Rollo L Hoare (1,2), Robin Callard (1,2), Paul Veys (1,3), Nigel Klein (1,3), Joseph F Standing (1,2,3)
(1) Institute of Child Health, University College London, 30 Guilford St, London, UK; (2) Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, Gower St, London, UK; (3) Great Ormond Street Hospital NHS Foundation Trust, Great Ormond St, London, UK.
Objectives: Before a haematopoietic stem cell transplant (HSCT), a child will usually be given a conditioning regimen to reduce or ablate the host immune system. This is to prevent graft rejection, graft versus host disease and relapse. Following HSCT, short-term complications and long-term successful outcomes are associated with the rate and extent of immune system recovery. Studying immune reconstitution in children is challenging due to the rapidly developing immune system; expected CD4 T cell counts (a key subset of lymphocytes) for age decrease three-fold [1]. This work presents an extension of our mechanistic model, describing reconstitution of CD4 cells in children following HSCT, to include a more biological explanation of competition for resources [2].
Methods: The model of CD4 cell count has two compartments, a resting and dividing compartment. Cells enter the resting compartment through a zero-order thymic output. They can then be activated to the dividing compartment from which two cells will return to the resting compartment. There are different death rates for cells in each compartment. The model is made more mechanistic in three ways: (1) using a mathematical function for thymic output [3] to account for age related changes; (2) allowing for impaired thymic output in the months following HSCT; (3) having density dependent death and activation rates to account for competition for resources. We apply this model to longitudinal data collected in the bone marrow transplant unit in Great Ormond Street Hospital.
Results: Fitting this model using NLME has proved difficult due to collinearities. After theoretical and practical identifiability analysis, by selecting density dependencies and parameter sets, it has been possible to find a model that is identifiable. The final model had good descriptive and simulation properties. In the long term, the modelled population average returned to, or very near to, the CD4 count expected for a healthy child.
Conclusions: A mechanistic model for immune reconstitution of CD4 cells following HSCT has been extended to include a more biological explanation for the competition for resources, using two compartments. We manage to fit this model to the data, finding a set of parameters that are identifiable. It is now possible to carry out a multivariate analysis and find which parts of the immune system are affected by covariates such as disease type, drug pre-conditioning, and graft-versus-host disease prophylaxis.
References:
[1] S Huenecke et al. Age-matched lymphocyte subpopulation reference values in childhood and adolescence: application of exponential regression analysis. Eur J Haematol 2008; 80(6): 532-39
[2] AJ Yates et al. Understanding the slow depletion of memory CD4+ T cells in HIV infection. PLoS Medicine 2007; 4(5): e177
[3] I Bains et al. Quantifying thymic export: combining models of naive T cell proliferation and TCR excision circle dynamics gives an explicit measure of thymic output. J Immunol 2009; 183: 4329-36
Reference: PAGE 23 (2014) Abstr 3068 [www.page-meeting.org/?abstract=3068]
Poster: Drug/Disease modeling - Paediatrics