Fanny Gallais

Loïc Ysebaert
email: ysebaert.loic@iuct-oncopole.fr

Fabien Despas

Sandra De Barros

Loïc Dupré

Anne Quillet-Mary

Caroline Protin

Fabienne Thomas

Lucie Obéric

Ben Allal

Etienne Chatelut

Mélanie White-Koning

Population Pharmacokinetics of Ibrutinib and Its Dihydrodiol Metabolite in Patients with Lymphoid Malignancies

Background and Objective

Ibrutinib is used for the treatment of chronic lymphocytic leukemia and other lymphoid malignancies. The aim of this work is to develop a population pharmacokinetic model for ibrutinib and its dihydrodiol metabolite to quantify pharmacokinetic inter-and intra-individual variability, to evaluate the impact of several covariates on ibrutinib pharmacokinetic parameters, and to examine the relationship between exposure and clinical outcome. Methods Patients treated with ibrutinib were included in the study and followed up for 2 years. Pharmacokinetic blood samples were taken from months 1 to 12 after inclusion. Ibrutinib and dihydrodiol-ibrutinib concentrations were assessed using ultra-performance liquid chromatography tandem mass spectrometry. A population pharmacokinetic model was developed using NONMEM version 7.4. Results A total of 89 patients and 1501 plasma concentrations were included in the pharmacokinetic analysis. The best model consisted in two compartments for each molecule. Absorption was described by a sequential zero first-order process and a lag time. Ibrutinib was either metabolised into dihydrodiol-ibrutinib or excreted through other elimination routes. A link between the dosing compartment and the dihydrodiol-ibrutinib central compartment was added to assess for high firstpass hepatic metabolism. Ibrutinib clearance had 67% and 47% inter-and intra-individual variability, respectively, while dihydrodiol-ibrutinib clearance had 51% and 26% inter-and intra-individual variability, respectively. Observed ibrutinib exposure is significantly higher in patients carrying one copy of the cytochrome P450 3A4*22 variant (1167 ng.h/mL vs 743 ng.h/mL, respectively, p = 0.024). However, no covariates with a clinically relevant effect on ibrutinib or dihydrodiolibrutinib exposure were identified in the PK model. An external evaluation of the model was performed. Clinical outcome was expressed as the continuation or discontinuation of ibrutinib therapy 1 year after treatment initiation. Patients who had treatment discontinuation because of toxicity had significantly higher ibrutinib area under the curve (p = 0.047). No association was found between cessation of therapy due to disease progression and ibrutinib area under the curve in patients with chronic lymphocytic leukemia. For the seven patients with mantle cell lymphoma studied, an association trend was observed between disease progression and low exposure to ibrutinib. Conclusions We present the first population pharmacokinetic model describing ibrutinib and dihydrodiol-ibrutinib concentrations simultaneously. Large inter-individual variability and substantial intra-individual variability were estimated and could not be explained by any covariate. Higher plasma exposure to ibrutinib is associated with cessation of therapy due to the occurrence of adverse events within the first year of treatment. The association between disease progression and ibrutinib exposure in patients with mantle cell lymphoma should be further investigated. Trial Registration ClinicalTrials.gov no. NCT02824159.

Introduction

Ibrutinib (Imbruvica ® ) is a targeted therapy first approved by the US Food and Drug Administration in 2013. It is now used for the treatment of various B-cell malignancies such as chronic lymphocytic leukemia (CLL), mantle cell lymphoma (MCL) and Waldenström's macroglobulinemia

Key Points

For the first time, a population pharmacokinetic model for ibrutinib and its dihydrodiol metabolite in a real-life population of patients was developed.

The final model was complex, linear and showed large inter-and intra-individual variability.

Higher plasma exposure to ibrutinib was associated with cessation of ibrutinib therapy for toxicity within the first year of treatment.

phase II clinical studies, but did not include data pertaining to metabolites. The objective of our work is to develop a new popPK model considering ibrutinib and its metabolite simultaneously based on real-life patient population data. The aim of this model is to describe the concentrations of both molecules, to quantify pharmacokinetic (PK) inter-and intra-individual variability, to evaluate the impact of several covariates on ibrutinib PK parameters in a population of patients treated with ibrutinib, to analyse the relationship between exposure to ibrutinib and response to treatment, and to discuss the potential benefit of TDM for ibrutinib.

Methods

Study Population

The subjects in this analysis include those in the ibrutinib cohort of the PK-E3i study, which was initiated within the hematology department of IUCT-Oncopole hospital (Toulouse, France) in 2016. PK-E3i is an observational PKpharmacodynamic (PD) study approved by the competent authority (ANSM, under No. 151668A-11) and the ethics committee (under No. CPP16-004a), registered by Clinical-Trials.gov under No. NCT02824159 and carried out by the university hospital of Toulouse. Patients treated by ibrutinib for CLL, MCL or WM were recruited from 2016 to 2018 and followed up for 2 years. All patients gave their written informed consent. Seven hospital visits were planned at months 1, 2, 3, 6, 12, 18 and 24 after inclusion (M1-M24 visits). Pharmacokinetic blood sampling was performed from M1 to M12. Ibrutinib was taken orally once daily at a starting dose of 420 mg (CLL, MW) or 560 mg (MCL). Because of the occurrence of adverse drug reactions, some patients subsequently had their dose reduced.

Data Collection

Rich PK blood sampling was performed at steady state during the M1 visit. A total of six blood samples were taken at t = 0 h (before drug administration) and 0.5, 1, 2, 4 and 6 h after administration. Single PK blood samples were collected at M2-M12 as before drug intake, to assess for trough concentrations. Samples were collected in heparinised lithium tubes of 5 mL. The tubes were centrifuged (1400 × g, room temperature, 10 minutes) and plasma was collected and frozen at -20 °C until analysis. An ultra-performance liquid chromatography in tandem with a mass spectrometer (Waters, St Quentin en Yvelines, France) was used for method development and validation in our laboratory. The method was built for a robust simultaneous quantification of a panel of tyrosine kinase inhibitors including ibrutinib and DHD-ibrutinib. The lower limit of quantification was (WM) [START_REF] Smith | Ibrutinib in B lymphoid malignancies[END_REF]. Ibrutinib was developed as a selective and irreversible inhibitor of the Bruton tyrosine kinase (BTK) [START_REF] Honigberg | The Bruton tyrosine kinase inhibitor PCI-32765 blocks B-cell activation and is efficacious in models of autoimmune disease and B-cell malignancy[END_REF], a non-receptor protein kinase that plays a central role in the B-cell antigen receptor (BCR) pathway. The BCR signaling pathway is crucial for the development and survival of B cells as it is involved in the regulation of their proliferation, differentiation, migration and apoptosis [START_REF] Niiro | Regulation of B-cell fate by antigen-receptor signals[END_REF]. The BCR has been shown to be involved in various B-cell malignancies [START_REF] Woyach | The B-cell receptor signaling pathway as a therapeutic target in CLL[END_REF] and given the essential role of BTK in this pathway, it has been investigated as a target for the treatment of these diseases [START_REF] Byrd | Targeting BTK with ibrutinib in relapsed chronic lymphocytic leukemia[END_REF]. Ibrutinib binds covalently to BTK cysteine-481 amino acid, leading to the irreversible inhibition of BTK phosphorylation and enzymatic activity, and therefore alters the BCR signaling cascade. The inhibition of BTK activity by ibrutinib is associated with several anti-leukemic effects on the lymphocytes including inhibition of proliferation, egress from lymph nodes (tumoral niches), inhibition of rehoming to niches, and death in blood and niches [START_REF] Ponader | The Bruton tyrosine kinase inhibitor PCI-32765 thwarts chronic lymphocytic leukemia cell survival and tissue homing in vitro and in vivo[END_REF][START_REF] De Rooij | The clinically active BTK inhibitor PCI-32765 targets B-cell receptor-and chemokine-controlled adhesion and migration in chronic lymphocytic leukemia[END_REF].

This work focuses on the study of ibrutinib pharmacokinetics. Ibrutinib is an oral drug administered once a day. The standard posology is 420 mg for CLL and WM and 560 mg for MCL. Ibrutinib is predominantly metabolised in the liver by the cytochrome P450 (CYP) 3A family members CYP3A4 and CYP3A5 [START_REF] Scheers | Absorption, metabolism, and excretion of oral 14 C radiolabeled ibrutinib: an open-label, phase I, single-dose study in healthy men[END_REF]. Its oral bioavailability is very poor (F = 2.9%; 90% confidence interval 2.1-3.9) owing to high first-pass hepatic metabolism [START_REF] Scheers | Absorption, metabolism, and excretion of oral 14 C radiolabeled ibrutinib: an open-label, phase I, single-dose study in healthy men[END_REF][START_REF] De Jong | Effect of CYP3A perpetrators on ibrutinib exposure in healthy participants[END_REF]. One of its active metabolites, dihydrodiol-ibrutinib (DHD-ibrutinib), is about 15 times less active than ibrutinib [START_REF]Committee for Medicinal Products for Human Use (CHMP)[END_REF] but exhibits lower plasma protein binding (91% binding compared with 97% for ibrutinib) and has concentrations up to twice those of ibrutinib. No specific clinical activity or particular toxicity related to DHD-ibrutinib is known.

