Benzekry, Sébastien

INRIA a CCSD electronic archive server

HAL Id: hal-02424452https://hal.inria.fr/hal-02424452v2Submitted on 27 Dec 2019HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Data-driven mechanistic modeling of metastasis: cancerat the organism scaleSébastien BenzekryTo cite this version:Sébastien Benzekry. Data-driven mechanistic modeling of metastasis: cancer at the organism scale.RITS conference (Recherche en Imagerie et Technologies pour la Sante) of the French Society ofBiomedical Engineering (SFGBM), May 2019, Tours, France. ￿hal-02424452v2￿MONCModeling in ONCologyInria Bordeaux Sud-Ouest 21 mai 2019Data-driven mechanistic modeling of metastasis: cancer at the organism scaleS. Benzekry• Breast• 94% of cases are local or regional at diagnosis but 30% will relapse Pollard, N Eng J Med, 2016• Estimate the amount of residual distant disease at diagnosis in order to personalize the adjuvant (chemo)-therapy  • Avoid unnecessary, heavy toxicities • Lung • 57% of cases are metastatic • Decide whether to use whole brain radiation therapy or just (stereotactic) surgery • Avoid cognitive impairment of the patientSteeg, Nat. Rev. Cancer, 2016• Metastases are the main cause of death (>90%) from solid cancers Lambert and Weinberg, Cell, 2017Institut Bergonié, BordeauxMetastasis (µ!"# = beyond, $"#$%& = place)!"#$%&'()'# *+,"-.+/.*")%()%)'# ,'(("*'&%)'+& %&,.01+2)$Growth rates of primary andsecondary tumors gp and gDissemination rate d(Vp) = !VpSize distribution of the metastases "(t,v)!"#$%#$#&' ()*+", -#.#$/ ,)0("* .1 0"#$%#$#&' '"//%2-3.04"*#52_[Y_]_[∂tρ(t, v) + ∂v(g(v)ρ(t, v)) = 0g(V0)ρ(t, V0) = d(Vp(t))ρ(0, v) = ρ0M(t) =⁄+∞V0vρ(t, v)dv =⁄ t0d (Vp(t − s)) V (s)ds67$#$ "#8$/9:8;8<=".* >&./:8?@@@dVpdt= (αp − βp ln(Vp)) Vpg(v) = (α − β ln(v)) vIwata, Kawasaki, Shigesada, J Theor Biol, 2000!"#$%"&$'()'()"($*"#)%"&"Time (days)0 10 20 30 40 50 60 70Primary tumor size (cells)1041061081010Metastatic burden (cells)1041061081010OrthotopicimplantationSurgery(t=34)Pre-surgicalPTPost-surgicalMBTime (days)0 10 20 30 40 50 60 70Primary tumor size (cell)105106107108109Metastatic burden (cell)105106107108109OrthotopicimplantationSurgery(t=34)Pre-surgicalPTPost-surgicalMBTime (days)0 10 20 30 40 50 60 70Primary tumor size (cell)105106107108109Metastatic burden (cell)105106107108109OrthotopicimplantationSurgery(t=34)Pre-surgicalPTPost-surgicalMBTime (days)0 10 20 30 40 50 60 70Primary tumor size (cell)105106107108109Metastatic burden (cell)105106107108109OrthotopicimplantationSurgery(t=34)Pre-surgicalPTPost-surgicalMBData primary tumorMedian model primary tumor10th and 90th percentiles model primary tumorData metastatic burdenMedian model metastatic burden10th and 90th percentiles model metastatic burden!"#$%#&'( *$+,%-,..,/&0)*'*%)*%+'$ ,"-&$./"(.%#*&(0'#%,'$.1'(%'2%$%*3θi = θpop + ηi, ηi ∼ N (0, ω2)4&#5&6(3 &*.'$7.892"):;.<'#+&(.=&);.>?@A! 0"*,)12'3&4 /"(.BC.'#-.,&*)D.!" #$!% &" #$&92") $'2=")E&$$.B'(6.<'#+&(.F#)*%*G*&Benzekry et al. (Ebos), Cancer Res, 2016Current work: implementing the mechanistic model into a statistical learning model• Use the model for predictions of time-to-relapse (TTR)SurgeryFirst cellCerebral MetastasesPrimary Tumor (PT)Dissemination law: d(Vp)=PT growth law: gp Metastases growth law: g Pre-diagnosis Post-diagnosis!(Vp)"ModeldVpdt= (αp − βp ln(Vp)) Vp∂tρ(t, v) + ∂v ((α − β ln(v)) vρ(t, v)) = 0g(V0)ρ(t, V0) = µVp(t)γρ(0, v) = 0Clinical database biomarkers at diagnosisBergonié Institute, Bordeaux!!"