Zhang, Yan, Briggs, David, Lowe, David Philip, Mitchell, Daniel A., Daga, Sunil, Krishnan, Nithya, Higgins, Rob and Khovanova, N. A. (2017) A new data-driven model for post-transplant antibody dynamics in high risk kidney transplantation. Mathematical Biosciences, 284 . pp. 3-11. doi:10.1016/j.mbs.2016.04.008

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Abstract

The dynamics of donor specific human leukocyte antigen (HLA) antibodies during early stage after transplantation are of great clinical interest as they are considered to be associated with short and long term outcomes (graft function and rejection). However, the limited number of such detailed donor-specific antibody (DSA) time series currently available and their diverse patterns have made the task of modelling difficult. Focusing on one typical dynamic pattern with rapid falls and stable settling levels, a novel data-driven model in the form of a third order differential equation has been developed to describe such post-transplant dynamics in DSAs for the first time. A variational Bayesian inference method has been applied to select a 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. Eigenvalues have been calculated for each fitting, and phase portraits have been plotted to show the trajectories of the system states for both groups. The results from our previous study with fewer cases have been further confirmed: the time series in the AMR group have significantly higher frequency of oscillations and faster dissipation rates, which may potentially lead to better laboratory measurement strategy and a better chance of understanding the underlying immunological mechanisms.

Item Type:	Journal Article
Subjects:	R Medicine > RD Surgery
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Kidneys -- Transplantation -- Mathematical models, Eigenvalues
Journal or Publication Title:	Mathematical Biosciences
Publisher:	Elsevier Science Inc.
ISSN:	0025-5564
Official Date:	February 2017
Dates:	Date Event February 2017 Published 14 May 2016 Available 25 April 2016 Accepted 18 January 2016 Submitted
Date of first compliant deposit:	6 May 2016
Volume:	284
Page Range:	pp. 3-11
DOI:	10.1016/j.mbs.2016.04.008
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/K02504X/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266
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