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