The pharmacokinetics of ibrutinib is highly variable in patients. If a relationship between drug exposure and toxicity or efficacy exists, therapeutic drug monitoring (TDM) would be beneficial for patients treated with ibrutinib. A first population pharmacokinetic (popPK) model for ibrutinib was proposed by Marostica et al. [11]. This model was built based on the data collected in three phase I and 0.98 ng/mL for both molecules. One saliva sample was collected for CYP3A4 and CYP3A5 genotyping at inclusion using a commercial kit (GeneFiX™ Saliva-Prep DNA Isolation kit). Based on previous work [START_REF] Elens | CYP3A4*22: promising newly identified CYP3A4 variant allele for personalizing pharmacotherapy[END_REF][START_REF] Lee | Functionally defective or altered CYP3A4 and CYP3A5 single nucleotide polymorphisms and their detection with genotyping tests[END_REF], we focused our interest on CYP3A4*22 and CYP3A5*3, which are the main clinically relevant alleles of CYP3A4 and CYP3A5 associated with altered drug metabolism. The presence of CYP3A5*1/CYP3A5*3 alleles was determined on genomic DNA with allele-specific real-time polymerase chain reaction using melt curve analysis as previously described [START_REF] Yates | The effect of CYP3A5 and MDR1 polymorphic expression on cyclosporine oral disposition in renal transplant patients[END_REF]. The CYP3A4*22 allele was genotyped using allelic discrimination with TaqMan assay (c_59013445_10) following the manufacturer's instructions.

Population-Pharmacokinetic Modelling

General Modelling Strategy

First, a popPK model for ibrutinib only was built. The structural model obtained for ibrutinib was then used to build a more complex model including the metabolite observations. Different methods of taking first-pass hepatic metabolism into account in the model were assessed. Inter-occasion variability was tested on all PK parameters considering one occasion for each hospital visit. Non-zero covariance terms were added in the OMEGA matrix to assess for correlations between ibrutinib and DHD-ibrutinib PK parameters. To ensure model stability, the covariate analysis was performed on the model with a diagonal OMEGA matrix. The final model was externally evaluated on an independent population of patients. Model development was performed with NONMEM version 7.4.1 (ICON Development Solutions, Ellicott City, MD, USA) using first-order conditional estimation with an interaction estimation method. Data management and graphical analyses were performed in R version 3.4.2.

Covariate Analysis

Morphological, biological and clinical covariates were selected from PK-E3i patient case report forms. Continuous covariates were added to the model in an allometric manner. Categorical covariates were added to the model in a multiplicative form. To assess for statistical significance of covariate effects, we performed a univariate analysis where all covariates were tested separately on the main PK parameters of interest: ibrutinib and DHD-ibrutinib elimination clearances ( CL ibru , CL DHD ), first-pass hepatic metabolism constant ( KA DHD ) and ibrutinib to DHD-ibrutinib metabolism clear- ance ( CL met ). Covariates were tested simultaneously on the last two parameters (one COV estimation for both parameters) because it was assumed that they described the same physiological process (hepatic metabolism). Covariates associated with a decrease of objective function value (OFV) greater than 3.84 (Chi-squared test, df = 1, p ≤ 0.05) and a decrease of interindividual variability greater than 1% were included in a multivariate model. Then covariates were removed one by one. Covariates associated with an increase of OFV greater than 6.6 (Chi-squared test, df = 1, p = 0.01) were kept in the model, others were definitively removed. This process was continued until only statistically significant covariates remained in the model. Multiple testing was accounted for by choosing low significance levels at each step of the covariate analysis (5% and 1% at the univariate and multivariable steps, respectively).

If a covariate (c) was missing at a visit (v) for patient i , the missing value was replaced by the value of c at the previous visit ( v -1 ). If no value was available at the previous visit, the missing value was replaced by the population median of c at visit v.

Model Evaluation

Model selection and evaluation was based on OFV value, goodness-of-fit plots, residual variability estimates, relative standard errors, stability of the estimates and shrinkage values. The model was externally evaluated on a second population that was independent from the model development population but similar to it. The second population consisted of 28 patients receiving treatment at the IUCT-Oncopole Hospital Hematology Department between 2014 and 2016. At the request of the prescribing clinician and to carefully monitor treatment, PK data were routinely collected at each hospital visit. Patient blood samples were collected for one PK exploration at steady state before drug administration and 0.5, 1, 2, 4 and 6 h after administration.

To perform the external evaluation of our model, all parameters were fixed to their estimated value and the NONMEM option MAXEVAL = 0 in the $ESTIMATION section was used. Median prediction error (%) [bias] and median absolute prediction error (%) [inaccuracy] were calculated. The prediction error (PE) is defined as

PE = C pred -C obs C obs
× 100 where C pred is the predicted concen- tration and C obs is the observed concentration [15]. In addition, we calculated the percentage of absolute PEs inferior to 20% and 30% ( F 20 and F 30 , respectively). Vis- ual predictive checks were also used to assess for predictive performance of the model.

Pharmacokinetic-Pharmacodynamic Evaluation

The PK-E3i study is currently on-going with some of the patients still being monitored. As a preliminary PK-PD analysis, the relationship between pharmacokinetics and continuation of ibrutinib therapy 1 year after treatment initiation was explored. We looked at the association between ibrutinib area under the curve (AUC) and clearance at the M1 visit and whether the patients had their treatment discontinued because of toxicity or a lack of efficacy or if it was continued 1 year after inclusion.

Results

A total of 93 patients were included in the study. Four were withdrawn from the study before the M1 visit and therefore unable to perform a plasma drug determination because of refusal to participate (n = 1), disease progression (n = 2) or death (n = 1). Therefore, a total of 89 patients and 1501 concentrations (including ibrutinib and DHD-ibrutinib) were used in the model development. Of these, 27 (30%) were women and 62 (70%) were men, with a mean age of 69 years (range: 31-84 years). Patients were treated for CLL (87%), MCL (11%) or WM (2%). Detailed information about patients' characteristics can be found in Table 1. Drug concentrations under the lower limit of quantification (4%) were considered equal to the lower limit of quantification/2 = 0.49 ng/mL. Concentrations over time profiles according to the dose received are represented in Fig. 1. Although variability is very important, Fig. 1 shows that plasmatic ibrutinib and DHD-ibrutinib concentrations increase as the dose is increased.

Step 1: Ibrutinib Population-Pharmacokinetic Model

First, a popPK model was built for ibrutinib. A model with two compartments was found to best describe the data. Several absorption models were tested. The best absorption model was a sequential zero-first absorption with a lag time. Bioavailability was fixed to the value F1 = 3% [START_REF]Committee for Medicinal Products for Human Use (CHMP)[END_REF] and inter-individual variability was estimated on F1. This last step was found to improve the model performances significantly (drop in OFV over 100 points). A schematic of the final popPK model for ibrutinib is available in the Electronic Supplementary Material (ESM).

Step 2: Ibrutinib and Dihydrodiol-Ibrutinib Population-Pharmacokinetic Model

The global structure of the model obtained in step 1 was kept for ibrutinib. As demonstrated in step 1 by the need to add the bioavailability parameter F1 in the model, a crucial question was how to take into account first-pass hepatic metabolism in the model to obtain a good description of the observed data. Dihydrodiol-ibrutinib volumes of distribution were fixed as equal to those of ibrutinib as the metabolised fraction was unknown and hence the metabolite volume of distribution could not be estimated. Finally, the best model (Fig. 2) consisted of one dosing compartment, two compartments for both ibrutinib and DHD-ibrutinib. Absorption was described by a lag time ( ALAG1 ) and a sequential zero first- order process ( D1 , KA ibru ). Ibrutinib can be either metabo- lised into DHD-ibrutinib ( CL met ) or excreted through other routes of elimination ( CL ibru ). Dihydrodiol-ibrutinib is then eliminated ( CL DHD ). A link between the dosing compart- ment and the DHD-ibrutinib central compartment was added to assess for high first-pass hepatic metabolism ( KA DHD ). Non-zero covariance terms in the omega matrix were found to improve the model (the detailed OMEGA matrix can be found in the ESM). Proportional residual variability was estimated for ibrutinib ( ibru ) and DHD-ibrutinib ( DHD ).

