1. in response to VB-111 Virotherapy
PCA Based Tumor Classification Algorithm And Dynamical Modeling Of Tumor Decay
PCA based Algorithm for Longitudinal Brain Tumor Stage Classification & Dynamical Modeling of Tumor Decay
in response to VB-111 Virotherapy
Amy W. Daali
Ph.D. Defense
Spring 2015
Electrical and Computer Engineering Department
University of Texas at San Antonio 

2. Outline Motivation Research Background Proposed Approach : Results
Classification Algorithm
Mathematical Model
Results
Conclusion
Future work
Publications

3. Contributions
Developed a novel principal component analysis (PCA) algorithm applied to a large temporal MRI brain scans (≈ 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-111
Analyzed stability analysis of system with & without VB-111 therapy
Introduced new interaction terms TNF-α and Fas-c
Introduced new rates α and β for anti-proliferation effect of TNF-α and killing effect of Fas-c respectively

4. Motivation Research 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
Gliomas
Glioblastoma
Ependymomas 
Oligodendrogliomas
Glioma is the general term describing all brain tumors. Every glioma is named based on the specific type of brain cell affected.
Glioblastoma originate from the supportive brain tissue (star shape)
Most of these brain tumors cannot be cured because they spread all through the normal brain tissue
The highest grade called glioblastomas, agressive

5. Needs in Neuro-Oncology & Our Research
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
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
Classify different temporal stages of brain tumors given a large time series of MRI images
Prognosis factor

6. Research Background Magnetic Resonance Imaging Experiment
Data Description
Biological Background on VB-111 mechanism

7. MRI Experiment
Intracranial xenografts performed in nude rats expressing U87 glioma cell line
Rats received intravenously a single dose of VB-111 at (vp)
Monitored 21 days post tumor cell implantation
Intracranial xenograft
Zenograft
A surgical graft of tissue from one species to an unlike species 
luciferase : tumor marker

8. Data Description Training dataset :
Time-Series MRI brain scans showing the progress of glioblastoma over different time points (≈ images)
Data collected on :
9/25/ (stage 1) used as Baseline
10/02/2009 (stage 2)
10/09/2009 (stage 3)
10/16/2009 (stage 4)
𝑇 1 and 𝑇 2 weighted sequences are used

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

10. Anti-Angiogenic Virotherapy with VB-111
What is VB-111?
Target the endothelial cells in the tumor vasculature
Non-replicating type 5 adenovirus (Ad-5) vector
Type 5 andenovirus (Ad-5) are responsible for several mild disorders such as respiration infections
arrangement of blood vessels inside the tumor
Mechanism of action of VB-111 (courtesy of Dr. Andrew Brenner, UTHSCSA)

11. Tumor that can grow and spread
National Cancer Institute
Understanding Cancer and Related Topics
Understanding Angiogenesis
Tumor Angiogenesis
Small localized tumor
Tumor that can grow and spread
Angiogenesis
Tumor angiogenesis is the proliferation of a network of blood vessels that penetrates into cancerous growths, supplying nutrients and oxygen and removing waste products
Tumor angiogenesis starts with cancerous tumor cells releasing molecules that send signals to surrounding normal host tissue
This signaling encourage growth of new blood vessels
Blood vessel
Signaling molecule
National Cancer Institute
NCI Web site:

12. 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

13. MRI Pre-processing Stage
Region of interest (ROI): extract the portion of the image that shows the tumor area.
Mask of size 66x45 is applied to all MRI slices

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

15. Applying PCA on Tumor ROI images
Obtain the feature matrix A from MRI data
Compute the covariance matrix 𝐶=𝐴 𝐴 𝑇
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 𝛺 1 and tumor feature 𝛺 𝑘 in the training database
The decision module outputs the stage the unknown tumor by returning the stage score and the class label y

16. Top 10 EigenTumors
Keep 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

17. Inverse Euclidean Classifier
An unknown tumor is classified to class or stage k when a minimum 𝜀 𝑘 is found between feature vectors 𝛺 1 and 𝛺 𝑘 .
To perform stage classification, the following Euclidean based similarity score is obtained:
𝑠 𝛺 1 , 𝛺 𝑘 = 𝑖 𝑁 𝛺 1,𝑖 − 𝛺 𝑘,𝑖 2
where
𝑖 𝑁 𝛺 1,𝑖 − 𝛺 𝑘,𝑖 2 = 𝛺 1 − 𝛺 𝑘
Such that 0≤𝑠 𝛺 1 , 𝛺 𝑘 ≤1 with a 𝑠 𝛺 1 , 𝛺 𝑘 =1 indicating a perfect match

