Mathematical modeling of differential effects of neo-adjuvant Sunitinib on primary tumor and metastatic growth
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(2) MONC. Mathematical modeling of differential effects. Modeling in ONCology. of neo-adjuvant Sunitinib on primary tumor and metastatic growth C. Nicolò1, M. Mastri2, A. Tracz2, J. ML Ebos2, S. Benzekry1 1 Inria. team MONC, Institut de Mathematiques de Bordeaux, Bordeaux, France. 2 Department of Cancer Genetics and Medicine, Roswell Park Cancer Institute, Buffalo, New York. BACKGROUND. DIFFERENTIAL EFFECTS OF SUNITINB ON PRIMARY TUMOR AND METASTASIS. Primary tumor growth: Untreated group. • Despite clear efficacy in reducing established tumor growth, recent preclinical studies have shown limited, or even opposing, efficacies in preventing metastatic spread.. 2500. 2500. 2000. 2000. 1500. 1000. 0. 0. 5. 10. 15. 20. 25. 30. 0. 35. 0. 10. <latexit sha1_base64="EiBdCe1kHTXuueTFETaH73T8kP4=">AAAB/XicbVBNS8NAFNzUr1q/qh69LBahgpREBPUgFL14rGDaQhvKZvtal26SZfdFKKHgr/CqJ0/i1d/iwf9iEnPQ6pyGmfd488ZXUhi07Q+rtLC4tLxSXq2srW9sblW3d9omijUHl0cy0l2fGZAiBBcFSugqDSzwJXT8yVXmd+5BGxGFtzhV4AVsHIqR4AxTqT8eqHr7CA/pBbUH1ZrdsHPQv8QpSI0UaA2qn/1hxOMAQuSSGdNzbIVewjQKLmFW6ccGFOMTNoZeSkMWgPGSPPOMHsSGYUQVaCokzUX4uZGwwJhp4KeTAcM7M+9l4n9eL8bRmZeIUMUIIc8OoZCQHzJci7QMoEOhAZFlyYGKkHKmGSJoQRnnqRin7VTSPpz57/8S97hx3rBvTmrNy6KYMtkj+6ROHHJKmuSatIhLOFHkkTyRZ+vBerFerbfv0ZJV7OySX7DevwDMlZR0</latexit>. metastatic burden (bioluminescence) pre-surgical molecular and cellular biomarkers, including Ki67 and CD31. -14 -11. -7. 0 Endpoint. Sunitinib [60mg/kg/day]. expression, circulating tumor cells (CTCs) and myeloid derived. Post-surgical. PT. MB. 9. 10. 9. 10 7. 10 7. 10 6. 10 6. 10 5. 10 5. 4. suppressor cells (MDSCs).. 20. 40. 60. 10. 80. 10. 4. Tx start Pre-surgical. Post-surgical. PT. MB. 10. 10. Surgery (t = 38). 10 10. 9. 10. 9. 10 8. 10 8. 10 7. 10 7. 10 6. 10 6. 10 5. 10 5. 10. 4. 0. 20. 40. Time (days). 60. 10. 80. 4. Time (days). Population fit assuming no effect of treatment on. Simulation of treatment also on. metastasis. metastasis. Treatment acts differently on primary and secondary tumor growth. monitoring of post-. LM2-4LUC+ human metastatic breast. 10. 10. 10 8. 0. Treated group (11 days). Orthotopic implantation. 10 8. 10. Bioluminescence. Orthotopic xenograft breast model:. 10. Surgery (t = 38). Pre-surgical 10. 40. during the phase of treatment. gp (V, t) = 0. Primary tumor size (cells). Tx ends. primary tumor kinetics, Primary tumor size (cells). • • •. 10. Tx start. 30. Gomp-Exp model with therapy. Metastatic burden (cells). Measurements of. Tumor removed. 