Inter-occasion variability was estimated for both ibrutinib and DHD-ibrutinib elimination clearances.

Step 3: Covariate Analysis

All tested covariates are summarised in Table 1. A univariate analysis led to the selection of the following covariates: CD4 + T cells, prior treatment and performance status on CL ibru , CYP3A4*22 genotype on CL DHD , and body mass index on KA DHD and CL met , with CD4 + T-cell count and body mass index being time-varying covariates (the value for each visit was used in the analysis). These covariates were then included in the multivariate analysis. Finally, none of the tested covariates had a significant statistical impact in the model (p = 0.01). Ibrutinib and DHD-ibrutinib AUC were simulated for virtual patients with each covariate varying from its 10th to its 90th percentile (while all other covariates were fixed to their typical value) [START_REF] Baverel | Population pharmacokinetics of durvalumab in cancer patients and association with longitudinal biomarkers of disease status[END_REF]. Ibrutinib AUC was calculated using model parameters as follows:

whereas DHD-ibrutinib AUC was calculated using the trapezoidal method with the population concentrations predicted by the model. Results are summarised in Fig. 3. None of the tested covariates led to a change of AUC greater than 30% except for the CYP3A4 genotype on CL DHD , which led to a 38% increase of DHD-ibrutinib AUC. Regarding this last result, the relationship between observed ibrutinib and DHD-ibrutinib AUC and CYP3A4/5 genotypes was evaluated: patients carrying the CYP3A4*22 variant associated with lower metabolic activity had mean observed ibrutinib and DHD-ibrutinib AUC 1.6-fold higher (1167 ng.h/ mL vs 743 ng.h/mL) and 1.5-fold higher (2597 ng.h/mL vs 1777 ng.h/mL) than in the reference group, respectively.

AUC ibru = DOSE × KA ibru KA DHD +KA ibru CL met + CL ibru ,
These associations were statistically significant (Wilcoxon test: p = 0.024 for ibrutinib and p = 0.028 for DHD-ibrutinib). No significant association was found for CYP3A5*3.

Concerning the potential dose-concentration relationship, no systematical decrease or increase of clearance values over time was observed. Percentage of clearance variation compared to occasion 1 was randomly distributed with a median close to 0% for both molecules. Final model parameter estimations are presented in Table 2. Goodness-of-fit plots are shown in Fig. 4.

Step 4: External Evaluation of the Model

The model represented in Fig. 2 was externally evaluated. A total of 28 additional patients and 352 concentrations were included in the analysis. This independent population was similar to the main population as it consisted of 11 (39%) women and 17 (61%) men, with a mean age of 69 years, treated with ibrutinib for CLL (86%) or MCL (14%). Median prediction error and median absolute prediction error were calculated with individual-and population-predicted concentrations for ibrutinib and DHD-ibrutinib (Fig. 5). According to individual model predictions, predictive performances are very satisfactory. Bias is less than 10% for ibrutinib and less than 5% for DHD-ibrutinib. Inaccuracy is less than 20% for ibrutinib and less than 15% for DHD-ibrutinib. Predictioncorrected visual predictive checks are good. For population predictions, bias values remain satisfactory (less than 10%) but predictions are not very accurate (around 50% and 40% imprecision for ibrutinib and DHD-ibrutinib respectively), only 23% of ibrutinib concentrations and 41% of DHD-ibrutinib concentrations are well predicted (PE < 30%).

Pharmacokinetic-Pharmacodynamic Relationship

A preliminary analysis of the ibrutinib PK-PD relationship was performed. One year after inclusion, 66 patients were still receiving therapy, eight discontinued their treatment for toxicity, 11 for inefficacy (disease progression) and four for other reasons (refusal to participate in the study, progression of other disease and death from other cause). Patients who discontinued therapy because of the occurrence of an adverse drug reaction had a 1.5-fold higher mean ibrutinib AUC at visit M1 than patients who did not discontinue treatment (Fig. 6) [Wilcoxon test, p = 0.048]. In terms of efficacy, patients with CLL and MCL were distinguished (the WM population was ignored as it contained only two patients).

In the CLL population, 62 patients were still receiving treatment at month 12, whereas six patients discontinued treatment because of disease progression. No difference was observed between the two groups in terms of exposure to ibrutinib at visit M1. In the MCL population, two patients were still receiving treatment at month 12, whereas five patients discontinued treatment because of disease progression. Patients with MCL who discontinued treatment had lower ibrutinib AUC (0.45-fold lower mean AUC) but this association was not statistically significant (Fig. 7).

Discussion

The popPK model we developed for ibrutinib is consistent with the model proposed by Marostica et al. [START_REF] Marostica | Population pharmacokinetic model of ibrutinib, a Bruton tyrosine kinase inhibitor, in patients with B cell malignancies[END_REF]. Several methods of modelling the first-pass hepatic effect were investigated. The reproduction of the model developed by Lindauer et al. for sunitinib [START_REF] Lindauer | Pharmacokinetic/pharmacodynamic modeling of biomarker response to sunitinib in healthy volunteers[END_REF] was not possible as no information was available concerning the ibrutinib fraction metabolised into DHD-ibrutinib. A model similar to that presented by Yu et al. [START_REF] Yu | Development of a pharmacokinetic model to describe the complex pharmacokinetics of pazopanib in cancer patients[END_REF] was also tested, with two dosing compartments, one representing ibrutinib and one representing the metabolite, and initialisation with part of the dose. ter Heine et al. proposed a model with a liver compartment and hypothesised rapid equilibrium between the liver and parent central compartment [START_REF] Ter Heine | Population pharmacokinetic modelling to assess the impact of CYP2D6 and CYP3A metabolic phenotypes on the pharmacokinetics of tamoxifen and endoxifen[END_REF]. These models were not selected because of the instability of parameter estimates and bad fit of the data. The model finally selected in our study was similar to that presented by Bertrand et al. [START_REF] Bertrand | Development of a complex parent-metabolite joint population pharmacokinetic model[END_REF] and Kerbusch et al. [START_REF] Kerbusch | Population pharmacokinetic modelling of darifenacin and its hydroxylated metabolite using pooled data, incorporating saturable first-pass metabolism, CYP2D6 genotype and formulation-dependent bioavailability[END_REF]. The simple addition of a link between Comparison of steadystate area under the curve (AUC) calculated from pharmacokinetic post-hoc parameters at hospital visit M1 between patients who discontinued ibrutinib within the first year of treatment because of the occurrence of an adverse event and patients who were still receiving therapy 1 year after inclusion. A statistically significant association was found: patients who underwent adverse events had higher ibrutinib AUC (p = 0.048) the dosing compartment and the metabolite central compartment was sufficient to describe the first-pass hepatic effect.

In their analysis, Marostica et al. showed a significant effect of food on bioavailability (decreased in the fasted condition) and on the absorption parameter D1 (increased in the fasted condition). These results could not be confirmed in our study as this covariate was not available for our population. The recommendation that ibrutinib should be taken 30 minutes before or 2 hours after food intake was explicitly given by the clinicians to the patients but there is no guarantee that they followed it, nor any data to assess it. Marostica et al. also found an effect of the coadministration of antacid drugs on D1 (increased in the presence of antacid comedications). This covariate was tested in our model but no statistically significant effect was found. However, in our study, the coadministration of antacids was only reported as "yes or no" the day of the hospital visit. As the time of antacid administration can vary, we may have missed a significant effect of antacid coadministration on ibrutinib concentrations. Furthermore, none of the tested covariates had a clinically relevant impact as none of them led to a change of AUC greater than 30% (except for the CYP3A4 genotype on CL DHD , which led to a 38% increase of DHD-ibrutinib AUC). Intra-individual variability was also quantified in the final model. The estimations were large, around 50% and 30% for ibrutinib and DHD-ibrutinib clearance of elimination, respectively. As mentioned above, this intra-individual variability could partly be explained by food conditions. The final model was externally evaluated (Fig. 5). The results of the evaluation proved that our structural model is accurate, as both molecule bias and inaccuracy in individual predictions were under 10% and 20%, respectively. Inaccuracy in population predictions (median absolute prediction error) was around 50% for ibrutinib and 40% for DHD-ibrutinib, which implies that covariate identification is still needed to account for the interindividual variability.

