in response to VB-111 Virotherapy

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 (≈ 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 (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 (≈ 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

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:

PCA based Tumor Stage Classification System
Now that you have the appropriate background on our experiment and the type of data available. I will introduce you to our proposed approach. Because classifying the stage of tumor is very important, we devoloped a PCA based tumor classification 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 Since eigenvectors have the same dimensionality as the original images, they are considered tumor images. Hence the name EigenTumors. Each EigenTumor represent a direction in which images differ from the mean tumor image. Each EigenTumors accentuate a different feature of the tumor. These eigentumors are used to represent the new unknown tumor images by projecting a new mean-shifted tumor image on a subset of the 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 = 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) The features of the new tumor is obtained and corresponding similarity score between feature vectors 𝛺 1 and 𝛺 𝑘 for each stage is calculated. Resulting into 3 different scores 𝑠 1 𝛺 1 , 𝛺 𝑘 , 𝑠 2 𝛺 1 , 𝛺 𝑘 , 𝑠 3 𝛺 1 , 𝛺 𝑘 .The decision module outputs the stage the unknown tumor by returning the stage score of the tumor 𝑧=max⁡( 𝑠 1 𝛺 1 , 𝛺 𝑘 , 𝑠 2 𝛺 1 , 𝛺 𝑘 , 𝑠 3 𝛺 1 , 𝛺 𝑘 as well as its class label 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 Tp: refer to the true positives, the total number of tumors correctly recognized 𝐹 𝑁 : total number of tumors falsely recognized 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 Classify different temporal stages of brain tumors given a large time series of MRI images Prognosis factor

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 Before discussing our mathematical model in details, let’s examine some of the important populations involved in VB-111 mechanism

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 Effector cells generic term for activated immune cells T cells: lymphocytes; type of white blood cell play central role in cell-mediated immunity, cytotoxic NK cells: cytotoxic lymphocyte faster reaction to the immune system VB-111 targets the expression of Fas-Chimera transgene

Therapeutic Protein Fas-c
gene -VB-111 consists of a non-replicating type 5 adenovirus (Ad-5) vector with a pre-proendothelin-1 promoter (PPE-1-3x) which regulates transcription of the death receptor Fas-Chimera (Fas-c) -The virus is used as a vector to deliver the therapeutic gene Fas-c by infecting the cell -The engineered protein Fas-c is composed of two parts, the first part consists of TNF receptor 1 which binds to tumor necrosis factor alpha (TNF-α) and the second part consists of Fas protein which triggers cell death 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 -Depending on the type of biological system in question , there are two types of analysis: macroscopic and microscopic analysis. The macroscopic analysis is more concerned with modeling the external population of the tumor such as blood vessels and the vascular capacity of endothelial cells. -Lymphatic vessels are similar to blood vessels, but they don't carry blood.

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 , 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 Rate of change of effector cells -First term represents effector cells growth stimulated by TNF-α -effector cells are also stimulated by tumor cells 𝑐𝑇 where c is a measure of the tumor antigenicity -The last term µ 𝐸 𝐸 represents the natural degradation rate of effector cells. 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 relates the rate of a reaction (production/degradation) dP/dt to the concentration of the substrate S S  P (product) The production rate of P is limited by the max rate achieved by the system 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 Rate of change of tumor cells -1st term represents logistic growth of the tumor -2nd term represents tumor cell death by effector cells -3rd term measures the amount of apoptosis induced by TNF-α triggered Fas-c in the presence of tumor cells 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 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 Table lists all parameter values used in the development of this mathematical model µ 𝐸 , 𝑔 𝑇 ,𝑐, 𝑟 ,𝑏, 𝑎 are obtained from litterature The half saturation constant 𝑔 𝐸 is TNF-α concentration that corresponds to half of the maximum production rate of effector cells

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

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 To better understand the dynamic of the model, it is necessary to study the system without gene therapy (F=0)

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 Trivial equilibrium point

3 eigenvalues: − µ 𝐸 , 𝑟 , − µ 𝐴 Trivial equilibrium point is a locally unstable saddle point Since eigenvalues are real and have opposite signs. The solution of the system approach asymptotically the eigenvector associated with positive eigenvalue

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 -The trivial equilibrium point is not realistic since it corresponds to zero tumor, effector and TNF-α cell population. -For therapy purposes, we consider nonzero coexisting equilibrium points with small tumor mass T and large population of E -Another interesting point is the case of tumor persistent equilibrium

Tumor persistent equilibrium
In the absence of treatment, tumor cells progressively increase (first 25 days) during this time the immune system is activated by increased production of effector cells (first 55 days). After the immune system is activated, tumor cells begin to decrease reaching a stable state. Since the cytokine TNF-α are produced by effector cells, it is expected that an increase in the production of effector cells corresponds to an increase in TNF-α. -Immune cells is not enough to drive tumor to low stable state

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 -Since some parameters vary over a range of values, a parameter sensitivity analysis is performed on the model -our model is most sensitive to the tumor antigenicity c and the maximum rate of anti-proliferation effect of TNF α.

