Abstract
The dynamics of donor specific human leukocyte antigen antibodies during early stage after kidney transplantation are of great clinical interest as these antibodies are considered to be associated with short and long term clinical outcomes. The limited number of antibody time series and their diverse patterns have made the task of modelling difficult. Focusing on one typical post-transplant dynamic pattern with rapid falls and stable settling levels, a novel data-driven model has been developed for the first time. A variational Bayesian inference method has been applied to select the best model and learn its parameters for 39 time series from two groups of graft recipients, i.e. patients with and without acute antibody-mediated rejection (AMR) episodes. Linear and nonlinear dynamic models of different order were attempted to fit the time series, and the third order linear model provided the best description of the common features in both groups. Both deterministic and stochastic parameters are found to be significantly different in the AMR and no-AMR groups showing that the time series in the AMR group have significantly higher frequency of oscillations and faster dissipation rates. This research may potentially lead to better understanding of the immunological mechanisms involved in kidney transplantation.
Highlights
Kidney transplantation is proven to be the best treatment for renal failure and success is dependent on the reaction of the immune system primarily against human leukocyte antigen (HLA) proteins of the transplant
We present the results of system and parameter identification by comparing solutions for linear first, second and third order dynamic equations only: Model 1 (M1) : Model 2 (M2) : Model 3 (M3) : dxtdt d2xt dt 2
With a unique dataset of donor-specific antibody (DSA) time series available, a mathematical model in the form of differential equations has been developed for the first time to describe the dynamic of the ‘falls’ in DSAs for patients with and without antibody-mediated rejection (AMR) episodes
Summary
Kidney transplantation is proven to be the best treatment for renal failure and success is dependent on the reaction of the immune system primarily against human leukocyte antigen (HLA) proteins of the transplant. Conventional transplantation is facilitated by immunosuppression which targets cellular components of the immune system. A significant number of patients develop antibodies to HLA following exposure to non-self HLA from pregnancy, blood transfusion or previous kidney graft [2,3]. These antibodies exist as multiple isoforms but it is Immunoglobulin G (IgG) which is deemed to be most detrimental to transplant outcome [4].
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