Personalized medicine by the use of mathematical models for angiogenesis: validation in a Mesenchymal Chondrosarcoma patient

Transcription

1 Personalized medicine by the use of mathematical models for angiogenesis: validation in a Mesenchymal Chondrosarcoma patient Agur Zvia Institute for Medical BioMathematics, IMBM

2 Agenda Medical problem: No scientific methods for forecasting patient s response to drug > Trial-and-Error Solution: BioMathematics can relate molecular changes to their effects on the patient The rationale of our angiogenesis modeling: search the dominant dynamics in Xenograft experiments construct simple (qualitative) mathematical model that describe the dynamics how simple? to learn what the minimal model structure that yields the dynamics is Modeling aim: model should enable predicting treatment efficacy vascular tumor growth model Validation in Pre/Clinical trials Use: treatment personalization The patient Model personalization Prospective preclinical model validation Predictions for the patient Prospective clinical validation Summary and open questions

3 Problem: Intracellular Interactions do not Suffice for Forecasting Patient Response March 22, 2004

4 cf cn Out (1 mm) Tumor (in) Xenograft experiments in ovary carcinoma

5 M I/f M o/f I/f M o/f I/o F I/f F o/f F I/o Mouse P -- f-3 f Analysis of xenograft experiments in ovary carcinoma Vessels volume 5 0 V tum tumor size Vessels volume M mature vessels F total vessels I inside tumor O-O outside tumor n,f reference sites For example: M o/f relates to the volume of mature vessels outside the tumor in relation to the reading in reference site f M I/n I/n M o/n M I/o I/o F F I/n I/n F F o/n F F I/o I/o Mouse GA - - n- n3 V tum Arakelyan et al., in: "Cancer Modelling and Simulation", Luigi Preziosi ed., CRC Press, LLC, (UK), tumor size

6 simplifyed model and its analysis Effective vessel density Time delay effect on tumor proliferation Tumor size - rate of change Protein1 - secretion rate (VEGF) Protein2 - secretion rate (Ang1) Immature vessel volume - rate of change Mature vessel volume - rate of change Agur et al, DCDS, 2004 N& = f1( E 1 τ ) N P & 1= f2( E) N δ 1P1 P & 2 = αn δ 2P2 V & 1= f3( P1 τ2) V1 f4( P2 ) V1 + f5( P V & 2 = f4( P2 ) V1 f5( P2 τ ) V 3 2 2τ 3 ) V 2 produced by the tumor at a rate which is a decreasing function, f2, of the effective vessel density produced by the tumor and decays at constant rates produced as a function f3 of VEGF; matures as an increasing function, f4, of ang1/ang2 For rationalizing the observed oscillation pattern it was necessary to introduce a significant time-delay between the tumor and vessels processes. This might underline the significance of time-delays in tumor growth dynamics.

7 Model response to antiangiogenic drugs Model has to Yield oscillation Take account of tumor growth Take account of new vessel formation and regression Consider different time scales of vasculature and tumor processes (to represent time delays) Enable modelling of drugs with different drug action mechanisms Rationalize and organize current angiogenesis information We organized the information scattered in experimental articles into one vascular tumor growth algorithm

8 Multiscale mechanistic model of vascular tumor progression Multi-scale mathematical model of vascular tumor growth. Tissues (light orange), cells (pink) and molecules (lavender); Vascular Endothelial Growth Factor (VEGF) and Platelet- Derived Growth Factor (PDGF) are secreted by the tumor cells. VEGF binds to endothelial cells and PDGF to pericytes, to generate new and mature blood vessels, respectively, and the ratio of Angiopoietin1 (Ang1) and Angiopoietin2 (Ang2), secreted both by the tumor and by endothelial cells, affects the stability of the mature vessels. Arakelyan et al., ASCO, 02; Angiogenesis, 02; Agur, Future Oncology, 10

9 Model simulations of mouse GA: Tumor volume/time cf cn Out (1 mm Medium increase 15 volume units in 1 month Tumor (in)

10 Validation of the Vascular Tumor Model: Demonstrating Prediction Accuracy The vascularization profile of tumor GA was predicted and compared with the actual MVD, experimentally measured by MRI. Model Predictions MRI readings SI Arakelyan et al., EJC, 2004 time Total vasculature Mature vessels Immature vessels

11 Clinical validation in metastatic breast cancer (MBC) patients treated by Docetaxel Model accurately predicted objective tumor response (RECIST) and tumor sizes/entire treatment period Predicted vs. measured tumor diameter. Model prediction accuracy of tumor size: R 2 =0.7 (p<0.001); objective tumor response assessed according to RECIST; 85.7% (Kappa=0.72, p<0.05). Regression model line (solid line); 95% confidence interval (dashed line).