Benefit of increasing α: anti-proliferation effect of TNF-α on tumor cells for c=0.035 & c=5 10 −5
the benefit of increasing the anti-proliferation effect of TNF-α on tumor cells for two different tumor antigenicity values c=0.035 (Figure 24, a,b,c) and 𝑐=5 10 −5 (Figure 24, d,e,f). The maximum rate of anti-proliferation effect of TNF α is varied from α= to α=0.1. -For unrecognizable tumor with a low tumor antigenicity parameter ( 𝑐=5 10 −5 ), the anti-proliferation effect of TNF-α on tumor cells is expected to be low which explains the unstable behavior of tumor cells ( d,e). When the anti-proliferation effect of TNF-α is increased (α=0.1), the tumor is stabilized (Figure 24 f ). -For a recognizable tumor with a high antigenicity parameter c=0.035, the anti-proliferation effect of TNF-α on tumor cells is expected to be high driving tumor cells to a lower stable state (Figure 24 c). Figure a displays the case of a high antigenic tumor when the anti-proliferation effect of TNF-α is manipulated and reduced to α= The result obtained shows that when the apoptotic effect of TNF-α is reduced, tumor cells oscillate around a large value ( cells). The immune response consisting of effector cells and their produced cytokines TNF-α respond by following similar oscillatory behavior of tumor cells. Comparing these observations for different types of tumor antigenicity, one can conclude that a low anti-proliferation effect of TNF-α is associated with the oscillatory behavior exhibited by tumor cells. For therapy purposes, it has been shown that increasing the anti-proliferation effect of TNF-α leads to tumor stabilit

-Our model was sensitive to another important parameter included in our analysis is the tumor antigenicity c -behavior of the immune system in response to low antigenic tumor (𝑐= 5 10 −5 ) and a high antigenic tumor (𝑐=0.05). -As expected, when tumor antigenicity c increases from c= −5 to 𝑐=0.05 , that is when Tumor is more detectable by the immune system, effector cells increase from 114 to 1302 cells and tumor cells decrease from 6*104 cells to 768 cells:

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) -The goal of this model is to …. -To explore stability of the tumor system and to better understand the dynamics when VB-111 is administered

Equilibrium Points Plotting 𝑓1 :
when plotting 𝑓 1 : 𝑑𝐸 𝑑𝑡 for different positive values of 𝑥 1 ≥0 and 𝑥 2 ≥0 and investigating point of intersection ( 𝑥 1 , 𝑥 2 ) with z=0 plane. Based on Figure 27, 𝑑𝐸 𝑑𝑡 =0 if only if 𝑥 1 = 𝑥 2 =0.The equilibrium point is therefore: (𝐸 0 ,𝑇 0 , 𝐴 0 , 𝐹 0 )=(0,0, 0, 𝐹 𝑖 µ ): Equilibrium Point (𝐸 0 ,𝑇 0 , 𝐴 0 , 𝐹 0 )=(0,0, 0, 𝐹 𝑠𝑡 µ ) with gene therapy

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 This equilibrium point is not biologically relevant since system will reach this equilibrium only if there is no tumor cells, effector cell and TNF-α (nonexistence of population).

Coexisting small tumor equilibrium
Equilibrium point ( 𝐸 ∗ ,𝑇 ∗ ,𝐴 ∗ , 𝐹 𝑠𝑡 µ ) where 𝐸 ∗ ,𝑇 ∗ ,𝐴 ∗ are small coexisting small population Figures illustrates how the therapeutic Fas-c protein successfully controls the trajectory of Tumor Cells to an equilibrium state that approaches zero (y=0.77). Treatment proved also successful in controlling TNF-α which approaches zero (x=0.0018). These results agree with the findings in actual biological experiments between Tumor cells, Effector cells and TNF-α. With virotherapy treatment, the system moved from a pathological state (Tumor cells ≠0) to a normal state where Tumor cells, effector cells and TNF-α are approaching zero 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 = and decay rate µ=1

Effect of killing rate β of Fas-c on cell dynamics
It can be observed form Figure 31 (c) that as β increases, tumor cells decrease proportionally and stabilizes at low value. Figure 31 (a) shows that when increasing β from 1 to 10, the overall response of effector cells retain its initial response pattern; the killing rate of the therapeutic protein only decreased the amplitude level of effector cells. From a biological point of view, these results match the intended outcomes. The effector cell levels at the tumor site decreased since tumor cells are decreasing as well. From Figure 31 (b), an interesting observation can made about the rate of change of TNF-α as β increases. TNF-α decreases as β is varied from 1 to 10. One plausible explanation that supports this behavior is due to the fact that the effector cells ,that are responsible to stimulate TNF-α, are decreasing. Consequently, a smaller effector cell levels will only stimulate a smaller level of TNF-α.

