PCA Based Tumor Classification Algorithm - PowerPoint Presentation

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PCA Based Tumor Classification Algorithm AndDynamical Modeling Of Tumor Decay

Amy W. Daali

Ph.D. DefenseSpring 2015Electrical and Computer Engineering Department University of Texas at San Antonio 

PCA based Algorithm for Longitudinal Brain Tumor Stage Classification & Dynamical Modeling of Tumor Decay

in response to VB-111 Virotherapy

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OutlineMotivation Research BackgroundProposed Approach :Classification Algorithm

Mathematical ModelResultsConclusion Future workPublications

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Contributions

Developed a novel principal component analysis (PCA) algorithm applied to a large temporal MRI brain scans (60 000 images)Implemented a novel Tumor Stage Detection module Introduced a new term EigenTumor, basis for stage tumor recognition

Developed a novel mathematical model that quantifies effect of VB-111Analyzed stability analysis of system with & without VB-111 therapyIntroduced new interaction terms TNF-α and Fas-cIntroduced new rates α and β for anti-proliferation effect of TNF-α and killing effect of Fas-c respectively 

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MotivationResearch focus on deadly brain cancer : Glioblastoma Highly malignant, cannot be cured : cells reproduce

quickly, supported by a large network of blood vessels Glioblastomas represent 54% of all gliomas

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Needs in Neuro-Oncology & Our Research

Developed novel principal component analysis (PCA) based tumor classification of a large temporal MRI brain scans

Quantified the effect of VB-111 in the presence of TNF-α at the tumor microenvironment

Need to detect the

stage of the tumor

to predict

the progression of

brain cancer

and patient

survival

Investigate

the efficacy of VB-111 clinically on solid tumors

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Research Background

Magnetic Resonance Imaging ExperimentData Description Biological Background on VB-111 mechanism

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MRI Experiment

Intracranial xenografts performed in nude rats expressing U87 glioma cell lineRats received intravenously a single dose of VB-111 at (vp)

Monitored 21 days post tumor cell implantation Intracranial xenograft

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Data Description Training dataset :

Time-Series MRI brain scans showing the progress of glioblastoma over different time points (60 000 images)Data collected on :9/25/2009 (stage 1) used as Baseline10/02/2009 (stage 2)

10/09/2009 (stage 3)10/16/2009 (stage 4)and weighted sequences are used  

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Montage of T2 weighted rat brain MRI scans collected on 10/16/2009

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Anti-Angiogenic Virotherapy with VB-111

What is VB-111?

Target the endothelial cells in the tumor vasculatureNon-replicating type 5 adenovirus (Ad-5) vectorMechanism of action of VB-111 (courtesy of Dr. Andrew Brenner, UTHSCSA)

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Tumor Angiogenesis

Blood vessel

Tumor that can grow and spreadSmall localized tumor

Signaling molecule

Angiogenesis

National Cancer Institute

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PCA based Tumor Stage Classification System

W. Daali, M. Jamshidi, A. Brenner and A. Seifi, “A PCA based algorithm for longitudinal brain tumor stage recognition and

classification” Engineering in Medicine and Biology Society (EMBC), 2015, 37th Annual International Conference of the IEEE EMBC

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MRI Pre-processing StageRegion of interest (ROI): extract the portion of the image that shows the tumor area

.Mask of size 66x45 is applied to all MRI slices

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Example of set of tumor ROI images used in the training matrix A at stage 4

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Applying PCA on Tumor ROI imagesObtain

the feature matrix A from MRI dataCompute the covariance matrix Computing the EigenTumors (eigenvectors) of the covariance C Retain only EigenTumors that are associated with largest eigenvalues

Project tumor images on the Eigenvector space (Tumor space)Compute the inverse Euclidean similarity score between new tumor feature vector and tumor feature in the training databaseThe decision module outputs the stage the unknown tumor by returning the stage score and the class label y 

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Top 10 EigenTumors

K

eep only the Eigentumors with largest eigenvalues that retain highest information about the input data (top 33 )These Eigentumors are what they call the principle components of the dataset

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Inverse Euclidean Classifier

An unknown tumor is classified to class or stage k when a minimum is found between feature vectors

and .To perform stage classification, the following Euclidean based similarity score is obtained:

where

Such

that

with a

indicating a perfect match

 

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Classification of the stage of an unknown tumor

