IMPROVED BREAST CANCERDIAGNOSIS AND PROGNOSIS
BY COMUTATIONAL MODELING
AND IMAGE ANALYSIS
David E. Axelrod
J.-A. Chapman, W.A. Christens-Barry, H.L. Lickley, N.A. Miller, J. Qian,
L. Sontag, B. Subramanian, Y. Yuan
NCI, NJCCR, Busch
BREAST CANCER
GOALClinical data Models Patient prognosis
OUTLINE
Breast cancer stages: in situ and invasive
Clinical data
Models
Prediction
Image analysis
Prognosis
Skarin, A.T. Breast Cancer I Slide Atlas of Diagnostic Oncology,Bristol-Myers Squibb Oncology
NORMAL BREAST ANATOMY
Skarin, A.T. Breast Cancer I Slide Atlas of Diagnostic Oncology,Bristol-Myers Squibb Oncology
BREAST CANCER
Normal Ductal Carcinoma In Situ Invasive Ductal Carcinoma Metastasis
( DCIS) (IDC) (M)
BREAST TUMOR PROGRESSION
Conventional View
Normal Ductal Carcinoma In Situ Invasive Ductal Carcinoma Metastasis
( DCIS) (IDC) (M)
BREAST TUMOR PROGRESSION
Conventional View
Normal Atypical Hyperplasia DCIS1 DCIS2 DCIS3 IDC1 IDC2 IDC3 M
(AH)
IMPORTANCE OF GRADING
DUCTAL CARCINOMA IN SITU
220,000 Breast Cancers / year
20% DCIS
32% recurrence free
DCIS outcome
68% recur (DCIS or IDC)
DCIS heterogeneity:
25% intermediate grade
50% mixed grades
PROGNOSIS BY PATHOLOGIST
Miller, N.A. et al. The Breast Journal 7: 292-302 (2001)
Nuclear grade No. Recurrence RecurrenceWorst DCIS Invasive
Grade 1 1 0 0
Grade 2 35 4 6
Grade 3 52 13 5
p = 0.18 p = 0.73
Conclude: Nuclear grade is not prognostic.
Normal Ductal Carcinoma In Situ Invasive Ductal Carcinoma Metastasis
( DCIS) (IDC) (M)
BREAST TUMOR PROGRESSION
Conventional View
Normal Atypical Hyperplasia DCIS1 DCIS2 DCIS3 IDC1 IDC2 IDC3 M
(AH)
CLINICAL OBSERVATIONS
Van Nuys Classification Holland Classification
IDC DCIS IDC DCIS
1 2 3 1 2 3
1 90.10 26.73 11.88 1 65.66 53.54 12.12
2 55.45 87.13 55.45 2 27.27 117.17 57.58
3 3.96 25.74 141.58 3 4.04 23.23 137.38
Sum of observations of Gupta, Cadman and Leong, normalized to 498.
DCIS1 DCIS2 DCIS3 IDC1 IDC2 IDC3
EXPECTATION
Normal Ductal Carcinoma In Situ Invasive Ductal Carcinoma Metastasis
( DCIS) (IDC) (M)
BREAST TUMOR PROGRESSION
Conventional View
Normal Atypical Hyperplasia DCIS1 DCIS2 DCIS3 IDC1 IDC2 IDC3 M
(AH)
Mommers et al. J. Pathol. 194: 327-333 (2001)
Buerger et al. J. Pathol. 187; 396-402 (1999)
" Unless you can express your knowledge with numbers, your knowledge is meager and unsatisfactory."