18. Classification of the stage of an unknown tumor
𝑠 1 𝛺 1 , 𝛺 𝑘
Stage 1
𝑠 2 𝛺 1 , 𝛺 𝑘
𝑠 3 𝛺 1 , 𝛺 𝑘
Stage 3
Stage 2
max
Decision output:
Stage score, Class label (z,y)

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

20. Classifier Performance
Ground Truth
MRI scan
Detection Score Stage 1
Detection 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
0.64 5
0.63
Sensitivity
98.70%
Stage 2
0.95
0.76
0.51
0.78
0.55
0.67
0.90
0.71
95.80%
Stage 3
0.46
0.56
0.99
0.49
0.52
0.82
0.69
0.59
0.72
94.01%
Classifier Performance
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑅𝑎𝑡𝑒= 𝑇 𝑝 𝑇 𝑝 +𝐹 𝑁

21. Needs in Neuro-Oncology & Our Research
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
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

22. Phase 1 study Results
By Brenner, et al. at Cancer Therapy & Research Center, UTHSCSA
Single dose of VB-111 in 33 patients with solid tumors  Increased survival rate
No existing model to quantify the effect of VB-111 on tumor system
We propose:
Novel mathematical model for antiangiogenic treatments effects of VB on tumor cells

23. Proposed Mathematical Model -Key Components-
Tumor cells
Cytokine 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

24. Therapeutic Protein Fas-c
gene
TNFR-1

25. Transcription controlled gene therapy of VB-111
transcription controlled gene therapy of VB-111 and how it selectively targets only tumor endothelial cell
TNF-α
TNFR-1

26. Goal Confirm & investigate the following biological results:
Confirm the therapeutic effect of Fas-c on tumor cells
Explore how the production of TNF-α changes with tumor antigenicity c
Investigate whether TNF-α is dysregulated under the presence of tumor and determine if VB-111 treatment correct this dysregulation
Determine if effector cells behave differently when ad-5 is administered
Antigenicity: A detectable tumor with larger values of c has higher antigen levels

27. 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

28. Interaction Diagram Activation
Diagram of the dynamics of different populations involved in VB-111 interactions
Activation

29. Mathematical Model with Therapy
𝑑𝐸 𝑑𝑡 = 𝑝 𝐸 𝐴𝐸 𝑔 𝐸 +𝐴 +𝑐𝑇− µ 𝐸 𝐸 1 𝑑𝑇 𝑑𝑡 =𝑟𝑇 1−𝑏𝑇 − 𝑎 𝑇𝐸 𝑔 𝑇 +𝑇 −𝛼 (1+𝛽𝐹)𝐴𝑇 (2) 𝑑𝐴 𝑑𝑡 = 𝑝 𝐴 𝑇𝐸 𝑔 𝐴 +𝑇 − µ 𝐴 𝐴 (3) 𝑑𝐹 𝑑𝑡 = 𝐹 𝑠𝑡 −µ𝐹 (4)
Activation
D. Kirschner, and J. C. Panetta, “Modeling immunotherapy of the tumor–immune interaction,” Journal of mathematical biology, vol. 37, no. 3, pp , 1998

30. Effector Cells Dynamics
𝑑𝐸 𝑑𝑡 = 𝑝 𝐸 𝐴𝐸 𝑔 𝐸 +𝐴 +𝑐𝑇− µ 𝐸 𝐸
Self limiting production of effector cells
Michaelis-Menten term
Activation

31. Michaelis-Menten Equation
S  P
Relates reaction rate (production/degradation) 𝑑𝑝 𝑑𝑡 to the concentration of the substrate S
𝑑𝑝 𝑑𝑡 = 𝑉 𝑚𝑎𝑥 [𝑠] 𝑘 𝑚 +[𝑠]
lim [𝑠]→∞ 𝑑𝑝 𝑑𝑡 = 𝑉 𝑚𝑎𝑥
𝒅𝒑 𝒅𝒕
Hence:
𝑑𝐸 𝑑𝑡 = 𝑝 𝐸 𝐸𝐴 𝑔 𝐸 +𝐴
Michaelis constant or
Half saturation constant
[S]

32. Tumor Cells Dynamics r: growth rate 1/b: carrying capacity of tumor
𝑑𝑇 𝑑𝑡 =𝑟𝑇 1−𝑏𝑇 − 𝑎 𝑇𝐸 𝑔 𝑇 +𝑇 −𝛼 (1+𝛽𝐹)𝐴𝑇
r: growth rate
1/b: carrying capacity of tumor
a: Immune-effector cell interaction rate
𝛼 : maximum rate of anti-proliferation effect of TNF-α
𝛼 𝐴𝑇 : apoptotic effect of TNF-α on tumor
(1+𝛽𝐹): therapeutic effect of Fas-c protein
𝛽 : killing rate of Fas-c
Activation