Unknown Tumor

  

 

 

Stage 1

 

 

 

 

 

 

Stage 3

 

Stage 2

max

 

Decision output:

 

Stage score, Class label (z,y)

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Example: Recognition and classification of an unknown tumor based on the detection score 0.87

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Classifier Performance

Ground Truth

MRI scanDetection Score Stage 1Detection Score Stage 2

Detection Score Stage 3

Stage 1

1

0.98

0.65

0.58

2

0.80

0.48

0.47

3

0.75

0.53

0.50

4

0.81

0.75

0.64

5

0.98

0.64

0.63

Sensitivity

98.70%

Stage 2

1

0.95

0.98

0.76

2

0.51

0.78

0.55

3

0.50

0.67

0.55

4

0.58

0.90

0.58

5

0.47

0.71

0.53

Sensitivity

95.80%

Stage 3

1

0.46

0.56

0.99

2

0.49

0.78

0.98

3

0.52

0.82

0.95

4

0.58

0.53

0.98

5

0.69

0.59

0.72

Sensitivity

94.01%

 

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Needs in Neuro-Oncology & Our Research

Developed novel principal component analysis (PCA) based tumor classification of a large temporal MRI brain scans

Quantifying the effect of VB-111 in the presence of TNF-α at the tumor microenvironment

Need to detect the

stage of the tumor

to predict

the progression of

brain cancer

and patient survival

Investigate the efficacy of VB-111 clinically on solid tumors

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Phase 1 study ResultsBy Brenner, et al. at Cancer Therapy & Research Center, UTHSCSA

Single dose of VB-111 in 33 patients with solid tumors  Increased survival rateNo existing model to quantify the effect of VB-111 on tumor system

We propose:Novel mathematical model for antiangiogenic treatments effects of VB-111 on tumor cells

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Proposed Mathematical Model-Key Components-

Tumor cellsCytokine tumor necrosis factor (TNF-α ): protein mediators of immune responses, important role in cancer immunotherapies

Effector Cells (T cells, Natural killer cells)Therapeutic protein Fas-c

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Therapeutic Protein

Fas-c

TNFR-1gene

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Transcription

controlled gene therapy of VB-111

TNFR-1TNF-αgene

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GoalConfirm & investigate the following biological results:

Confirm the therapeutic effect of Fas-c on tumor cellsExplore how the production of TNF-α changes with tumor antigenicity cInvestigate whether TNF-α is dysregulated under the presence of tumor and determine if VB-111 treatment correct this dysregulationDetermine if effector cells behave differently when ad-5 is administered

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Mathematical Models developed under different biological scales

Gene Expression

Microscopic

Changes

Macroscopic

Manifestations

Tumor Volume , Endothelial vessel, Lymphatic vessels

Tumor Cells,

Immune Cells

,

Endothelial

Cells

 

Fas-c, TNF-α , TNFR-1

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Interaction Diagram

Activation

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Mathematical Model with Therapy

 

 

 

Activation

D.

Kirschner

, and J. C. Panetta, “Modeling immunotherapy of the tumor–immune interaction,”

Journal of mathematical biology,

vol. 37, no. 3, pp. 235-252, 1998

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Effector Cells Dynamics

Self limiting production of effector cells

 

Michaelis-Menten term

Activation

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Michaelis-Menten EquationS

 PRelates reaction rate (production/degradation) to the concentration of the substrate S

 

 

[S]

Michaelis constant

or

H

alf saturation constant

 

Hence:

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Tumor Cells Dynamics

r: growth rate

1/b: carrying capacity of

tumora: Immune-effector cell interaction

rate

: maximum

rate of

anti-proliferation effect

of TNF-α

: apoptotic

effect of TNF-α

on tumor

(

therapeutic

effect of Fas-c

protein

: killing rate of Fas-c

 

Activation

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TNF-α Dynamics

TNF-α growth due

to E(t) in the presence of T(t)  

Activation

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Fas-c Dynamics

:steady state value of therapeutic protein : protein natural decay rate  Activation

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Parameter Values

Parameter

DescriptionValue

Maximum rate of effector cell proliferation stimulated by TNF-α, TNF-α independent recruitment of effector cells

days

-1

Half saturation constant, TNF-α on effector cells

100-165

pg/ml

c

Tumor antigenicity

 

Effector cells have natural lifespan of

days

 