William Thompson Lord Kelvin 1824-1907
Smithsonian Institution of Washington, 1857
B. Subramanian and D.E. Axelrod Progression of Heterogeneous Breast Tumors J. Theoret. Biol. 210: 107-119 (2001)
Purpose: Pathways for tumor progression (compartment models)Transition rates between compartments
Data: Co-occurrence frequencies of DCIS and IDC
Method: Genetic algorithm (GA) search for transition rates
Result: GA can’t reproduce data with models
Conclusion: GA and/or models not adequate
PROBLEMS
1. Genetic algorithm
limitations, stuck in local minimum
2. Pathway models
not describe the biological situation
3. Polluted data
combined data from five labs
different criteria to classify grades
PROBLEMS SOLUTIONS
1. Genetic algorithm 1. Directed search
limitations, stuck in local minimum seed Nelder-Mead simplex
2. Pathway models 2. New pathway
not describe the biological situation relax assumption DCIS -> IDC
3. Polluted data 3. Combine similar data
combined data from five labs combine data from three labs
different criteria to classify grades same criteria to classify grades
CLINICAL OBSERVATIONS
Van Nuys Classification Holland Classification
IDC DCIS IDC DCIS
1 2 3 1 2 3
1 90.10 26.73 11.88 1 65.66 53.54 12.12
2 55.45 87.13 55.45 2 27.27 117.17 57.58
3 3.96 25.74 141.58 3 4.04 23.23 137.38
Sum of observations of Gupta, Cadman and Leong, normalized to 498.
AH
DCIS 1
DCIS 2
DCIS 3
IDC 1
IDC 2
IDC3
M
AH
DCIS 1DCIS 2 DCIS 3
IDC 1 IDC 2 IDC3
M
AH
DCIS 1 DCIS 2 DCIS 3
IDC 1 IDC 2 IDC3
M
PATHWAYS
Linear Nonlinear Branched
DIFFERENTIAL EQUATIONS
Linear Pathway
d[AH]
dt k0[AH]
d[DCIS1]
dtk0[AH] k1[DCIS1]
d[DCIS2]
dtk1[DCIS1] k2 [DCIS2]
d[DCIS3]
dtk2[DCIS2] k 3[DCIS3]
d[IDC1]
dtk3[DCIS3] k4 [IDC1]
d[IDC2]
dtk4[IDC1] k5[IDC2]
d[IDC3]
dtk5[IDC2] k6 [IDC3]
Non-linear Pathway
d[DCIS2]
dtk1[DCIS1] (k2 k4)[DCIS2]
d[DCIS3]
dtk2[DCIS2] k 5[DCIS3]
d[IDC1]
dtk3[DCIS1] k6[IDC1]
d[IDC2]
dtk4[DCIS2] k 6[IDC1] k7[IDC2]
d[AH]
dt k0[AH]
d [DCIS1]
dtk0[AH ] (k1 k3)[DCIS1]
d[IDC3]
dtk5[DCIS3] k7[IDC2] k8[IDC3]
Branched Pathway
d[DCIS2]
dtk1[AH] k3[DCIS1] (k4 k6)[DCIS2]
d[AH]
dt (k0 k1 k2)[AH]
d[DCIS1]
dtk0 [AH ] (k3 k5 )[DCIS1]
d[DCIS3]
dtk2[AH] k4[DCIS2] k7[DCIS3]
d[IDC1]
dtk5[DCIS1] (k8 k10)[IDC1]
d[IDC2]
dtk6[DCIS2] k8[IDC1] (k9 k11)[IDC2]
d[IDC3]
dtk7[DCIS3] k9[IDC2] k12[IDC3]
BRANCHED PATHWAY
AH
DCIS 1DCIS 2 DCIS 3
IDC 1 IDC 2 IDC 3
M
k0 (0.1464)
k1(0.0125)
k2 (0.0322)
k3 (0.0919) k4 (0.0604)
k5 (0.0794) k6 (0.0688) k7 (0.1076)
k8 (0.1463)
k9 (0.0281)
k10 (0.0151)
k11 (0.0990)
k12 (0.1125)
PATHWAY SIMULATIONS
Linear
IDC DCIS
1 2 3
1 94.62 49.80 0
2 0 114.54 74.70
3 0 0 164.34
Non-linear
IDC DCIS
1 2 3
1 60.00 0 0
2 84.00 120.00 78.00
3 0 0 156.00
Branched
IDC DCIS
1 2 3
1 103.48 0 0
2 64.68 103.48 71.14
3 0 0 155.22
PATHWAY SIMULATIONS