33. TNF-α Dynamics 𝑑𝐴 𝑑𝑡 = 𝑝 𝐴 𝑇𝐸 𝑔 𝐴 +𝑇 − µ 𝐴 𝐴
𝑑𝐴 𝑑𝑡 = 𝑝 𝐴 𝑇𝐸 𝑔 𝐴 +𝑇 − µ 𝐴 𝐴
TNF-α growth due to E(t) in the presence of T(t)
Rate of change of cytokine tnf-alpha
Activation

34. Fas-c Dynamics
𝑑𝐹 𝑑𝑡 = 𝐹 𝑠𝑡 −µ𝐹 𝐹 𝑠𝑡 :steady state value of therapeutic protein µ𝐹 : protein natural decay rate
Fas-c has been shown to be a potent killer gene which is the basis for an effective anti-angiogenic gene therapy
Activation

35. Parameter Values Parameter Description Value 𝑝 𝐸
Maximum rate of effector cell proliferation stimulated by TNF-α, TNF-α independent recruitment of effector cells
5 10 −2 days-1
𝑔 𝐸
Half saturation constant, TNF-α on effector cells
pg/ml c
Tumor antigenicity
0≤𝑐≤0.05
µ 𝐸
Effector cells have natural lifespan of 1/ µ 𝐸 days
0.03 days-1 𝑟
Intrinsic tumor growth rate
0.18 days-1 b
1/b is carrying capacity of tumor
10 −9 a
Immune-effector cell interaction rate 1

36. Parameter Values (cont’d)
Description
Value
𝑔 𝑇
Half saturation constant
10 5 𝛼
Maximum rate of anti-proliferation effect of TNF-α, TNF-α induced apoptosis of tumor cells
days-1
𝑝 𝐴
Maximum rate of TNF-α production in the presence of effector cells stimulated by tumor cells
−3 −2 10 −2
pg/ml
𝑔 𝐴
Half saturation constant, tumor cells on TNF production
10 3 − cells
µ 𝐴
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
𝐹 𝑠𝑡
Steady state value of therapeutic protein Fas-c
10 3 pg/ml

37. Case 1: Stability Analysis without VB-111 virotherapy
𝑓 1 : 𝑑𝐸 𝑑𝑡 = 𝑝 𝐸 𝐴𝐸 𝑔 𝐸 +𝐴 +𝑐𝑇− µ 𝐸 𝐸 𝑓 2 : 𝑑𝑇 𝑑𝑡 =𝑟𝑇 1−𝑏𝑇 − 𝑎 𝑇𝐸 𝑔 𝑇 +𝑇 −𝛼 𝐴𝑇 𝑓 3 : 𝑑𝐴 𝑑𝑡 = 𝑝 𝐴 𝑇𝐸 𝑔 𝐴 +𝑇 − µ 𝐴 𝐴

38. Stability of Equilibrium Points
Setting : 𝑑𝐸 𝑑𝑡 = 𝑑𝑇 𝑑𝑡 = 𝑑𝐴 𝑑𝑡 =0
Jacobian Matrix after linearization around 𝐸 1 =(0,0,0):
𝐽= 𝜕 𝑓 1 𝜕 𝑥 1 𝜕 𝑓 2 𝜕 𝑥 1 𝜕 𝑓 3 𝜕 𝑥 𝜕 𝑓 1 𝜕 𝑥 𝜕 𝑓 2 𝜕 𝑥 𝜕 𝑓 3 𝜕 𝑥 𝜕 𝑓 1 𝜕 𝑥 3 𝜕 𝑓 2 𝜕 𝑥 3 𝜕 𝑓 3 𝜕 𝑥 = 𝑝 𝐸 𝑧 𝑔 𝐸 +𝑧 − µ 𝐸 𝑐 𝑝 𝐸 𝑥𝑔 𝐸 𝑔 𝐸 +𝑧 −𝑎𝑦 𝑔 𝑇 +𝑦 𝑟−2𝑟𝑏𝑦− 𝑎𝑥 𝑔 𝑇 𝑔 𝑇 +𝑦 2 −𝛼𝑦 𝑝 𝐴 𝑦 𝑔 𝐴 +𝑦 𝑝 𝐴 𝑥 𝑔 𝐴 𝑔 𝐴 +𝑦 2 − µ 𝐴

