Mathematically Modelling CD19+ B Cell Reconstitution After Insult to the Immune System: Paediatric Allogeneic Haematopoietic Stem Cell Transplantation, Rituximab Therapy and Epstein-Barr Viral Reactivation
Soumya Perinparajah , Juliana M.F. Silva , Reem Elfeky , Natalia Builes Restrepo , Oscar J. Charles, John Booth, S.Y. Amy Cheung, James W.T. Yates, Nigel Klein, Persis J. Amrolia[1,2], Joseph F. Standing[1,6]
 Infection, Immunity and Inflammation Research & Teaching Department, UCL Great Ormond Street Institute of Child Health, London, United Kingdom,  Department of Bone Marrow Transplantation, Great Ormond Street Hospital for Children, London, United Kingdom,  Digital Research, Informatics and Virtual Environment Unit, NIHR Great Ormond Street Hospital Biomedical Research Centre, London, United Kingdom,  Integrated Drug Development, Certara, Princeton, New Jersey, United States,  DMPK Modelling, In-Vitro In-Vivo Translation, GlaxoSmithKline, Stevenage, United Kingdom,  Department of Pharmacy, Great Ormond Street Hospital for Children, London, United Kingdom
Introduction: To date, studies of immune recovery after haematopoietic stem cell transplantation (HSCT) have focussed on T cells and adult patients. Therefore, there is an unmet need to better understand B cell reconstitution post-HSCT in children [1-4]. A loss of virus-specific cytotoxic T cells (CTLs) post-HSCT predisposes patients to reactivations of latent viral reservoirs such as Epstein-Barr virus (EBV), resulting in opportunistic outgrowth of EBV-infected B cells . EBV reactivation is the leading cause of post-transplant lymphoproliferative disorder (PTLD) with reduced intensity conditioning (RIC), anti-thymocyte globulin (ATG) and low donor histocompatibility increasing the risk [6-8]. Rituximab is given off-label for EBV, as it targets B cells for depletion by binding to CD20+. In routine clinical monitoring post-HSCT, quantitative PCR (qPCR) is used to measure EBV DNA and quantify viral load (VL), especially in the first three months when reactivation is most common. Studying the kinetics of EBV reactivation post-HSCT as patients’ immune systems reconstitute presents an opportunity to elucidate the underlying biological mechanisms .
Objectives: To quantify CD19+ B cell reconstitution in children post-HSCT, identify the pharmacodynamics of rituximab in children with EBV post-HSCT, identify risk factors for EBV reactivation in the first 100 days post-HSCT and assess the suitability of a previously reported mathematical model to mechanistically model EBV reactivation kinetics in this cohort .
Methods: Retrospective electronic data from routine clinical practice were collected from children who underwent HSCT at a tertiary paediatric hospital between 2000-2016 and had EBV reactivation post-HSCT. Data were collected by HSCT clinicians and subsequently extracted by the Digital Research Environment (DRE) team.
EBV was monitored by qPCR weekly; if EBV DNA was detected in the first three months post-HSCT, qPCR was performed twice weekly to quantify VL until treatment started or VL declined. The threshold to treat with rituximab was above VL of 40,000 copies/mL whole blood on two consecutive occasions within the first three months of HSCT. Rituximab was dosed by body-surface area and administered via intravenous infusion at a dose of 375 mg/m2 weekly, with patients receiving a single dose on a conservative regimen or four doses on a pre-emptive regimen.
To scale for age-related effects, a B cell maturation function was developed using non-linear least squares. Rituximab pharmacokinetics (PK) were not measured therefore rituximab effect was assumed to decay by first-order kinetics. Covariates were identified using the stepwise covariate modelling approach in Perl-speaks-NONMEM version 4.8.1 .
Cox proportional hazards (Cox-PH) modelling was performed to assess time to EBV reactivation in the first 100 days post-HSCT using the survival package. Covariates considered were: type of donor, HSC source, whether patient had primary immunodeficiency (PID) diagnosis, age, number of rituximab doses, EBV serostatus of donor and recipient, type of conditioning regimen, administration of alemtuzumab or ATG pre-HSCT, and area under the curve from 0 to 100 days post-HSCT (AUC0-100) for the following immune cell subsets; absolute lymphocyte count (ALC), CD19+ B cells, CD4+ T cells and CD8+ T cells. Collinearity between covariates was assessed before analysis. Variables significant in univariable analysis (P < 0.05) were taken forward to a multivariable analysis.
A previously reported nine-compartment 25-parameter mechanistic mathematical model of EBV viral kinetics was implemented using the deSolve package. Considering the latently infected memory B cell compartment (Bm) to be a proxy for EBV VL, VL sensitivity to each of the 25 parameters was determined by setting each in turn to a range of values (0.00001-1000) and simulating the VL trajectory.
Data analyses were performed in R version 3.5.1  and models were fitted in NONMEM® version 7.4.3 using the Laplacian conditional estimation with interaction algorithm .
Results: 4115 measurements of CD19+ B cell counts from 359 children (median age, 3.02 years; range, 0.08-17 years) were used to construct a one-compartment turnover model. The parameter estimates were (% residual standard error); CD19+ B cell production rate constant (λ), 1.68x106 cells/day (1.09); CD19+ B cell death rate constant (μ), 0.015 cells day-1 (1.17); Hill exponent, 4.17 (0.13); time to half-maximal CD19+ B cell output (T50), 58 days (1.19). A B cell maturation function was applied to λ and μ a priori. Three covariates were found to significantly affect T50 (effect size); HSCT indication of PID (-0.55), receiving myeloablative conditioning (MAC) (0.17) and having a matched donor (0.01).