20. Time (days). Gomp-Exp model ✓ ✓ ✓ ◆◆ ◆ V gp (V ) = min V, ↵0 ln V Vc. Orthotopic implantation. Tx starts. Vehicle. 500. Primary tumor - metastatic growth dynamics:. Implantation. Day. 1000. Time (days). EXPERIMENTAL DATA. 3 Days ON/11 Days OFF 7 Days ON/ 7 Days OFF 14 Days ON. 1500. 500. • In this work, we evaluated a mathematical model of the metastatic process to describe primary tumor and metastatic dynamics in response to sunitinib in a clinically relevant ortho-surgical mouse model of spontaneous metastatic breast cancer.. 14 Days OFF. Volume (mm 3). Volume (mm 3). • It is currently evaluated in clinical trials in the neo-adjuvant setting.. Treated group (11 days). Metastatic burden (cells). • Sunitinib is a drug with anti-angiogenic activity used in the treatment of patients with metastases from renal cell carcinoma or gastrointestinal tumors.. surgical metastasis. carcinoma cells.. Mixed-effects population approach.. Table: Population parameters for the treated group.. Log-normal distribution for the individual parameters:. log( i ) ⇠ log( <latexit sha1_base64="3y0Y/lRA9jqmg8sROyaEsDcYQ2A=">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</latexit>. AN ELEMENTARY THEORY OF METASTATIC DYNAMICS:. MLE of. pop. pop ) + ⌘i ,. estimate (CV %). ⌘i ⇠ N (0, ! 2 ). µpop ↵0,pop. 1.009e-04 (117.476) 1.907 (22.919) 9.116e-02 (24.490). pop. through the SAEM algorithm.. unit mm. 3. · day day 1 day 1. r.s.e. (%) 1. 23.483 6.208 6.682. <latexit sha1_base64="gPotZc/Z7//zcoqqX7dnFJmKUE8=">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</latexit>. <latexit sha1_base64="MBXh531w1NgkpD44GABrXsAmIMU=">AAAB+3icbVC7TsNAEDzzDOEVoKQ5ESFRRTYCAV0kGsogYRKRWNH5sgmnnM+nuzVSZIWvoIWKCtHyMRT8C7ZxAQlTjWZ2tbMTaiksuu6ns7C4tLyyWlmrrm9sbm3XdnZvbZwYDj6PZWw6IbMghQIfBUroaAMsCiW0w/Fl7rcfwFgRqxucaAgiNlJiKDjDTLrraSv6qY71tF+ruw23AJ0nXknqpESrX/vqDWKeRKCQS2Zt13M1BikzKLiEabWXWNCMj9kIuhlVLAIbpEXiKT1MLMOYajBUSFqI8HsjZZG1kyjMJiOG93bWy8X/vG6Cw/MgFUonCIrnh1BIKA5ZbkRWBdCBMIDI8uRAhaKcGYYIRlDGeSYmWTfVrA9v9vt54h83Lhru9Um9eVoWUyH75IAcEY+ckSa5Ii3iE04UeSLP5MV5dF6dN+f9Z3TBKXf2yB84H99C5ZV3</latexit>. PT growth law: gp Primary Tumor (PT). 8 > < > :. Metastases growth law: g. <latexit sha1_base64="GaITYh0koZVDj/Cal8Xcv/YtVZE=">AAACE3icbVA9SwNBEN2LXzF+RS1tFoOQgISLCJpCCNhYRjAfkIRjbjOJS/bult05IRxp/Qn+ClutrMTWH2Dhf/ESU2j0VW/em2Fmnq+VtOS6H05maXlldS27ntvY3Nreye/uNW0UG4ENEanItH2wqGSIDZKksK0NQuArbPmjy6nfukNjZRTe0FhjL4BhKAdSAKWSl+fdgQGR9JueniR9mvALPvR0MS2LVDrmVPLyBbfszsD/ksqcFNgcdS//2e1HIg4wJKHA2k7F1dRLwJAUCie5bmxRgxjBEDspDSFA20tmn0z4UWyBIq7RcKn4TMSfEwkE1o4DP+0MgG7tojcV//M6MQ3Oe4kMdUwYiukikgpni6wwMo0IeV8aJILp5chlyAUYIEIjOQiRinGaWS7No7L4/V/SOClXy+71aaFWnQeTZQfskBVZhZ2xGrtiddZggt2zR/bEnp0H58V5dd6+WzPOfGaf/YLz/gXyfZ0x</latexit>. d(Vp) = μVp. 10 9. 