39. Stability of Equilibrium Points
3 eigenvalues: − µ 𝐸 , 𝑟 , − µ 𝐴
Trivial equilibrium point is a locally unstable saddle point

40. Biologically realistic equilibrium points
Case of small tumor mass with existence of large effector cells :
𝐸,𝑇,𝐴 =( 10 5 ,10,1.8)
eigenvalues are {−0.03, − 𝑖, −0.96−0.4𝑖}
system is stable
Tumor persistent equilibrium: large tumor cells under the presence of large effector cells

41. Tumor persistent equilibrium

42. Parameter Sensitivity Analysis
Parameters vary over a range of values
Our model is most sensitive to :
α: maximum rate of anti-proliferation effect of TNF α
c: tumor antigenicity

43. Benefit of increasing α: anti-proliferation effect of TNF-α on tumor cells for c=0.035 & c=5 10 −5

45. Case 2: Stability Analysis with VB-111 virotherapy
Goal: capture the decay and stabilization of tumor cells by VB-111 monotherapy
𝑓 1 : 𝑑𝐸 𝑑𝑡 = 𝑝 𝐸 𝐴𝐸 𝑔 𝐸 +𝐴 +𝑐𝑇− µ 𝐸 𝐸
𝑓 2 : 𝑑𝑇 𝑑𝑡 =𝑟𝑇 1−𝑏𝑇 − 𝑎 𝑇𝐸 𝑔 𝑇 +𝑇 −𝛼 (1+𝛽𝐹)𝐴𝑇 (2)
𝑓 3 : 𝑑𝐴 𝑑𝑡 = 𝑝 𝐴 𝑇𝐸 𝑔 𝐴 +𝑇 − µ 𝐴 𝐴 (3)
𝑓 4 : 𝑑𝐹 𝑑𝑡 = 𝐹 𝑠𝑡 −µ𝐹 (4)

46. Equilibrium Points Plotting 𝑓1 :
Equilibrium Point (𝐸 0 ,𝑇 0 , 𝐴 0 , 𝐹 0 )=(0,0, 0, 𝐹 𝑠𝑡 µ ) with gene therapy

47. Stability of Equilibrium Points
𝐽= − µ 𝐸 𝑔 𝐸 µ 𝐴 𝑔 𝐴 µ 𝐴 𝑐 𝑔 𝐸 𝑔 𝐴 𝑟 𝑔 𝑇 −µ 𝐴 𝑔 𝐴 −µ
Eigenvalues: {− , , , -1}
 Equilibrium point is stable

48. Coexisting small tumor equilibrium
Equilibrium point ( 𝐸 ∗ ,𝑇 ∗ ,𝐴 ∗ , 𝐹 𝑠𝑡 µ ) where 𝐸 ∗ ,𝑇 ∗ ,𝐴 ∗ are small coexisting small population
Tumor Cells versus Effector Cells phase portrait
Tumor Cells versus TNF-α phase portrait b

49. Rise of the therapeutic protein Fas-c
dF dt = F st −µF
where F st = and decay rate µ=1

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

51. Comparison of System Dynamics
With Therapy
Without Therapy

52. Conclusions
Need to detect the stage of the tumor to predict the progression of brain cancer and patient survival
Developed novel principal component analysis (PCA) based tumor classification of a large temporal MRI brain scans

53. Conclusions
Investigate the efficacy of VB-111 clinically on solid tumors
Quantified the effect of VB-111 in the presence of TNF-α at the tumor microenvironment

54. Future Work Image based modeling approach
Patient 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

55. Publications
[1] A. W. Daali, Y. Huang, and M. Jamshidi, "A system based approach to construct a Kaposi sarcoma-associated herpesvirus (KSHV) specific pathway crosstalk network“. System of System Engineering, IEEE pp
[2] A. 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), th Annual International Conference of the IEEE Aug Milano, Italy
[3] A. W. Daali, M. Jamshidi, A. Brenner and A. Seifi, “Mathematical model of dynamical behaviour of tumor system in response to VB-111 Virotherapy” IEEE Transactions on Biomedical Engineering, 2015 (submitted)
[4] A. W. Daali, A. Kaissi, “Telemedicine: Opportunities & Challenges ”, Engineering in Medicine and Biology Society (EMBC), th Annual International Conference of the IEEE Aug Milano, Italy (submitted)

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57. Thanks to: Mo Jamshidi, Ph.D., Chair Chunjiang Qian, Ph.D.
Artyom Grigoryan, Ph.D.
David Akopian, Ph.D
Ali Seifi, M.D.
UTHSCSA
Dr. Andrew Brenner, M.D., Ph.D.
Dr. John Floyd, M.D.

58. Questions?