); p<1E-10M(800-900) < M(600-800); p=2E-8
Error bars = ±1 SEM
Age-Specific Mortality for Dose = 75 ppm: Death Caused by Neoplasms
0
5
10
15
20
25
30
35
40
0 200 400 600 800 1000
Age (days)
Per
cen
t o
f P
op
ula
tion
at
Ris
k (
per
10
0
da
ys
Animals Dead
Beta model fit for dose=0
M(400-600) > M(200-400); p=0.0006M(600-800) > M(400-600); p=2E-7M(800-1001) > M(600-800); p=0.01
18
ED01 Age-specific Mortality for All Neoplasms Causes of Death vs. Dose
of 2-AAF, With Beta Function Fit.
Age-Specific Mortality for Dose = 100 ppm: Death Caused by Neoplasms
0
5
10
15
20
25
30
35
40
0 200 400 600 800 1000
Age (days)
Per
cen
t o
f P
op
ula
tio
n a
t R
isk
(p
er 1
00
da
ys)
Animals Dead
Beta model fit for dose=0
M(400-600) > M(200-400); p=0.0002M(600-800) > M(400-600); p=9E-5M(800-900) > M(600-800); p=0.02M(900-1001) < M(800-900); p=0.15
Error bars = ±1 SEM
Age-Specific Mortality for Dose = 150: Death Caused by Neoplasms
0
5
10
15
20
25
30
35
40
45
50
0 200 400 600 800 1000
Age (days)
Per
cen
t o
f P
op
ula
tio
n a
t R
isk
(p
er 1
00
da
ys)
Animals Dead
Beta model fit for dose=0
M(400-600) > M(200-400); p=7E-5M(600-800) > M(400-600); p=2E-5M(800-1001) > M(600-800); p=0.17
19
Cell Replicative Senescence As Biological Cause
of the Turnover
Widely accepted characteristics of replicative senescence:
1. That cellular replicative capacity is limited has been known for 40 years.
2. Has been observed in vitro and in vivo for many cell types, both animal and human.
3. Is closely related to the ageing process.
4. Is a dominant phenotype when fused with immortal tumor-derived cells.
5. Considered to be an important anti-tumor mechanism.
6. Cells senesce by fraction of population, rather than all at the same time.
7. Senescent cells function normally, but are unable to repair or renew themselves.
20
Cell Replicative Senescence: Cells Retaining
Proliferative Ability Decrease With Number of Cell Divisions.
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80
In v itro populat ion doublings
Per
cen
t of
cel
ls a
ble
to
pro
life
rate
Normal f ibroblasts (Hart et al1976)
U V irradiated f ibro blasts (Hart etal 1976)
Normal fibroblasts (Wynford-Thomas 1999)
AGO7086A (Thomas e t al 1997)
DD1 (Thomas et al 1997)
21
Cell Replicative Senescence: Increase in Age Decreases
the Number of Cells With Replicative Capacity.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 20 40 60 80 100
Donor age (years)
Rep
lica
tiv
e ca
pa
city
(n
orm
aliz
ed t
o h
igh
est
va
lue
mea
sure
d)
Vascular smooth musclecells (Ruiz-Torres et al1999)
Adrenocortical cells (Yanget al 2001)
22
Cell Replicative Senescence:
Beta Model
Cells In Vitro Age
Non
-sen
esce
nt
cell
s
Cells In Vivo Age
Rem
ain
ing
poo
l of
cell
s ab
le t
o ca
use
can
cer
Cells in “Cancer Pool” = No(1-t)
= (lifespan)-1
I(t) = (t)k-1(1-t)
23
Influence of Senescence Rate on Age-Specific Cancer
Incidence in Mice.
Age-Specific Cancer M ortality: Beta and MVK/s Models of
Senescence Effects
0
5
10
15
20
25
0 200 400 600 800 1000
Age (days)
Age
sp
ecif
ic m
or
tali
ty (
perc
en
t o
f p
opu
lati
on
at
risk
per
10
0 d
ay
s)
ED01 mice contro ls (P om pei e t al 2001)
B eta model
MVK /s model
Normal senescen ce
Norm al senescence x 1.21
Normal senescence x 0.5
24
Probability of Tumors in p53 Altered Mice Compared to Beta and MVK-s Model Predictions.
Effect of Senescence on Tumor Probability in Mice
0
10
20
30
40
50
60
70
80
90
100
p53+/+(Tyneret al
2002)
Beta MVK-s p53+/m(Tyneret al
2002)
Beta MVK-s p53+/-(Tyneret al
2002)
Beta MVK-s
Per
cen
t of
mic
e w
ith
tu
mor
s
Normal senescence
Enhanced senescence
Reduced senescence
25
Age-Specific Cancer Mortality for Female CBA Mice Dosed with
Melatonin vs. Controls.
Effect of Melatonin Dose on Cancer Mortality
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 200 400 600 800 1000
Average age at death (days)
Ag
e-s
pec
ific
mo
rtal
ity
(pe
r 90
an
ima
l-d
ays
at r
isk
)
Controls
Melatonin Dosed
Data from Anisimov et al 2001.
26
Influence of Senescence on
Cancer Mortality and Lifetime
Mice Cancer Mortality and Lifetime vs. Senescence
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Normalized senescence
Can
cer
mor
atlit
y or
rel
ativ
e lif
etim
e
p53+/+ mice cancer mortality
p53+/m mice cancer mortality
p53+/- mice cancer mortality
p53-/- mice cancer mortality
p53+/+ mice lifetime
p53+/m mice lifetime
p53+/- mice lifetime
p53-/- mice lifetime
Melatonin controls cancer mortality
Melatonin dosed cancer mortality
Melatonin controls lifetime
Melatonin dosed lifetime
ED01 mice cancer mortality
Human cancer mortality
Beta model of cancer mortality
Beta model of lifetime
------- Curve fit for lifetime data
27
Senescence and Dietary Restriction
Liver Tumors vs. Weight for Female Control B6C3F1 Mice
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60 70Weight (g)
Liv
er t
um
or r
ate
Haseman 1991
Seilkop 1995
Beta-senescence model
28
Senescence and Dietary Restriction
Rodent Longevity vs. Deitary Restriction
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.4 0.6 0.8 1 1.2
Caloric intake relative to ad libitum
Rel
ativ
e L
onge
vity
Weindruch et al 1986Weindruch et al 1982Masoro et al 1982Fernandes et al 1976Sheldon et al 1995Ad libitumBeta-senescence model
29
Conclusions
1. Cancer incidence turnover likely caused by cellular senescence
2. Reducing senescence might be an attractive intervention to prolong life, even if cancer is increased.
3. Dietary restriction might be an example of interventions that both reduce senescence and reduce carcinogenesis. There may be others.
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