12 Main processes in the solid tumor model - partial scheme of Vascular Tumor Model Tumor growth and angiogenesis are regulated by Effective Vessel Density (EVD). EVD represents the level of perfusion in the system which affect: Living Cells EVD Apoptotic /Necrotic Cells Proliferation rate Cell Death: Apoptosis and necrosis Growth factor generation Creation/maturation of vessels VEGF Immature Vessels Vessels Cells Ang2 Ang1 Mature Vessels PDGF

13 Mathematical Formulation: System of Ordinary Differential Equations (Example) λ M Living Cells µ A Apoptotic /Necrotic Cells dl dt L() t µ f L() t ( EVD) ( EVD) = up f up (EVD) λ Proliferation Rate M f EVD EVD Vessels Cells f down (EVD) down A Death Rate EVD

14 Mathematical Formulation Integration of PD into Mechanistic Model Possible Drug Effects Reduce proliferation rate Increase rate of cell death Angiogenic processes λ M Living Cells µ A Apoptotic /Necrotic Cells dl dt PD down (C) 0.5 PD Effect on Proliferation Conc f EVD PD Effect on Death Conc Vessels Cells down up PD ( C()) t λ ( EVD) L() t PD ( C()) t µ ( EVD) L() t = M M up A A down PD up (C) 4 2 f

15 Treatment Personalization A new treatment personalization method, combining tumor xenografts and the vascular tumor growth model was put forward, validated and used to suggest an improved treatment schedule for a particular Mesenchyma ChondroSarcoma (MCS) patient Gorelik et al., Cancer Research, 68: (21) 2008, PP

16 Mesenchymal Chondrosarcoma (MCS) MCS accounts for about 1% of all chondrosarcomas Overall, 5-year survival is 55% This disease usually follows an aggressive course, with a high rate of distant metastases Rare condition = deficiency in experience

17 The patient VN a 45-year old white male in excellent health Growing mediastinal mass was found in 2004 Primary tumor was resected Multiple new bilateral pulmonary nodules thirty days after the operation. Aggressive chemotherapy with Ifosphamide, cisplatin and etoposide for 6 cycles, VACA (vincristine, doxorubicin, cyclophosphamide, and dactinomycin) for 2 cycles, and sunitinib orally for 8 weeks Additional liver and bone metastases Severe myelosuppression with pancytopenia

18 Methodology

19 Model predictions of treatment efficacy and prospective validation in xenograft experiments Gorelik et al, 2008 Regimen Drug Dose (mg/kg) Route Schedule Predicted Results (TGI 1 ) Observed Results (TGI 1 ) Accuracy 1 Control % 2 CPT-11 Bevacizumab IP IP Q7Dx3 Q3Dx % 59.4 % 96.2 % Gemcitabine 40 IP Q3Dx4 3 Docetaxel 6.3 IV Q2Dx % % 70.1 % Bevacizumab 10 IP Q3Dx10 4 Doxorubicin Bevacizumab 2 10 IV IP QDx5 Q3Dx % 56.4% 84.2 % 5 Sorafenib 60 PO QDx % 38.9% 96.1 % 6 Sorafenib Bevacizumab PO IP QDx10 Q3Dx % 87.2 % 81.4 % 1 Tumor Growth Inhibition Average prediction accuracy: 87.2 %

20 Scaling to human The scaling was done using expression analysis of several key proteins Ang1, Ang2, VEGF, etc

21 Treatment Personalization Predictions of improved schedule in the MCS patient Gorelik et al, 2008 Regimens containing Bevacizumab applied intravenously in combination with onceweekly Docetaxel are predicted more efficacious in the MCS patient than all other simulated Docetaxel schedules.