10 9. 10 8. 10 8. 10 7. 10 7. 10 6. 10 6. 10 5. 10 5. 10 4. 10 4. 0. 20. 40. 60. t œ]0, +Œ[, V œ]V0 , +Œ[ t œ]0, +Œ[ ANALYSIS V COVARIATES œ]V0 , +Œ[. 80. Post-surgical. PT. MB. 10 10. 10 10. 10 9. 10 9. 10 8. 10 8. 10 7. 10 7. 10 6. 10 6. 10 5. 10 5. 10 4. 0. 20. 40. 60. 80. 10. 10 4. Surgery (t = 38) Pre-surgical. Post-surgical. PT. MB. 10. 10 10. 10 8. 10 8. 10 6. 10 6. 10 4. 10 4 0. 20. 40. 80. Time (days). Time (days). Time (days). 60. Metastatic burden (cells). 10. Pre-surgical. Primary tumor size (cells). MB 10. 8 > < ˆt fl(t, V ) + ˆV (g(t, V )fl(t, V )) = 0 t œ]0, +Œ[, V œ]V0 , +Œ[ g(t, V0 )fl(t, V0 )Size = —(V t œ]0, +Œ[ distribution of the p (t)) > : fl(0, v) = fl0 V œ]V0 , +Œ[ metastases ρ(t,v). Biomarkers VS individual parameters 0.45. 70. 0.4. r = -0.6392. 0.35. p = 0.0103. 0.3. 8 > < ˆt fl(t, v) + ˆv (g(v)fl(t, v)) = 0. g(V0 )fl(t, V0 ) = d(Vp (t)) > : fl(0, v) = fl0. 0.25 0.2 0.15. 60. r = 0.5832. 50. p = 0.0111. 40 30 20. 0.1. 10. 0.05. Z +Œ g(V0 )fl(t, V0 ) = —(V —(V )fl(t, V ) dV p (t)) + Metastatic burden (total metastatic V0 number of cells). Z. PT. Metastatic burden (cells). dVp – = )gp=(VmV p (t), t) —(V dt ˆt fl(t, V ) + ˆV (g(t, V )fl(t, V )) = 0 R +Œ g(t, V0 )fl(t, V0 ) = —(Vp (t)) + V0 —(V )fl(t, V ) dV Dissemination rate fl(0, v) = fl0. Dissemination law: d(Vp)= μVp. Metastases. Post-surgical. Post-surgical. Orthotopic implantation. Surgery (t = 38). Gr1 Low. Pre-surgical Surgery Sunitinib. Orthotopic implantation. Pre-surgical. CTC. Injection (or first cell). 10. Surgery (t = 38). Primary tumor size (cells). Growth rates of primary and secondary tumors gp and g. 10. Primary tumor size (cells). Individual dynamics. Orthotopic implantation. Metastatic burden (cells). DISSEMINATION + GROWTH. t. ˆt fl(t, )) = M (t) V =) + ˆd(V s))VV(s) ds0 V (g(t, p (t V )fl(t, 0. 0 -18. 0 -16. -14. -12. -10. -8. log(µ). •. 0. 0.5. 1. 1.5. µ. 2. 2.5. 3 ×10. -4. Biomarkers can be included in the model as covariates in order to explain part of the variability in the individual parameters. xi. : individual covariate. <latexit sha1_base64="Mfl42tmEebeczytDQgaehnT7PVY=">AAAB9HicbVC7TsNAEDyHVwivACXNiQiJKnIQEiBRRKKhDAKTSIkVrS+bcMr5obs1EFn5BFqoqBAt/0PBv2AbF5Aw1WhmVzs7XqSkIdv+tEoLi0vLK+XVytr6xuZWdXvn1oSxFuiIUIW644FBJQN0SJLCTqQRfE9h2xtfZH77HrWRYXBDkwhdH0aBHEoBlErXj33Zr9bsup2Dz5NGQWqsQKtf/eoNQhH7GJBQYEy3YUfkJqBJCoXTSi82GIEYwwi7KQ3AR+MmedQpP4gNUMgj1Fwqnov4eyMB35iJ76WTPtCdmfUy8T+vG9Pw1E1kEMWEgcgOkVSYHzJCy7QD5AOpkQiy5MhlwAVoIEItOQiRinFaSiXtozH7/TxxjupndfvquNY8L4opsz22zw5Zg52wJrtkLeYwwUbsiT2zF+vBerXerPef0ZJV7OyyP7A+vgFwrZIq</latexit> sha1_base64="Y0WCs03Gg+J9qyBgbcBNzAHK9Qo=">AAAB43icbVC7TsNAEFyHVzABQk1zIkKiimwaoEOioQwSJpESK1pfNuGU80N3a6TIyg/QUlEhPouCf8E2KYAw1WhmVzs7UaaVZc/7cBobm1vbO81dd6/l7h8ctlsPNs2NpECmOjWDCC1plVDAijUNMkMYR5r60fym8vtPZKxKk3teZBTGOEvUVEnkUuqN2x2v69UQ68RfkQ6sMG5/jiapzGNKWGq0duh7GYcFGlZS09Id5ZYylHOc0bCkCcZkw6KOuRSnuUVORUZGKC1qkX5uFBhbu4ijcjJGfrR/vUr8zxvmPL0MC5VkOVMiq0OsNNWHrDSq/J/ERBlixio5CZUIiQaZySiBUpZiXhbilnX4f59fJ8F596rr3XnQhGM4gTPw4QKu4RZ6EICECTzDi2OdV+ftu7WGs6rvCH7Bef8CAxGOhg==</latexit> sha1_base64="5mka0O5rHvnLFJgL4Wsl8MJG6oQ=">AAAB6XicbZA/T8MwEMUv5V8pBQori0WFxFQlLMCGxMJYBKGV2qhy3Gux6jiRfQGqqB+BFSYmxIdi4LuQhA7Q8qan92zd3S9MlLTkup9OZWV1bX2julnbqm/v7Db26nc2To1AX8QqNt2QW1RSo0+SFHYTgzwKFXbCyWXRdx7QWBnrW5omGER8rOVICk55dPM0kING0225pdiy8eamCXO1B42v/jAWaYSahOLW9jw3oSDjhqRQOKv1U4sJFxM+xl5uNY/QBlm56owdpZZTzBI0TCpWhvj7R8Yja6dRmL+MON3bxa4I/+t6KY3OgkzqJCXUohhEUmE5yAojcwbIhtIgES82RyY1E9xwIjSScSHyMM2h1HIe3uL1y8Y/aZ233GsXqnAAh3AMHpzCBVxBG3wQMIZneIFX59F5c95/wFWcOcF9+CPn4xsla5DR</latexit> sha1_base64="Ddw71Mm9mCHfd4siUGamb469+MU=">AAAB9HicbVC7TsNAEDzzDOEVoKQ5ESFRRTYNIFFEoqEMApNIiRWtL5twyvmhuzUQWfkEWqioEC3/Q8G/YBsXkDDVaGZXOzt+rKQh2/60FhaXlldWK2vV9Y3Nre3azu6tiRIt0BWRinTHB4NKhuiSJIWdWCMEvsK2P77I/fY9aiOj8IYmMXoBjEI5lAIok64f+7Jfq9sNuwCfJ05J6qxEq1/76g0ikQQYklBgTNexY/JS0CSFwmm1lxiMQYxhhN2MhhCg8dIi6pQfJgYo4jFqLhUvRPy9kUJgzCTws8kA6M7Mern4n9dNaHjqpTKME8JQ5IdIKiwOGaFl1gHygdRIBHly5DLkAjQQoZYchMjEJCulmvXhzH4/T9zjxlnDvrLrzfOymArbZwfsiDnshDXZJWsxlwk2Yk/smb1YD9ar9Wa9/4wuWOXOHvsD6+Mbb22SJg==</latexit>. <latexit sha1_base64="ucSjmCXhNNWFdW/+kw3iz7dOgcw=">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</latexit>. log(µi ) = log(µpop ) + xi + ⌘i ,. ⌘i ⇠ N (0, ! 2 ). fl(t, V ) ≥ e⁄0 t (V ) REFERENCES. Z +Œ V0. CONCLUSIONS. fl(t, V )dV. Z +Œ . V fl(t,Munoz, V )dV W. R., [1] Ebos, J. M. L., Mastri, M., Lee, C. R., Tracz, A., Hudson, J. M., Attwood, K., CruzV0 Jedeszko, C., Burns, P., and Kerbel, R. S. (2014). Neoadjuvant antiangiogenic therapy reveals contrasts in j j j j Yi = M (ti , — ) + Ei primary and metastatic tumor efficacy. EMBO Mol Med, 6(12):1561–1576. These results confirm a differential effect of sunitinib on primary (localized) tumors compared to secondary (metastatic) disease. Our results suggest that Ki67+/CD31+, CTCs and MDSCs measurements might help in personalized prediction of j j 1 N p p◊p metastatic potential and thus aid in predicting benefit in overall survival for preoperative = M (tji ,D., — j )and + EEbos, , — , . . . , — ≥ N (µ, Ê), µ œ R , Ê œ R [2] Benzekry, S., Tracz, A., Mastri, M., Corbelli, R.,YiBarbolosi, J. M. L. (2016). Modeling i spontaneous metastasis following surgery: an in vivo-in silico approach. Cancer Res, 76(3):535–547. antiangiogenic treatments. Ç. Z. å.
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