Ibrutinib is extensively metabolised in the liver by CYP3A4 and to a lesser extent by CYP3A5. It has been shown that exposure to ibrutinib is lower or higher when administered with CYP3A inducers or inhibitors, respectively [START_REF] De Jong | Effect of CYP3A perpetrators on ibrutinib exposure in healthy participants[END_REF]. Based on previous work [START_REF] Elens | CYP3A4*22: promising newly identified CYP3A4 variant allele for personalizing pharmacotherapy[END_REF], we focused our interest on CYP3A4*22 and CYP3A5*3. CYP3A4*22 is found in 5.3% of the Caucasian population and is associated with a lower metabolic activity than wild-type genotype CYP3A4*1/*1. The CYP3A5*3 variant is carried by 83% of the Caucasian population and is associated with a lower metabolism than the wild-type allele CYP3A5*1 [START_REF] Elens | CYP3A4*22: promising newly identified CYP3A4 variant allele for personalizing pharmacotherapy[END_REF][START_REF] Lee | Functionally defective or altered CYP3A4 and CYP3A5 single nucleotide polymorphisms and their detection with genotyping tests[END_REF]. We found that carrying the CYP3A5*3 variant had no effect on ibrutinib PK presence, which is in agreement with its low contribution to ibrutinib metabolism [START_REF] Scheers | Absorption, metabolism, and excretion of oral 14 C radiolabeled ibrutinib: an open-label, phase I, single-dose study in healthy men[END_REF] but could also be due to the low number of heterozygous patients (only five patients had the CYP3A5*1/CYP3A5*3 genotype). For CYP3A4, nine patients had the CYP3A4*1/CYP3A4*22 genotype. Ibrutinib observed AUC was significantly higher in patients carrying one copy of the CYP3A4*22 allele (p = 0.024) but CYP3A4*22 was not a significant covariate for ibrutinib clearance in our model. Higher DHDibrutinib observed AUC was also found in patients carrying Fig. 7 Comparison of steadystate area under the curve (AUC) calculated from pharmacokinetic post-hoc parameters at hospital visit M1 between patients who discontinued ibrutinib within the first year of treatment because of disease progression and patients who were still receiving therapy 1 year after inclusion. Patients were separated according to their disease (chronic lymphocytic leukemia [CLL] or Mantle cell lymphoma [MCL]). No statistically significant association was observed for either of the two groups. A trend of under-exposure in patients who had disease progression was observed for patients with MCL indicating that this association should be further explored CYP3A4*22 (p = 0.027). CYP3A4*22 was found to be a significant covariate impacting DHD-ibrutinib clearance in a univariate analysis and we showed through model simulations that the presence of CYP3A4*22 led to a 38% increase in DHD-ibrutinib steady-state AUC. These results suggest that DHD-ibrutinib is also metabolised through CYP3A4. This hypothesis was also mentioned in a previous study [START_REF]Committee for Medicinal Products for Human Use (CHMP)[END_REF]. Regarding these results, the association between ibrutinib, DHD-ibrutinib exposure and CYP3A4 genotype status should be further investigated in larger populations to determine whether this information should be taken into account when choosing ibrutinib dosing.

Previous studies showed a decrease of BTK levels over time under ibrutinib treatment [START_REF] Chen | BTK inhibition results in impaired CXCR4 chemokine receptor surface expression, signaling and function in chronic lymphocytic leukemia[END_REF][START_REF] Cervantes-Gomez | Decrease in total protein level of Bruton's tyrosine kinase during ibrutinib therapy in chronic lymphocytic leukemia lymphocytes[END_REF]. Based on this observation and on the assumption that a stoichiometry law describes ibrutinib efficacy, Chen et al. conducted a pilot study in 11 patients with CLL to test the impact of reducing the ibrutinib daily dose as treatment progresses [START_REF] Chen | A pilot study of lower doses of ibrutinib in patients with chronic lymphocytic leukemia[END_REF]. In their study, patients received three cycles of treatment from 420 mg/day (cycle 1), to 280 mg/day (cycle 2) and 140 mg/day (cycle 3). The authors observed globally similar plasmatic concentrations of ibrutinib and BTK occupancy during the three cycles, suggesting that reducing the dose of ibrutinib over time would have no impact on a patient's response to treatment. The same conclusion was reported in another study [START_REF] Mato | Comparable outcomes in chronic lymphocytic leukaemia (CLL) patients treated with reduced-dose ibrutinib: results from a multi-centre study[END_REF]. It is concordant with our results as we observed no trend between the progression group and the responding group, suggesting that the dose of 420 mg is above the required dose and that lowering it would not be associated with modification of the efficacy. Yet, while we do not question this conclusion, the assumption that a lower dose of ibrutinib will suffice to stoichiometrically inhibit BTK is in contradiction with our study and observed data. Such a phenomenon, which could be assimilated to the target-mediated drug disposition described for monoclonal antibody drugs, would be associated with a systematic decrease of ibrutinib clearance over time. In our population, no systematical decrease of clearance values over time was observed. Mean plasmatic ibrutinib and DHD-ibrutinib concentrations increased proportionally with the dose (Fig. 1). The model showed no evidence of a target-mediated drug disposition for ibrutinib and as described by the model equations, ibrutinib pharmacokinetics is linear and does not depend on the dose nor on time.

Finally, we explored the relationship between ibrutinib plasmatic exposure at the M1 visit and discontinuation of ibrutinib therapy 12 months after inclusion. This endpoint is an important surrogate as it has been shown that stopping ibrutinib treatment during the first year of therapy has a negative impact on overall survival and progression-free survival [START_REF] Follows | Outcomes of patients post ibrutinib treatment for relapsed/refractory CLL: a UK and Ireland analysis[END_REF]. Patients who had treatment discontinuation for toxicity had higher plasmatic ibrutinib exposure. This association was found to be statistically significant despite the substantial intra-individual variability. No trend was observed in the case of treatment discontinuation for disease progression in patients with CLL. A trend was visible for patients with MCL: patients having disease progression had lower exposure. This result is not statistically significant and is observed in a small number of patients, it should be further investigated. A complete and final PK-PD relationship analysis will be conducted when all patients complete their clinical monitoring. Our PK model could be used to improve adherence to ibrutinib by optimising dosing regimens, especially during the first year of treatment and consequently increase overall survival.

The results we present in this work are useful to assess the relevance of practicing TDM for ibrutinib. To date, no reference levels or TDM recommendations for ibrutinib have been published. Ibrutinib stability at ambient temperature within plasma samples makes TDM practically feasible. Additionally, the model could be used to estimate this daily AUC from a limited number of samples. On the one hand, ibrutinib shows high inter-individual variability and we found no covariate that could be assessed a priori to reduce this variability. Furthermore, higher ibrutinib AUC was found to be associated with the occurrence of adverse drug reactions. Therefore, TDM could be useful to predict which patients are at higher risk of drug-induced toxicity. On the other hand, intra-individual variability is high, which is not in favor of establishing TDM, but this variability could be reduced by better control of food conditions at the moment of drug intake. Regarding these results, the interest in establishing TDM for ibrutinib should be further investigated.

Conclusions

This popPK model based on both ibrutinib and DHDibrutinb concentrations fits the data well and was validated on an external population. No covariates with a clinically relevant effect on ibrutinib or DHD-inbrutinib exposure were identified. A significant association was found between treatment discontinuation for toxicity and exposure to ibrutinib. This PK-PD relationship concurs with the large interindividual PK variability of ibrutinib, and was observed despite substantial intra-individual variability. This finding represents a first rationale for TDM of ibrutinib, which the present PK model can help develop and thus improve patients' adherence to ibrutinib and increase response to treatment. Furthermore, this PK model can be used for PK-PD modelling describing lymphocyte dynamics under ibrutinib treatment.

Fig. 1

 1 Fig. 1 Observed concentrations of ibrutinib (a, b) and dihydrodiolibrutinib (c, d) according to dose. Figures (a) and (c) represent the data obtained with rich sampling (six samples from 0 to 6 hours after administration) at the M1 visit (1 month after inclusion and treatment

Fig. 2

 2 Fig. 2 Final population pharmacokinetic model for ibrutinib and its dihydrodiol (DHD) metabolite. Absorption is delayed with a lag time ( ALAG1 ) and is modelled by a zero first-order sequential process with parameters D1 and KA ibru for zero and first-order process, respectively. First-pass hepatic metabolism is modelled by a link between the dosing compartment and metabolite central compartment with parameter KA DHD . Both molecules have a distribution compart-

Fig. 4 Fig. 5 Fig. 6

 456 Fig. 4 Goodness-of-fit plots of the final population pharmacokinetic model for ibrutinib (a-c) and dihydrodiol (DHD)-ibrutinib (d-f). For observations vs individual predictions (a, d) and observations vs population predictions (b, e), the blue line is linear regression and the gray dotted line is the identity line. For prediction-corrected visual