! "##!$ptumor size clinical 0.00165tumor size histological 0.4grade 0.358histology 0.0041TNM T 0.146TNM N 0.599nb invaded ganglions 0.619menopausal status 0.000471ER 0.543PR 0.34Ki67 3.09e-05HER2 0.17HER2 intensity 0.482CK56 0.793EGFR 0.016VIM 0.226ALDH1 0.674CD24 0.894CD44 0.397E cadherin 0.207TRIO 0.0646BCL2 0.727age at diagnosis 0.0599diagnosis year 0.101radio 0.276!!"! "##!$!!"! "##!$AUROC Accuracy NPV PPVRandom forest 0.727 87 91.7 22.5Logistic regression 0.772 90.1 91 25Cox regression 0.728 87.4 91.1 16.7Bio-based 0.641 89.7 91.3 31.2AUROC = Area Under the ROC curve, NPV = Negative Predictive ValuePPV = Positive Predictive ValueNicolò et al., in preparation, 2019TTRi = infÓt > 0; Nvis1t, θi2> 1Ôxi• Implement clinical variables and biomarkers as biologically meaningful covariatesFeatures selection based on Cox regressionSurgeryFirst cellCerebral MetastasesPrimary Tumor (PT)Dissemination law: d(Vp)=PT growth law: gp Metastases growth law: g Pre-diagnosis Post-diagnosis!( p)"PredictionGood signaturePoor signatureP<0.0010.00.20.40.60.81.0120 2 4 6 8 10YearsOverall SurvivalRVolume (cells)10010510101015Number of mets051015202530Imaging detection limitPrognosisSimulation and individualization of therapylDiagnosisdVpdt= (αp − βp ln(Vp)) Vp∂tρ(t, v) + ∂v ((α − β ln(v)) vρ(t, v)) = 0g(V0)ρ(t, V0) = µVp(t)γρ(0, v) = 0li i l t  i r r  t i iln1µi2= ln (µpop) + βTµ xiµ + ηiµ, ηiµ ∼ N (0, ω2µ)ln1αi2= ln (αpop) + βTαxiα+ ηiα, ηiα∼ N (0, ω2α)!"#$%&'!"#$%$&'('%"')(*&$(')"+,"(-'"&'.-$/*)(*."&+0'12"344%'5*$(*+/!"%2)2'26"%'1$(*5'")($/0$%0"'%%+%!"#$%&()&#$%$&'('%"')(*&$(')"+,"(-'",*/$1"&+0'1"7*(-".+5$%*$(')2"8$%$&'('%)"7'%'"+4($*/'0"49"Data of a NSCLC patient with brain metsInstitut Bergonié, Bordeaux, FRPrimary tumor sizeBrain CT scanMetastases sizeMonths post-diagnosis0 10 20 30 40 50Nb of visible mets02468101214161820Number of visible metsLung CTMonths post-diagnosis0 10 20 30 40 50Primary tumor diameter (mm)051015202530354045TK I CT1 mTK I CT2TGI fi tDataMonths post-diagnosis0 10 20 30 40 50Metastases diameter (mm)051015202530354045DataGompertz growth predictionDiagnosisFirst cancer cellBrain MetastasesPrimary TumorSecondary dissemination?Growth law: gp(Vp)=Vp(!p-"pln(Vp)) Growth law: g(V)=V(!-"ln(V))  Dissemination law: d(Vp)= #(Vp) $Delay?Dormancy?treatmentSame growth?The model with dormancy could describe best the dataMonths post-diag-20 0 20 40 60Nb of visible mets0510152025ModelDataFrom “best fit”15 20 25 30 35 40 45 50Months post-diagnosis01020304050Met diameter (mm)Bilous et al. (Benzekry), biorXiv, 2018Model Patient 1 Patient 2Base 5.51 2.53Secondary 5.43 2.3Delay 5.23 1.53Dormancy 4.93 1.71Diff. growth 4.95 1.79Objective functionDormancy estimated to 133 days ± 4.2%2 Combination bevacizumab - chemotherapy• Bevacizumab = anti-VEGF monoclonal antibody ⇒ anti-angiogenic action (first approved in 2004) • Only proved clinical efficacy when combined (concomitantly) with cytotoxicsVascular normalization: a time window  for improved pharmacokinetics?b daJain, Nat Med, 2001Vakoc et al., Jain, 2009, Nat MedTherapeutic question What is the optimal time gap between administration of bevacizumab and cytotoxic chemotherapy? How to capture inter-individual variability for designing personalized therapies?