Comparison of System Dynamics
With Therapy Without Therapy Figure 32 compares cells dynamics between two cases: with and without VB-111 treatment and for different antigenic tumors. It is apparent that our model captured the therapeutic properties of Fas-c on tumor cells, effector cells and TNF-α. In the case gene therapy is not administered , regardless of the level of tumor antigenicity , the cell dynamics exhibit oscillatory behavior alternating between different states (fig c,d). When VB-111 gene therapy is administered, however, the previously perturbed states are stabilized with a Fas-c protein killing rate of β=10 (fig a,b).

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 -In this dissertation, we addressed several critical needs in the neuro-oncology field -We propose an algorithm that addresses the challenging task of classifying stage of tumor over period of time while the tumor is being treated with VB-111 -we propose a new framework to detect and classify temporal longitudinal MRI with high accuracy rates. A sensitivity rate of 98.7%, 95.8% and 94.01% for stage 1, 2 and 3 are reported

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 -The second part of this dissertation addresses another critical need in the neuro-oncology field that is investigating tumor dynamics in response to VB-111 virotherapy through mathematical modeling. -We proposed the first model which consists of a set of nonlinear differential equations describing the complex interactions between tumor cells, effector cells, the cytokine tumor necrosis factor TNF-α and the anti-angiogenic therapeutic protein Fas-c -it is apparent that our model successfully captures the decay and stabilization of tumor cells by VB-111 monotherapy

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

References: [1] A. Webb, and G. C. Kagadis, “Introduction to biomedical imaging,” Medical Physics, vol. 30, no. 8, pp , 2003. [2] M. Poustchi-Amin, S. A. Mirowitz, J. J. Brown, R. C. McKinstry, and T. Li, “Principles and Applications of Echo-planar Imaging: A Review for the General Radiologist 1,” Radiographics, vol. 21, no. 3, pp , 2001. [3] J. Hennig, A. Nauerth, and H. Friedburg, “RARE imaging: a fast imaging method for clinical MR,” Magnetic Resonance in Medicine, vol. 3, no. 6, pp , 1986. [4] D. Carr, J. Brown, G. Bydder, R. Steiner, H. Weinmann, U. Speck, A. Hall, and I. Young, “Gadolinium-DTPA as a contrast agent in MRI: initial clinical experience in 20 patients,” American Journal of Roentgenology, vol. 143, no. 2, pp , 1984. [5] A. B. T. Association, “Glioblastoma and Malignant Astrocytoma ”, 2012. [6] A. Jain, J. C. Lai, G. M. Chowdhury, K. Behar, and A. Bhushan, “Glioblastoma: Current Chemotherapeutic Status and Need for New Targets and Approaches,” Brain Tumors: Current and Emerging Therapeutic Strategies, InTech, Rijeka, pp , 2011. [7] M. C. Tate, and M. K. Aghi, “Biology of angiogenesis and invasion in glioma,” Neurotherapeutics, vol. 6, no. 3, pp , 2009. [8] V. Therapeutics. "Phase I/II study shows safety and efficacy of VB-111 in patients with rGBM," [9] A. J. Brenner, Y. C. Cohen, E. Breitbart, L. Bangio, J. Sarantopoulos, F. J. Giles, E. C. Borden, D. Harats, and P. L. Triozzi, “Phase I Dose-Escalation Study of VB-111, an Antiangiogenic Virotherapy, in Patients with Advanced Solid Tumors,” Clinical Cancer Research, vol. 19, no. 14, pp , 2013. [10] A. Brenner, Y. Cohen, E. Breitbart, J. Rogge, and F. Giles, "Antivascular activity of VB111 in glioblastoma xenografts." p. e13652. [11] B. A. Draper, W. S. Yambor, and J. R. Beveridge, “Analyzing pca-based face recognition algorithms: Eigenvector selection and distance measures,” Empirical Evaluation Methods in Computer Vision, Singapore, pp. 1-15, 2002. [12] J. Zhou, E. Tryggestad, Z. Wen, B. Lal, T. Zhou, R. Grossman, S. Wang, K. Yan, D.-X. Fu, and E. Ford, “Differentiation between glioma and radiation necrosis using molecular magnetic resonance imaging of endogenous proteins and peptides,” Nature medicine, vol. 17, no. 1, pp , 2011. [13] C. Solomon, and T. Breckon, Fundamentals of Digital Image Processing: A practical approach with examples in Matlab: John Wiley & Sons, 2011. [14] A. d’Onofrio, and A. Gandolfi, “Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al.(1999),” Mathematical biosciences, vol. 191, no. 2, pp , 2004. [15] P. Hahnfeldt, D. Panigrahy, J. Folkman, and L. Hlatky, “Tumor development under angiogenic signaling a dynamical theory of tumor growth, treatment response, and postvascular dormancy,” Cancer research, vol. 59, no. 19, pp , 1999. [16] U. Ledzewicz, and H. Schättler, “Antiangiogenic therapy in cancer treatment as an optimal control problem,” SIAM Journal on Control and Optimization, vol. 46, no. 3, pp , 2007.

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.

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