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 

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

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-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

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

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

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

MRI Experiment Intracranial xenografts performed in nude rats expressing U87 glioma cell line Rats received intravenously a single dose of VB-111 at 10 11 (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

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 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

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

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)

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: http://cancer.gov/cancertopics/understandingcancer

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

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

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

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

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

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 = 1 1+ 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

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)

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

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

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

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-111 on tumor cells

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

Therapeutic Protein Fas-c gene TNFR-1

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

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

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

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

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. 235-252, 1998

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

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]

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

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

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

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 100-165 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

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 0.1-0.8 days-1 𝑝 𝐴 Maximum rate of TNF-α production in the presence of effector cells stimulated by tumor cells 0.3 10 −3 −2 10 −2 pg/ml 𝑔 𝐴 Half saturation constant, tumor cells on TNF production 10 3 − 10 4 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

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

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 1 𝜕 𝑓 1 𝜕 𝑥 2 𝜕 𝑓 2 𝜕 𝑥 2 𝜕 𝑓 3 𝜕 𝑥 2 𝜕 𝑓 1 𝜕 𝑥 3 𝜕 𝑓 2 𝜕 𝑥 3 𝜕 𝑓 3 𝜕 𝑥 3 = 𝑝 𝐸 𝑧 𝑔 𝐸 +𝑧 − µ 𝐸 𝑐 𝑝 𝐸 𝑥𝑔 𝐸 𝑔 𝐸 +𝑧 2 −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

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

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, −0.96+0.4𝑖, −0.96−0.4𝑖} system is stable Tumor persistent equilibrium: large tumor cells under the presence of large effector cells

Tumor persistent equilibrium

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

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

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 1   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)

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

Stability of Equilibrium Points 𝐽= − µ 𝐸 𝑔 𝐸 µ 𝐴 𝑔 𝐴 0 0 0 µ 𝐴 𝑐 𝑔 𝐸 𝑔 𝐴 𝑟 𝑔 𝑇 0 0 0 0 −µ 𝐴 𝑔 𝐴 0 0 0 0 −µ Eigenvalues: {−5.5 10 4 , -1.1 10 4 , -1.8 10 4 , -1}  Equilibrium point is stable

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

Rise of the therapeutic protein Fas-c dF dt = F st −µF where F st = 10 3 and decay rate µ=1

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

Comparison of System Dynamics With Therapy Without Therapy

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

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

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

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 2013 pp. 273-278 [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), 2015 37th Annual International Conference of the IEEE. 25-29 Aug. 2015. 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), 2015 37th Annual International Conference of the IEEE. 25-29 Aug. 2015. Milano, Italy (submitted)

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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.

Questions?