Table 1

 1 Patient covariates at baseline (n = 89)

	Characteristics	Mean [range]	Characteristics	Mean [range]
	Age (years)	69 [31-84]	CD4 + T cells (/mm 3 )	1682 [1034-7571]
	Height (cm)	169 [146-189]	CD8 + T cells (/mm 3 )	1296 [66-6814]
	Weight (kg)	73 [40-113]	CrCL (mL/min)	64 [27-81]
	BMI (kg/m 2 )	25.5 [16.6-36.3]	Total bilirubin (µmol/L)	13 [4-228]
	BSA (m 2 )	1.8 [1.3-2.4]	GGT (g/L)	6.4 [1.2-28.0]
	Lymphocytes (g/L)	101.6 [0.3-430]	LDH (UI/L)	276 [108-892]
	Neutrophils (g/L)	4.3 [2.0-14.0]	ALT (UI/L)	30 [11-109]
	Platelets (g/L)	141.2 [7.0-343.0]	AST (UI/L)	26 [9-71]
	Hemoglobin (g/dL)	11.0 [3.6-16.0]
	Characteristics	Number (%)	Characteristics	Number (%)
	Sex		CYP3A4 genotype
	Female	27 (30)	*1/*1	80 (90)
	Male	62 (70)	*1/*22	9 (10)
	Disease
	CLL	77 (87)	CYP3A5 genotype
	MCL	10 (11)	*3/*3	84 (14)
	WM	2 (3)	*1/*3	5 (6)
	Prior treatment		Smoking
	Yes	70 (79)	Yes	18 (20)
	No	19 (21)	No	71 (80)
	Performance status		Alcohol consumption
	0	22 (25)	Yes	9 (10)
	1	51 (57)	No	80 (90)
	2	16 (18)
	Coadministration with antacids
	Yes	26 (29)
	No	63 (71)

ALT alanine aminotransferase, AST aspartate aminotransferase, BMI body mass index, BSA body surface area, CLL chronic lymphocytic leukemia, CrCL creatinine clearance, CYP cytochrome P450, GGT gamma globulins total, LDH lactate dehydrogenase, MCL mantle cell lymphoma, WM Waldenström's macroglobulinemia

  ). Dihydrodiol-ibrutinib is then eliminated ( CL DHD ). All clearance and volume parameters are apparent

	Fig. 3 Evaluation of the impact
	of significant covariates in a
	univariate analysis on ibruti-
	nib and dihydrodiol (DHD)-
	ibrutinib area under the curves
	(AUCs). The solid black vertical
	line is the AUC for a typical
	patient. Dotted black lines cor-
	respond to variations of AUC of
	20% and 30%. Blue horizontal
	bars represent a change in the
	AUC for the corresponding
	covariate varying from its 10th
	to its 90th percentile. Percent-
	age changes in AUCs are writ-
	ten in orange
	Table 2 Parameter estimates for the final ibrutinib and dihydrodiol-ibrutinib population	Parameters	Estimation (RSE)	Interindividual variability CV% (RSE) [shrinkage]	Inter-occasion variability CV% (RSE) [shrinkage]
	pharmacokinetic model	ALAG1(h)	0.238 (16%)	80.6% (16%) [16%]	NE
		D1(h)	0.989 (19%)	115.2% (16%) [12%]	NE
		KA ibru h -1	1.56 (18%)	NE	NE
		KA a DHD (h -1 )	1.21 (20%)	64.2% (24%) [4%]	NE
		CL a IBRU (L∕h)	242 (11%)	66.5% (24%) [2%]	46.7% (13%) [17%]
		V2 a (L)	1010 (9%)	81.8% (19%) [1%]	NE
		Q IBRU (L∕h)	171 (16%)	NE	NE
		V3 a (L)	1480 (9%)	76.9% (20%) [4%]	NE
		CL a MET (L∕h)	150 (19%)	64.4% (21%) [12%]	NE
		CL a DHD (L∕h)	181 (9%)	50.7% (12%) [0%]	25.7% (8%) [23%]
		Q DHD (L∕h)	50 (13%)	NE	NE
		Proportional residual variability CV% (RSE) [shrinkage]
		IBRU	37% (13%) [24%]
		DHD	25.7% (8%) [25%]
		Variance-covariance matrix is available in the ESM. Proportional residual variability was 37% for ibrutinib
		and 25.7% for DHD-ibrutinib. All clearance and volume parameters are apparent
		Interindividual variability was estimated for every parameter except KA ibru and inter-compartmental clear-
		ances. Inter-occasion variability was estimated for both elimination clearances. Non-zero covariance terms
		were estimated between D1 and ALAG1 , and between all parameters a

ALAG1 lag time for absorption, CL ibru and CL DHD ibrutinib's and DHD-ibrutinib's elimination clearances, CL met ibrutinib's clearance of metabolisation into DHD-ibrutinib, CV% percentage coefficient of variation, DHD dihydrodiol, D1 and KA ibru zero and first-order absorption parameters, KA DHD FPHM parameter, Q ibru and Q DHD are inter-compartmental clearance for ibrutinib and DHD-ibrutinib, RSE relative standard error, V2 and V3 are central and peripheral volumes of distribution for both molecules

Funding This study has been supported by the French National Drug Agency (ANSM), the French National Research Agency (ANR, project CAPTOR PHUC-001), and the AVIESAN, INCa and INSERM Plan Cancer program (project C15092BS).

Conflict of interest Loïc Ysebaert received grant support and honorarium fees from Roche, Abbvie, Gilead and Janssen, but not in the scope of the present study. Lucie Obéric received honorarium fees from Roche and Janssen, but not in the scope of the present study. Fanny Gallais, Fabien Despas, Sandra De Barros, Loïc Dupré, Anne Quillet-Mary, Caroline Protin, Fabienne Thomas, Ben Allal, Etienne Chatelut and Mélanie White-Koning have no conflicts of interest that are directly relevant to the content of this article.

Ethics Approval

The study was conducted in compliance with ethical standards.

Consent to Participate

All patients gave their written informed consent.


Clément Weinreich

Mathis Brunat

Mélissa Bruzat

Corentin Lucas

Jean-Marc Salotti
email: jean-marc.salotti@ensc.fr

Human Resilience to Giant Asteroid Impact

Keywords: giant steroid impact, giant comet impact, humanity extinction

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Numerous authors examined the consequences of asteroid impacts [START_REF] Collins | Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[END_REF][START_REF] Gritzner | The asteroid and comet impact hazard: risk assessment and mitigation options[END_REF][START_REF] Harris | Asteroid impacts and modern civilization: Can we prevent a catastrophe?[END_REF][START_REF] Toon | Environmental perturbations caused by the impacts of asteroids and comets[END_REF]. It is well known that if the energy of the impact is high enough, numerous plant and animal species may be in danger of extinction, humanity included. However, as humans may build shelters and use dedicated technologies to survive in harsh environments, the exact cause of humanity extinction is not clear. It is proposed here to review the consequences of a gigantic asteroid or comet impact and then to discuss two case studies to better understand survival issues. In the first case, survival is possible, and in the second, humanity disappears.

Direct impact effects 2.1 Energy transfer at impact

When the object touches the ocean or the ground, part of its energy is converted into a shock wave, tsunami or seismic waves [START_REF] Collins | Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[END_REF]. But most of the energy is released both in the form of thermal energy, which heats the impactor and the impact zone, and in the form of kinetic energy transferred to the ejecta.

When the object hits the ocean or the ground, series of shock waves are generated and propagate through the object and the impact zone. The pressure of these shock waves is sufficient to toss some pieces of the object back into space.

According to Shultz, the heat is sufficient to vaporize and / or melt 1 to 10 times the mass of the impactor (depending on the impactor velocity, typically between 15 and 50 km / s) [START_REF] Schultz | Prolonged global catastrophes from oblique impacts, book chapter[END_REF].

If a meteorite falls into the ocean, then objects with a diameter of more than 1/12 of the depth of the ocean will crater the ocean floor. In addition, water will be sent into the atmosphere and to space.

Shock wave

The most important local effect occurs when the object enters in the atmosphere, creating a powerful shock wave. Shock waves are devastating and may cause great damages thousand kilometres away from the impact zone. However, as their effect decreases with the distance to the impact zone, they do not represent a threat to populations located very far and cannot be the primary cause of humanity extinction.

Ejecta

When the impactor is very big, the size and number of ejected rocks are very important [START_REF] Collins | Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[END_REF][START_REF] Toon | Environmental perturbations caused by the impacts of asteroids and comets[END_REF]. With very large objects, heavy rocks can be sent above the atmosphere and fall back onto the Earth almost everywhere, even at the antipodal zone of the impact location [START_REF] Marinova | Geophysical consequences of planetary-scale impacts into a Mars-like planet[END_REF]. As they would be heated up during atmospheric re-entry, they would cause forest fires all over the world, killing almost all terrestrial plants and participating to a global increase of temperatures.