• Possible explanation: transient normalization of the otherwise abnormal (leaky, tortuous)  vascular architecture Lung cancer modelHypothesis: sequential use of bevacizumab associated with chemotherapy would achieve better efficacy and modeling support could help to define the optimal time-windowCurrent beva-chemo regimen are underpoweredExperimental therapeuticsBreast cancer modelMollard et al. (Benzekry), Oncotarget 2017Experiment 1Experiment 2Modeling and SimulationCalibrationPredictionImbs et al. (Benzekry), CPT: Pharmacometrics Syst Pharmacol, 2017Prolif. CellsVZ1 Z2 Z3Vasc. QualityQBevacizumabACytotoxicsCCell deathDamaged cellsα, β!δ"k kSemi-mechanistic mathematical model + PK models for beva A(t) and CT C(t) concentrationsSimeoni et al., Rocchetti, Cancer Res, 2004 Benzekry et al., CRAS, 2012 Mollard et al., Benzekry, Oncotarget, 2017 Imbs et al., Benzekry, CPT: Pharmacometrics Syst Pharmacol, 2018����= � − � ln��7� − ���� � � = 0 = �E� � = 	1 + �� � − ���)��= ���� − ��) �) � = 0 = 0��G��= � �) − �G 	 �G � = 0 = 0��H��= � �G − �H �H � = 0 = 0� = � + �) + �G + �H	 �E0 20 40 60 80Days00.0050.010.015Chemotherapy concentration (mg/g)00.050.10.150.2Bevacizumab concentration (mg/ml)ConcentrationPemCisBevaModel fits: individual + population level (NLME)SimultaneousTime (days)0 20 40 60 80Bioluminescence (p/s)1081010BevaChemoSequential B/CTime (days)0 20 40 60 80Bioluminescence (p/s)1081010BevaChemoControlTime (days)0 20 40 60 80Bioluminescence (p/s)1081010Sequential C/BTime (days)0 20 40 60 80Bioluminescence (p/s)1081010BevaChemoTime (days)0 10 20 30 40 50 60 70Bioluminescence (p/s)×10100123456BevaChemoBevaChemoBevaChemoMedian growth curvesImbs et al., Benzekry, CPT: Pharmacometrics and Systems Pharmacology, 2017Days0 10 20 30 40 50Bioluminescence (p/s)×109024681012141618Days0 10 20 30 40 50 60 70Bioluminescence (p/s)×109012345678BevaChimioDays0 10 20 30 40 50 60 70Bioluminescence (p/s)×10900.511.522.533.544.5BevaChimioDays0 10 20 30 40 50 60 70Bioluminescence (p/s)×10900.511.522.533.544.5BevaChimio) (Prediction of the optimal delay⇒ to be tested experimentallyGap (days)0 2 4 6 8 10AUC×10112.533.544.555.56Days0 20 40 60 80Bioluminescence (p/s)×101000.511.522.533 days 8 daysVSInter-animal variability of the optimal gapDays012345678910Imbs et al., Benzekry, 2017, CPT: Pharmacometrics and Systems Pharmacology⇒ personalized schedulingTime (days)0 10 20 30 40 50 60 70 80 90Fluorescence (p/s)0200040006000800010000120001400016000180008 days3 daysAcknowledgements !J. Ebos !M. Mastri• Preclinical data of ortho-surgical animal models of metastasesRoswell Park Cancer Institute, Buffalo, NY, USA!A. TraczBiology Clinic!F. Barlesi• Brain metastasis from lung tumors!"#$%"#&'(!"#!"#$%%&'()*)+&,-%./&"')01.'2%./&"'.%34$'56)7"189"15$)01.'2%./&"'.%34$#2&#$)–):-'();.'5$1)AP-HM, Marseille, FR!F. Chomy Bergonié Institute, Bordeaux, FRModeling!"#$%"#&'(Pr. D. Barbolosi !"#!"#$%%&'()*)+&,-%./&"')01.'2%./&"'.%34$'56)7"189"15$)01.'2%./&"'.%34$#2&#$)–):-'();.'5$1)!D. Barbolosi!C. Nicolò!X. Muracciole• Beva + cytotoxics study!"#$%"#&'(!"#!"#$%%&'()*)+&,-%./&"')01.'2%./&"'.%34$'56)7"189"15$)01.'2%./&"'.%34$#2&#$)–):-'();.'5$1)Dr. J. Ciccolini Thanks for listening!We are looking for postdocs!sebastien.benzekry@inria.fr

Data-driven mechanistic modeling of metastasis: cancer at the organism scale

https://hal.inria.fr/hal-02424452/document

Data-driven mechanistic modeling of metastasis: cancer at the organism scale

Abstract

Similar works

Full text

Available Versions

INRIA a CCSD electronic archive server