Linear
IDC DCIS
1 2 3
1 94.62 49.80 0
2 0 114.54 74.70
3 0 0 164.34
Non-linear
IDC DCIS
1 2 3
1 60.00 0 0
2 84.00 120.00 78.00
3 0 0 156.00
Branched
IDC DCIS
1 2 3
1 103.48 0 0
2 64.68 103.48 71.14
3 0 0 155.22
Observed - Van Nuys Classification
IDC DCIS
1 2 3
1 90.10 26.73 11.88
2 55.45 87.13 55.45
3 3.96 25.74 141.58
AH
DCIS 1
DCIS 2
DCIS 3
IDC 1
IDC 2
IDC3
M
AH
DCIS 1DCIS 2 DCIS 3
IDC 1 IDC 2 IDC3
M
AH
DCIS 1 DCIS 2 DCIS 3
IDC 1 IDC 2 IDC3
M
PATHWAYS
Linear Nonlinear Branched
Parallel
IDC 1 2 3
DCIS 1 2 3
CP
PARALLEL PATHWAY
IDC 1 2 3
DCIS 1 2 3
CPCommon Progenitor
PARALLEL PATHWAY
p (0.642)
11 12 13
21 22 23
31 32 33
IDC 1 2 3
DCIS 1 2 3
CP
PARALLEL PATHWAY
p (0.642) p (0.326)
11 12 13
21 22 23
31 32 33
11 12 13
21 22 23
31 32 33
IDC 1 2 3
CP
IDC 1 2 3
DCIS 1 2 3
CP
IDC 1 2 3
DCIS 1 2 3
CP
PARALLEL PATHWAY
p (0.642) p (0.326) p (0.032)
11 12 13
21 22 23
31 32 33
11 12 13
21 22 23
31 32 33
11 12 13
21 22 23
31 32 33
IDC 1 2 3
DCIS 1 2 3
IDC 1 2 3
DCIS 1 2 3
CP
CP
IDC 1 2 3
CP
IDC 1 2 3
DCIS 1 2 3
CP
IDC 1 2 3
DCIS 1 2 3
CP
PATHWAY SIMULATIONS
Linear
IDC DCIS
1 2 3
1 94.62 49.80 0
2 0 114.54 74.70
3 0 0 164.34
Non-linear
IDC DCIS
1 2 3
1 60.00 0 0
2 84.00 120.00 78.00
3 0 0 156.00
Branched
IDC DCIS
1 2 3
1 103.48 0 0
2 0 103.48 71.14
3 0 0 155.22
Parallel
IDC DCIS
1 2 3
1 106.57 40.59 7.97
2 40.59 106.57 40.59
3 7.97 40.59 106.57
COMPARISON OF RESULTS
Clinical Observation Model Simulation
Van Nuys Classification Parallel Model
IDC DCIS IDC DCIS
1 2 3 1 2 3
1 90.10 26.73 11.88 1 106.57 40.59 7.97
2 55.45 87.13 55.45 2 40.59 106.57 40.59
3 3.96 25.74 141.58 3 7.97 40.59 106.57
COMPARISON OF RESULTS MODEL SIMULATIONS vs. CLINICAL OBERVATIONS
Comparison RMSD
Holland Observations vs. Van Nuys Observations 18.38
Parallel Model vs. Observations 18.82
Branched Model vs. Observations 20.62
Linear Model vs. Observations 21.15
Non-linear Model vs. Observations 24.54
Root mean squared deviation.Totals normalized to 498. RMSD =
(bi, j ci , j) 29
,
BREAST TUMOR PROGRESSION
Normal
Common Progenitor
Ductal Carcinoma In Situ
Invasive Ductal Carcinoma
Metastasis
New View - Parallel Progression
Conventional View - Linear Progression
Normal Ductal Carcinoma In Situ Invasive Ductal Carcinoma Metastasis
PARALLEL PATHWAY
IDC 1 2 3
DCIS 1 2 3
Common Progenitor
L. Sontag and D. E. Axelrod
Evaluation of pathways for progression of heterogeneous breast tumors
J. Theoret. Biol. 232: 179-189 (2005)
Slides 34-45 are excluded.
They include data on diagnosis and prognosis of breast ductal carcinoma in situ by image analysis
which has been submitted for publication.
CONCLUSION
GOAL:
Clinical data Models Patient prognosis
OUTCOME:
Clinical data Models Improved Patient prognosis
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