Global heat and winter impact

A global increase of temperatures is expected after the impact. The intensity and duration of this period depends on numerous parameters (size and structure of asteroid, velocity, impact location, etc.). Even if humanity survives this period, there would be a prolonged period of cold weather due to the dust and clouds that would block the sunlight [START_REF] Napier | Giant comets and mass extinctions of life[END_REF][START_REF] Pollack | Environmental effects of an impact-generated dust cloud: implications for the cretaceous-tertiary extinctions[END_REF][START_REF] Sleep | Annihilation of ecosystem by large asteroidal mpacts on the early Earth[END_REF].

Scenario 1

Scenario definition

This scenario is proposed to assess the survival of human species in a very hostile environment, mainly at the climatic level. An asteroid 50 km in diameter would crash into East Asia. It would be of type C and would consist of porous rocks with a density of 1.3. The asteroid would collide with Earth at a speed of 20 km / s and an angle of 45 degrees. The kinetic energy would be 4.07 × 10 9 𝑀𝑇. The crater created by the impact would have a diameter of 360 km, and a depth of 1.74 km [START_REF] Collins | Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[END_REF].

Preparation before impact

During the 10 years of preparation, different behaviours would be observed. Part of the population would live in denial; they would not accept the idea that an asteroid is about to collide with Earth. In general, however, many shelters would be built and lots of consumables and tools would be accumulated into them. Even though the shelters would have been tested, there would remain some uncertainty about the resistance of these at the time of the impact. In this study, we do not consider the possibility of leaving the Earth and going to space.

One week before the impact, the organization and evacuation of some populations to shelters would begin. Some states would have failed to contain their population and would suffer a civil war or would have been reorganized into several communities. The most likely organization within the shelters is a pyramidal hierarchy. Opinion differences among populations could indeed cause the loss of control of the shelter and a military regime could be appropriate.

Day of impact

Just after the impact, a devastating shock wave would cross half the globe. This would cause significant damages, but it would not pose a threat on a global scale. At the time of impact, lots of ejecta would be sent back into space and then would re-enter the atmosphere. This ejecta would be heated to incandescence (+ 500 ° C). They are calling the "shooting stars" by Toon et al. [START_REF] Toon | Environmental perturbations caused by the impacts of asteroids and comets[END_REF]. In addition, 0.1% of the ejecta would be pulverized (30% of the mass of the impactor). It would be submicrometer in size, be taken in the rise of the plume and then diffused globally around the globe, following ballistic trajectories. The soot and ash generated by such fires would envelop the Earth in less than an hour [START_REF] Toon | Environmental perturbations caused by the impacts of asteroids and comets[END_REF]. The light level would then drop quickly to too low a level for photosynthesis and human vision. People still living on the surface without protection would not survive a long time even if located at the opposite side of the Earth because of the shooting stars and fires. Because of the very random phenomenon of the fallout of shooting stars and the size of these, some shelters would be strongly impacted and their population collapsed.

First week

The first week of survival is essential. Indeed, the survivors would be aware of the consequences of the impact, which can lead to significant trauma. The uncertainty of the situation and the lack of control will also accentuate the stress of survivors. Some of them could be plunged into confusion and could no longer make sound judgments and make appropriate decisions. Depression would also affect survivors. Discouragement and the impression that nothing makes sense could cause a physical and mental exhaustion of survivors.

This first week of survival is therefore an essential phase. Even if all the infrastructures put in place to allow the survival of the population have been tested, the risk of malfunction is not zero, which can cause stress on managers or technicians of the shelter. In addition, this week will allow the viability of the political organization of shelters to be tested. Some shelters will face unexpected behaviour from the population, such as refusals to respect established rules. Depending on the type of political regime, we can imagine more or less harsh sanctions to maintain an effective organization.

This week spent in the shelter will also cause the creation of small groups. These groups can be formed in particular according to social class or the function entrusted to the shelter. The size of these groups may have a weight in the future for the decisions made in the shelter.

Regarding the situation on the surface, the surface of the globe is facing terrible fires caused by shooting stars [START_REF] Toon | Environmental perturbations caused by the impacts of asteroids and comets[END_REF]. The light level is lower than the minimum required for photosynthesis and human vision. All populations that did not take refuge in shelters do not survive. Despite the fires and an increase of temperatures at the beginning, at the end of the week, the average temperature has finally dropped drops of 8K. The biggest cooling would take place in the northern hemisphere, with areas cooled from 0 to 10° C.

First month

A period of two weeks spent in a shelter is often sufficient to cause major psychological consequences in the population such as irritability and depression. These behaviours can lead to aggressive behaviour, and withdrawal into oneself.

There are conflicts between certain groups of people within the shelters. These conflicts can interfere with the proper functioning of the shelter, which is why they are managed quickly by the leaders. But it is possible that these conflicts will turn into riots or even overthrow of the organization and the power established in the shelter. Those reversals can sometimes be detrimental to IAC-21-E5.4x63136

Page 3 of 8 the survival of residents if infrastructures are impacted by conflicts. In other shelters that do not experience riots, one can imagine the appearance of new social classes according to their place in the shelter. Technicians having a very important place for the survival of the shelter can, for example, be part of the upper social classes of the shelter. Survivors who participate in the proper functioning shelter might therefore be better rewarded than other survivors. It depends obviously of the type of organizational regime established initially, and would not be applied in all shelters. We can also show optimism with very docile and reliable populations, contenting themselves with the first floor of the pyramid of Maslow. One can imagine that from one month on, scientists study the state of the surface using sensors or remotely controlled robots to take readings in different places. These readings make it possible to study the composition of the air, debris and to deduce more precisely the dates from which it will be possible to make the first outings. Findings in this regard could be transmitted by means of telecommunication set up between the shelters.

During this period of extreme confinement underground, communities will try to find a life cycle more or less similar to their life cycle before the disaster. Establishing routines helps reducing stress and depression, it is therefore normal to wish to find a stable cycle allowing to rest on the temporal elements Temporary education systems can be set up to allow children to continue learning despite difficult conditions. Art, entertainment and sport must also have an important place in the lives of long-term survivors.

Depending on the resources available to communities and health can also be set up to meet the needs of survivors. Survivors may experience health issues or psychological problems. It is therefore important to have doctors and psychologists. We may also consider the involvement of complementary care or health specialists such as nurses, dentists, dermatologists, etc.

Regarding the external situation, the fires are no longer active, but the level of light is still very low. A simulation of the evolution of dust clouds in the stratosphere by Pollack et al showed that the drop of light intensity below the level necessary for photosynthesis cannot exceed one year [START_REF] Pollack | Environmental effects of an impact-generated dust cloud: implications for the cretaceous-tertiary extinctions[END_REF].

Six months after impact

After 6 months, only the communities living in shelters with a stable organization survive. A routine is probably installed within the shelter to maintain a life cycle close to a classic life cycle. However, it is quite possible that some unstable communities managed to survive, despite more difficult conditions.

There are several reasons for the disappearance of some communities.

Firstly, it is psychologically difficult to remain locked up underground for several months. One can therefore assume that riots would be the main cause of destruction of some communities. These riots may impact the infrastructure, organization or facilities that allow the shelter to function properly. These riots may lead some individuals to sabotage facilities, causing the disappearance of the community that depended on the shelter.

Secondly, there is the element of randomness that can affect the survivors. Malfunctions can occur in ventilation systems, water treatment systems or even in the water treatment systems or even the geothermal pump installation. If these malfunctions are significant and it is not feasible to make a repair, these communities can disappear.

Randomness can also intervene in the appearance of disease within the communities. It is difficult to assess the source of these potential diseases, which may be due to the food, the ventilation system, etc. Depending on the severity of the diseases, great damage can be caused within the communities, even to the point of causing the end of them. Another element of randomness is the incorrect prediction of the situation by scientists. It is quite possible that scientific research into the survival of humanity after a meteorite impact has not covered a major issue. It is also possible that some communities were relying on the presence of resources that unexpectedly disappeared as a result of the long-term damage of the impact. For example, simulations by Covey show that precipitation decreases by 90% for several months [START_REF] Covey | Global climatic effects of atmospheric dust from an asteroid or comet impact on Earth[END_REF]. This effect dissipates, allowing the recovery of half of the average precipitation rate (before impact) at the end of the first year after impact. This would cause a global drought. This drought could negatively impact some communities that relied on water recovery from the surface. All these random parameters are part of the risks that survivors must consider.