0.03

days

-1

Intrinsic tumor growth rate

 

0.18

days

-1

b

1/b is carrying capacity of tumor

a

Immune-effector cell interaction rate

 

1

Parameter

Description

Value

Maximum rate of effector cell proliferation stimulated by TNF-α, TNF-α independent recruitment of effector cells

Half saturation constant, TNF-α on effector cells

100-165

pg/ml

c

Tumor antigenicity

0.03

days

-1

Intrinsic tumor growth rate

 

0.18

days

-1

b

1/b is carrying capacity of tumor

a

Immune-effector cell interaction rate

 

1

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Parameter Values (cont’d)

Parameter

DescriptionValue

Half saturation constant

Maximum rate of anti-proliferation effect of TNF-α, TNF-α induced apoptosis of tumor

cells

0.1-0.8

days

-1

Maximum rate of TNF-α production in the presence of effector cells stimulated by tumor cells

pg/ml

Half saturation constant, tumor cells on TNF production

cells

TNF-α half life, degradation rate of TNF-α

1.112

days

-1

β

Maximum rate of TNF-α induced apoptosis of tumor cells induced by

VB-111

Estimate

Steady state value of therapeutic protein Fas-c

pg/ml

Parameter

Description

Value

Half saturation constant

Maximum rate of anti-proliferation effect of TNF-α, TNF-α induced apoptosis of tumor

cells

0.1-0.8

days

-1

Maximum rate of TNF-α production in the presence of effector cells stimulated by tumor cells

Half saturation constant, tumor cells on TNF production

TNF-α half life, degradation rate of TNF-α

1.112

days

-1

β

Maximum rate of TNF-α induced apoptosis of tumor cells induced by

VB-111

Estimate

Steady state value of therapeutic protein Fas-c

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Case 1: Stability Analysis without VB-111 virotherapy

 

 

 

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Stability of Equilibrium PointsSetting :

Jacobian Matrix after linearization around ):

 

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Stability of Equilibrium Points3 eigenvalues:

, Trivial

equilibrium point is a locally unstable saddle point 

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Biologically realistic equilibrium points

Case of small tumor mass with existence of large effector cells :

eigenvalues are {system is stable Tumor persistent equilibrium: large tumor cells under the presence of large effector cells 

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Tumor persistent equilibrium

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Parameter Sensitivity AnalysisParameters vary over a range of valuesOur

model is most sensitive to :α: maximum rate of anti-proliferation effect of TNF α c: tumor antigenicity

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Benefit of increasing α: anti-proliferation effect of TNF-α on tumor cells for

c=0.035 &  

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Case 2: Stability Analysis with VB-111 virotherapyGoal: capture

the decay and stabilization of tumor cells by VB-111 monotherapy

:

 

 

 

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Equilibrium Points

Equilibrium Point

 

Plotting

1

:

 

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Stability of Equilibrium Points

Eigenvalues: {

, -1.1

, -1.8

, -

1}



Equilibrium

point is

stable

 

Slide48

Coexisting small tumor equilibrium

Equilibrium point (

where are small coexisting small population 

b

Tumor Cells versus Effector Cells phase portrait

Tumor Cells

versus TNF-α

phase portrait

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Rise of the therapeutic protein Fas-c

where decay rate

 

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Effect of killing rate β of Fas-c on cell dynamics

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Comparison of System Dynamics

With Therapy

Without Therapy

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Conclusions

Developed novel principal component analysis (PCA) based tumor classification of a large temporal MRI brain scans

Need to detect the

stage of the tumor

to predict

the progression of

brain cancer

and patient

survival

Slide53

Conclusions

Quantified the effect of VB-111 in the presence of TNF-α at the tumor microenvironment

Investigate the efficacy of VB-111 clinically on solid tumors

Slide54

Future WorkI

mage based modeling approachPatient Specific and Disease Specific Parameters estimated from different imaging modalities

-Examples: tumor growth, the diffusion tensor for tumor cells….One major challenge: lack of available human MRI time series data

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References:

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Thanks to:Mo

Jamshidi, Ph.D., ChairChunjiang Qian, Ph.D.Artyom Grigoryan, Ph.D.David Akopian, Ph.DAli Seifi, M.D

.UTHSCSADr. Andrew Brenner, M.D., Ph.D.Dr. John Floyd, M.D.

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Questions?