Fifty-six patients received rituximab for EBV reactivation (median age, 2.96 years; range, 0.3-14 years), for whom 683 measurements of CD19+ B cell counts and 3547 measurements of EBV VL were collected (one dose, n = 41; four doses, n = 15). A kinetic-pharmacodynamic model, incorporating rituximab effect with an Emax model, gave the following parameter estimates; λ, 1.4x106 cells/day; μ, 0.018 day-1; Hill exponent, 3.18; T50, 44.8 days; rituximab elimination rate (Ke), 0.11 day-1; Emax, 84.4 and ED50, 18.5 mg. Elimination half-lives of rituximab and CD19+ B cells were 6.3 days and 38.5 days respectively. Covariate effects were (effect size); receiving MAC (0.95), PID indication (-0.47), and having a matched donor (-0.47).
Of 56 patients, 67.9% had EBV reactivation in the first 100 days since HSCT, with median time to reactivation of 40 days. EBV seropositivity of the HSCT recipient and pre-HSCT administration of ATG were found to significantly increase risk of EBV reactivation in the multivariable Cox-PH model (adjusted hazard ratio (AHR) = 2.32, P = 0.02; AHR = 2.55, P = 0.04).
According to RMSE values, five parameters in the previously reported model were identified as sensitive for EBV VL: CTL killing rate of infected B cells expressing the default programme; proliferation rate of latently infected memory B cells; reactivation rate of latently infected memory B cells to lytically infected memory B cells; death rate of latently infected memory B cells and death rate of CTLs responding to the default compartment.
Conclusion: We have developed models to quantify CD19+ B cell dynamics post-HSCT in children and identify the pharmacodynamics of rituximab for EBV reactivation in this cohort. In addition, we identified pre-HSCT ATG and EBV seropositivity of the HSCT recipient to be significant risk factors for EBV reactivation in the first 100 days post-HSCT. Future work will include simulating rituximab dosing regimens to optimise the dose and mechanistically modelling the patient EBV VL data. This will allow us to delineate the viral, drug and immune mechanisms in this patient cohort and ultimately inform their clinical management to improve their post-HSCT outcomes.
 Hoare, R. L., Veys, P., Klein, N., Callard, R., & Standing, J. F. (2017). Predicting CD4 T‐cell reconstitution following pediatric hematopoietic stem cell transplantation. Clinical Pharmacology & Therapeutics, 102(2), 349-357.
 Bartelink, I. H., Belitser, S. V., Knibbe, C. A., Danhof, M., de Pagter, A. J., Egberts, T. C., et al (2013). Immune reconstitution kinetics as an early predictor for mortality using various hematopoietic stem cell sources in children. Biology of blood and marrow transplantation, 19(2), 305-313.
 Toor, A. A., Sabo, R. T., Roberts, C. H., Moore, B. L., Salman, S. R., Scalora, A. F. et al (2015). Dynamical system modeling of immune reconstitution after allogeneic stem cell transplantation identifies patients at risk for adverse outcomes. Biology of Blood and Marrow Transplantation, 21(7), 1237-1245.
 Mensen, A., Ochs, C., Stroux, A., Wittenbecher, F., Szyska, M., Imberti, L. et al (2013). Utilization of TREC and KREC quantification for the monitoring of early T-and B-cell neogenesis in adult patients after allogeneic hematopoietic stem cell transplantation. Journal of translational medicine, 11(1), 1-9.
 Hislop, A. D., Taylor, G. S., Sauce, D., & Rickinson, A. B. (2007). Cellular responses to viral infection in humans: lessons from Epstein-Barr virus. Annu. Rev. Immunol., 25, 587-617.
 Cohen, J., Gandhi, M., Naik, P., Cubitt, D., Rao, K., Thaker, U. et al (2005). Increased incidence of EBV‐related disease following paediatric stem cell transplantation with reduced‐intensity conditioning. British journal of haematology, 129(2), 229-239.
 Brunstein, C. G., Weisdorf, D. J., DeFor, T., Barker, J. N., Tolar, J., van Burik, J. A. H. et al (2006). Marked increased risk of Epstein-Barr virus-related complications with the addition of antithymocyte globulin to a nonmyeloablative conditioning prior to unrelated umbilical cord blood transplantation. Blood, 108(8), 2874-2880.
 Landgren, O., Gilbert, E. S., Rizzo, J. D., Socié, G., Banks, P. M., Sobocinski, K. A. et al (2009). Risk factors for lymphoproliferative disorders after allogeneic hematopoietic cell transplantation. Blood, The Journal of the American Society of Hematology, 113(20), 4992-5001.
 Burns, D. M., Tierney, R., Shannon-Lowe, C., Croudace, J., Inman, C., Abbotts, B. et al (2015). Memory B-cell reconstitution following allogeneic hematopoietic stem cell transplantation is an EBV-associated transformation event. Blood, The Journal of the American Society of Hematology, 126(25), 2665-2675.
 Akinwumi, S (2018). Modelling the Kinetics of EBV in Primary Carriers and Transplant Recipients. PhD thesis. Department of Mathematical and Statistical Sciences, University of Alberta.
 Lindbom, L., Pihlgren, P., & Jonsson, N. (2005). PsN-Toolkit—a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM. Computer methods and programs in biomedicine, 79(3), 241-257.
 Core Development Team R. A Language and Environment for Statistical Computing. 2020. http://www.r-project.org.
 Sheiner, L. B., & Beal, S. L. (1983). Evaluation of methods for estimating population pharmacokinetic parameters. III. Monoexponential model: routine clinical pharmacokinetic data. Journal of pharmacokinetics and biopharmaceutics, 11(3), 303-319.