After 6 months, light begins to return to the surface and humans can finally discern elements [START_REF] Pollack | Environmental effects of an impact-generated dust cloud: implications for the cretaceous-tertiary extinctions[END_REF]. However, this light remains superficial because it corresponds to the light emitted at night by a full moon. The photosynthesis is still not possible. Hope returns to the survivors because the first exits on the surface are carried out by scientists. These exits allow to make an inventory of the current situation, and to foresee the possibilities concerning an extraction of the population towards the surface.

One year after impact

According to Pollack, the period during which the temperature is below 0°C corresponds roughly to twice the period without light [START_REF] Pollack | Environmental effects of an impact-generated dust cloud: implications for the cretaceous-tertiary extinctions[END_REF]. We can therefore assume Copyright 2021 by Jean-Marc Salotti. Published by the IAF, with permission and released to the IAF to publish in all forms.

IAC-21-E5.4x63136

Page 4 of 8 here that the global terrestrial temperatures will start to exceed 0°C after one year. Moreover, the level of light would reach a sufficient level to allow photosynthesis. allow photosynthesis. The temperature is still too low in the northern hemisphere to consider cultivate the land. However, in the southern hemisphere, the level of luminosity being sufficient for photosynthesis, we can suppose that certain communities are beginning to establish crops (in small proportions) around the shelters. However, the yield would probably not be sufficient to consider feeding the entire shelter. Hydroponics and insects would therefore remain the main source of food.

These outings allow some communities to plan a return to the surface. It is indeed important to study the feasibility of establishing an outdoor base.

For that, it is necessary to study several parameters such as the ground or the weather conditions. These external bases must however remain close to the shelters to allow access to drinking water, a viable food source, and enough to shelter the population from the external conditions which are still difficult.

Five years after impact

Five years after the impact, the communities that have survived so far have established camps outside the shelters. Although the shelters remain heavily used, outdoor housing is emerging. "Cities" are beginning to develop around the shelters. Survivors have even been able to meet other peers from relatively close shelters. These shelters provide for the needs of the inhabitants such as food, waste disposal, etc. The materials in the shelters are also used outside to rebuild homes, tools, etc.

Humanity is thus summarized in several agglomerations of shelters, communities scattered over the part of the globe that was not directly affected by the impact, where the shelters were present.

Twenty years after impact

Twenty years after the impact, the society is in the process of reconstruction. It is not at all comparable to the society before the impact. Agriculture has been stabilized, which allows the survivors to meet their needs. A re-implantation of certain animal species has begun as well as the planting of seeds from the Svalbard world seed reserve. This allows to start rebuilding selfregulating ecosystems as it could be the case before impact.

The large shelter agglomerations constitute large development poles which can be similar to states as we know them today.

However, the territories of East Asia are still heavily impacted by the disaster. The devastating effects of the impact are still felt in the climate and the total disappearance of any ecosystem. Some populations are coming to resettle on the extremities of these territories, but the impact zone remains completely deserted. As a reminder, the diameter of the crater created is 360 km.

Discussion

Finally, in this scenario, humanity has managed to survive the catastrophe. However, this survival comes mostly from the human preparation before the impact. Without the establishment of shelters with all the means to provide for human needs, humanity could not have survived such a catastrophe. Furthermore, we have not found reliable information concerning the breathability of the air, which does not allow us to take into account this very important element. Finally, most of the choices are based on hypotheses or even speculations. This interdisciplinary field of research is so vast that the study of a particular part such as the facilities present in the shelters could constitute a complete research project on its own. We have therefore had to base our research on elements that are sometimes incomplete, which can impact the veracity of the scenario.

Scenario 2

Scenario definition

In this scenario, there is the fall of a hypothetical 100 km diameter asteroid in the middle of the Pacific Ocean. The meteorite collides with the Earth at a speed of 20 km/s and an angle of 45 degrees. The kinetic energy of the meteorite is 7.57 x 1010 MT, that is more than ten times the energy of the asteroid of the first scenario.

One week before impact

Ten years have passed since the news of the future impact. One can imagine that on a population scale, the reaction would not be so different than if the meteorite was "only" 50 km in diameter. There have been several mass exoduses, notably from the Asian (Japan, China, etc.) and American (California, Mexico, etc.) coasts. Although the planned area of destruction covers a larger area, these regions, very dynamic in globalization, have become very unstable. The host geographical areas, Europe, Africa, Central Asia, also having to think about their own population, have been put under great tension. Inevitably, many civil wars broke out. States have also fallen, either because of the hysteria of the population, or because of the covetousness of resources or advantageous territories in view of the catastrophe. In the midst of this apparent chaos, a majority of the population will have remained astonished, stunned. It is a population that will have tried to maintain its daily life by covering its eyes, not particularly active for its survival. The threat seems too great, and the hopes of escape from the Earth or of destruction/avoidance of the asteroid have been extinguished since the first year.

IAC-21-E5.4x63136

Page 5 of 8

During these 10 years, the few States, very militarized, which will not have succumbed have put in place authoritarian regimes, and will have prepared post-impact plans to follow. It is also the case of private communities with strong power (economic, political, etc.) which will have organized themselves independently of the States, according to their means. The first ones then had the necessity to set up a plan of sorting of the population according to corruption, genetic heritage and capacities for the times to come. This sorting has still caused serious civil wars. This is not the case for the private communities which are already a limited number (of the order of several thousands), and which thus set up their solutions for all their population. The shock arrives in a week, and the selected populations are moved to the shelters, with all the equipment and food not yet installed. These populations, which will be hastily estimated at only a few million people, are subjected to enormous psychological and moral pressure, but this is small compared to the rest of the Earth. Indeed, the forgotten of survival, condemned by all the forecasts, oscillate between collective suicides, total chaos (unleashing of violence), and mute ataraxic for the resigned.

We believe that the most likely organization within the shelters is a pyramidal hierarchy. Indeed, the decisions to be taken imply a high level of knowledge of the situation and of the possible evolutions of the surface state. Differences of opinion within the populations could then cause the loss of control of the shelter. It is also possible that democratic regimes could be established, especially in private communities. However, these regimes would likely be more unstable due to the psychological evolution of the survivors. Some shelter functions will be assigned to certain survivors to ensure the smooth running of the shelter. This could be, for example, technicians, scientists, or law enforcement personnel. For the sake of efficiency, most of the people accepted in shelters should be active. Some less specific functions such as maintaining hygiene or distributing food can be listed.

Day of impact

The final crater created by the impact has a diameter of about 1000 km, and a depth of 2.5 km [START_REF] Collins | Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[END_REF]. Note that the crater at impact reaches a depth of 180 km. Thus, the atmosphere comes into contact with the asthenosphere. On half of the globe, all the infrastructures are destroyed by the shock wave. However, it takes 16 hours to reach the opposite point of the globe, with gusts of 150 km/h. While in only 1 hour, an earthquake of magnitude 11,9 shakes this opposite point. Nothing was designed to support such an earthquake, almost 100 times stronger than the most powerful earthquake recorded. It is very likely that many shelters will not withstand the earthquake, dooming their populations. During the impact, debris is sent into space and then reenters the atmosphere. This ejecta is heated to incandescence (+500°C). These falling debris are called "shooting stars" [START_REF] Toon | Environmental perturbations caused by the impacts of asteroids and comets[END_REF]. In addition, 0.1% of the sprayed ejecta (30% of the impactor mass), of sub-micrometer size is caught in the rising plume and is diffused globally around the globe in a ballistic manner. Soot and ash generated by shooting star fires will add to the debris floating in the air resulting in an envelopment of the Earth in less than an hour. The sub-micrometer dust and soot repel light rays into space, but the soot will also absorb sunlight. The light level will then drop rapidly to a level too low for the photosynthesis mechanism and human vision. Added to this is the staggering amount of water vapor, on the order of 100 GigaTons, rising into the atmosphere.

The coastlines of the Pacific Ocean are affected by titanic tsunamis, on the order of 100 meters. A mass of water over the entire depth of the ocean has been displaced. The water movement is global, and coastlines throughout the Pacific will be razed. People still living on the surface without protection will not survive in the long term even if they are on the opposite side of the globe from the point of impact due to shooting stars and fires. Because of the very random phenomenon of the shooting stars' fallout and their size (in fact like small meteorites), some shelters are strongly impacted and the sheltered population is doomed not to survive. It should also be noted that despite the size of the asteroid, the astronomical constants of the Earth, i.e. the length of the day, the Earth's mass or the Earth's orbit, will not be impacted or hardly impacted at all [START_REF] Collins | Earth Impact Effects Program: A Web-based computer program for calculating the regional environmental consequences of a meteoroid impact on Earth[END_REF]. Thus, at the end of this first day, it is predictable that most of humanity outside of a shelter will be killed (about 99%). The only potentially earthquake-resistant subsurface shelters will not be numerous, perhaps half or a third of the sheltered population.