22 Treatment Personalization Predictions Weekly Docetaxel in the patient resulted in stable metastatic disease and relief of pancytopenia Gorelik et al, 2008

23 Summary Mathematical models can formalize complex drug-patient interactions The minimal model describing the observed oscillatory pattern of angiogenesis was designed.. showing that a time-delay between the tumor and vessels processes drives the oscillations On this basis a detailed multiscale angiogenesis model was constructed yielding precise predictions of drug efficacy Successful validation enables models to be employed for identifying improved regimens & personalize treatment A successful treatment personalization endeavor improves patient s survival and quality of life Once weekly Docetaxel is advantageous for patients with intense angiogenesis

24 Selected publications 1. Arakelyan L, Vainstain V., Agur Z. A computer algorithm describing angiogenesis and vessel maturation and its use for studying the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth, Angiogenesis, 5 (3), 2002 (pp ). First comprehensive model for cancer angiogenesis. 2. Agur Z., Arakelyan L., Daugulis P., Ginosar Y. Hopf point analysis for angiogenesis models. Discrete and Continuous Dynamical Systems Series B, 4 (1), 2004 (pp ). Mathematical analysis determining the driving forces in angiogenesis. 3. Arakelyan L, Merbl Y., Agur Z. Vessel maturation effects on tumour growth: validation of a computer model in implanted human ovarian carcinoma spheroids Eur. Jour. Cancer, 41, 2005 (pp ). Experimental validation of the comprehensive model. 4. Gorelik B., Ziv I., Shohat R., Wick M., Webb C., Hankins D., Sidransky D., Agur Z. Efficacy of once weekly docetaxel combined with bevacizumab for patients with intense angiogenesis: validation of a new theranostic method in mesenchymal chondrosarcoma xenografs. Cancer Research, 68: (21) November, , PP Use of angiogenesis model for treatment personalization prospective validation in man. 5. Arakelyan L., Merbl Y., Daugulis P., Ginosar Y., Vainstein V., Selister V., Kogan Y., Harpak H., Agur Z. Multi-scale analysis of angiogenic dynamics and therapy, Ch. 7, in: "Cancer Modelling and Simulation", Luigi Preziosi ed., CRC Press, LLC, (UK), Book chapter on rationale of angiogenesis modelling. 6. Z Agur, N Bloch, B Gorelik, M Kleiman, Y Kogan, Y Sagi, D Sidransky, Y Ronen. Developing oncology drugs using virtual patients of vascular tumor diseases. In "Systems biology in Drug Discovery and Development"; Ed. Daniel L. Young and Seth Michelson; Series: Technologies for the Pharmaceutical Industry; Series Editor: Dr. Sean Ekins; John Wiley & Sons, Book chapter on use of angiogenesis modelling in the clinic and Pharma industry.

25 Thank You

26 Paolo Magni Is the model unique (best) for retrieving the system at hand? How can you validate the precision of the PK/PD model? Time scale of accuracy?

27 Discussion modelling angiogenesis What type of models should we use to describe angiogenesis? Stochastic models vs. deterministic models Discrete vs. continuous ODE vs. PDE Simple vs. complex Analytical vs. simulations Statistical vs. mathematical Top-down vs. bottom-up Biochemistry-driven vs. physics-driven Data-driven vs. mechanism-driven Spatial vs. mass action. An ill-defined question

28 Model Evaluation 1. Does the model add insight to the problem at hand? 2. Are the model assumptions about the driving forces in the biological system sufficiently justified? If the problem at hand is qualitative, then satisfying 1 and 2 may suffice If the model is expected to yield quantitative predictions 3. How robust are the model s predictions? 4. What are the data to be used for model validation? 5. What is the time scale over which prediction is to be made? 6. Over how long it yields consistent and precise predictions? 7. What are the limitations of the model?

29 Do mathematical models of angio. add insight? They can underline the critical parameters (bistability) They can predict comprehensive behaviour in response to small changes upstream They can predict population response to a drug Due to variations in disease parameters Due to varaition in PK Etc. They can be used to personalize medicine (theranostics)

30 Collaboration Collaboration bet experimentalists and theorists is mutually important: The experimentalist direct and help refining the theory and, reciprocally, aided by it to refine their view of the important (vs secondary or even negligible) forces in the system. How can we join forces? How can we collaborate to improve the angio. modelling? Of different solid cancer indication? Get good human disease model (data on untreated?)?.