One week after impact

During the first week, catastrophic events follow one another. Fire hurricanes have broken out in all the major forests of the world and continue to wreak havoc, still releasing huge amounts of ash and water vapor [START_REF] Marinova | Geophysical consequences of planetary-scale impacts into a Mars-like planet[END_REF]. Moreover, the impact has unbalanced the earth's crust, awakening volcanoes and super volcanoes (e.g., Yellowstone) or causing new earthquakes, especially in sensitive areas such as the San Andreas Fault in California. These disasters in turn bring their share of damage and consequences, such as new tsunamis or the addition of dust and volcanic ash in the atmosphere. And this is true for the whole world.

During the first few weeks, the energy released by the impact, the fiery hurricanes, and the suspended IAC-21-E5.4x63136

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water vapor cause the temperature of the atmosphere to remain above 500°C [START_REF] Harris | Asteroid impacts and modern civilization: Can we prevent a catastrophe?[END_REF]. It is unclear if there are areas that are not less affected by this temperature rise, but they would be exceptional. The coastlines are certainly part of this, benefiting from the thermostat effect of the Ocean. However, we have seen that these coastlines were hardly a solution, because already ravaged by tsunamis and particularly sensitive to earthquakes (because of subduction zones). Thus, life on the surface was virtually annihilated, leaving mostly insects or small animals.

In the shelters, the cooling and air filtering systems must be optimally efficient to maintain livable conditions, and technical problems due to the extreme conditions may already occur. At this point, we may only be talking about a hundred thousand survivors spread across the globe.

The first month

As far as life in the remaining shelters is concerned, it does not diverge so far from the case of a smaller impact (50 km diameter scenario). Indeed, as long as the shelter is functioning, the external conditions do not impact the internal conditions, at least for now.

Conflicts between certain groups of people shelters are emerging. These conflicts can be detrimental to the smooth running of the shelter, so they are dealt with quickly by the leadership. But it is possible for these conflicts to turn into riots that could overthrow the organization and power established in the shelter. These overthrows can sometimes be detrimental to the survival of the inhabitants if the infrastructure is impacted.

In other shelters that do not experience riots, one can imagine the emergence of new social classes depending on their place in the shelter. Technicians with a very important place in the survival of the shelter may, for example, be part of the upper social classes of the shelter. Survivors who are involved in the smooth running of the shelter might therefore be better rewarded than other survivors. This obviously depends on the type of organizational regime initially established, and would not be true in all shelters. One can also be optimistic with populations that are very docile and reliable, settling for the second floor of Maslow's pyramid.

During this period of extreme confinement, communities will try to return to a life cycle more or less similar to their life cycle before the disaster. Establishing a routine decreases stress and depression. Temporary education systems can be put in place to allow children to continue learning despite difficult conditions. Those of working age may be able to make themselves useful in shelter maintenance, food distribution, or other essential function that allows the shelter to function properly. Art, entertainment, and sports should also have an important place in the lives of survivors in the long run. To allow survivors to think about something other than the disaster, sports or several forms of art may be considered. This would likely be beneficial in curing the depression of some survivors.

Depending on the resources available to communities and shelters, health systems may also be developed to provide for the needs of survivors.

Regarding the outside, the temperature remains well above 100°C, continuing to kill everything that can be killed. Volcanic eruptions have apparently calmed down, and fewer and fewer earthquakes are shaking the Earth. The atmosphere is still largely unbreathable, due to the fines particles in suspension. The weather conditions are totally unpredictable during this period. Thus, going outside is almost impossible and of little interest. Of the life on the earth's surface, there is already not much left.

Six months after impact

Again, the sheltered life is quite similar to that in the "50 km" scenario. However, the even harsher outdoor conditions (including higher temperatures) will have tended to bring more life support systems to their knees. Thus, the number of remaining shelters gets smaller and smaller.

At the end of six months, only the communities with shelter and relatively stable organization have survived. A routine is probably established within the shelter to maintain a life cycle close to a conventional life cycle.

There are several reasons that may be the cause of the collapse of some communities. Firstly, it is psychologically difficult to remain locked up underground for several months without any perspective and room for improvement. Therefore, we can assume that riots would be the main cause of destruction of some communities. These riots may impact the infrastructure, organization, or facilities that allow the shelter to function properly. These riots may lead some individuals to sabotage facilities, which may cause significant irreparable damage, causing the disappearance of the community that depended on the shelter.

Secondly, there is the element of randomness that can affect the survivors. Malfunctions can occur in many life support systems and it is doubtful that there would be enough resources and the necessary industrial tools to repair everything.

Randomness may also be involved in the occurrence of disease within communities. It is difficult to assess the source of these potential diseases, which may be due to malnutrition, the presence of toxic molecules in the air, etc. Depending on the severity of the diseases, the communities could slowly but surely collapse. IAC-21-E5.4x63136

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Another important issue is the difficulty to predict what are all the resources, tools and industrial processes that are needed for survival. The lack of a single important resource could lead to the collapse of the community. It could be for example water. As a severe drought is expected on the surface, some communities that relied on water recovery from the surface or from a small underground reservoir would die. All these random parameters are part of the risks that survivors must consider. Although the external luminosity goes up a little, the temperature remains above 100°C. However, the coastlines are cooling faster. In fact, at this stage, the outside is not an issue for survival. The only elements allowing the survival of the tens of thousands of people remaining are inside the shelters.

One year after impact

It is around this period that we will witness a reversal of the phenomenon. For almost a year, the Earth was overheated. But the impact winter will finally begin. Indeed, it has been a year since solar energy was almost completely absorbed by the pile of ash, dust, and water vapor in the atmosphere. And a large part of these elements has not yet fallen back to the ground. Thus, the planet will see a drastic decrease in its average temperature compared to normal (about 7 degrees less). More than a third of the Northern Hemisphere would then be under ice, with another third resembling the tundra of the Siberian deserts. The final third would have no life at all, even if outside conditions would be more favorable.

Five or ten years after impact

The duration of the overheated period is not clear. It could be five to ten years, perhaps more. At some point, however, the impact winter should settle down durably. The life annihilated by the post-impact period cannot restart under these conditions. The climatic and meteorological conditions hardly allow expeditions outside the shelters, which for the most part have already reached their limits and seen their population die out. From a physical point of view, most of the surviving humans are at the end of their tether, due to the lack of vitamins and the lack of physical exercise. As for the mental state of the survivors, it is difficult to determine, between resignation, hope, questioning, fear, frustration etc. It is likely that the population of numerous remaining shelters has fallen below the threshold of healthy reproducibility. And the perspectives are bad.

Decades after impact

After ten years or perhaps decades, terrestrial temperatures will drop down and become livable for simple organisms and plants in some places on Earth. However, even if some people were still alive in wellorganized shelters, there is no guarantee that these places would be safe and full of useful resources for living. There are numerous reasons to believe that nobody would survive [START_REF] Salotti | Minimum Number of Settlers for Survival on Another Planet[END_REF]:

 Environmental issues New volcanoes and tsunamis could destroy the remaining shelters. The atmosphere could also become unbreathable due to the presence of toxic gases. Acid rains could be dangerous to all terrestrial life forms.

 Insufficient resources For survival, huge amounts of water are needed, to grow plants and for many other usages. As 100% recycling is not possible, many shelters might collapse due to a lack of this resource if their reservoir is limited. Similar issues exist for repairing capabilities.

 Insufficient energy Lots of energy is needed, especially in the form of electricity, for the photosynthesis of plants using artificial lighting, and also for many complex systems (life support, pumps), and industrial processes.

 Insufficient human resources There is an issue with genetics and also with the needs to implement all human activities required for survival (maintenance of life support, agriculture, industry, growing babies, etc.) [START_REF] Salotti | Minimum Number of Settlers for Survival on Another Planet[END_REF].

 Anarchy A strong and effective organization is required to obtain a synergy of all human activities and avoid riots and wars among the different communities.

 Insufficient adaptation capacities Without experience, the communities will have to face many unexpected problems without appropriate tools and solutions.

For all these reasons, the total annihilation of humanity cannot be demonstrated, but the long term survival capability seems to be very weak. Regarding living organisms in general, they will resume from the ocean floor, or close to hydrothermal vents but the settlement of the surface will probably last centuries.

Conclusions

In view of these scenarios, the limiting size of the asteroid allowing for human resilience in the event of an impact with the Earth is in the range 50-100km. In spite of the effort made in the research and the linkage of the latter, these scenarios remain nevertheless the result of several choices made in the analysis and of several assumptions. This is moreover why the range given is wide. However, we do manage to obtain an order of magnitude of asteroids fatal to humanity. This allows us to better situate the risks and to better evaluate the need to protect ourselves from this kind of impact, for example by colonizing new exoplanets.