Novel data-driven stochastic model for antibody dynamics in kidney transplantation∗

Falls in the serum levels of donor specific HLA antibodies (DSA) after kidney transplantation are of great clinical interest, as they are associated with resolution of rejection and good long term outcomes in patients at high risk of graft loss. A data-driven model in the form of third order differential equation has been developed to describe the dynamics of the falls in DSA after renal transplantation. The model characterises the post transplant DSA behaviour for two groups of renal transplant recipients: those who experienced acute antibody mediated rejection (AMR) in the first days after operation and those who did not. A variational Bayesian inference method was employed to find the form of the model, infer the system parameters and extract the information of the recognisable patterns and the common features in DSA post transplant dynamics. Three models of different order have been investigated, and the third order linear model with four parameters outperformed the models of lower orders. The inferred deterministic parameters were found to be significantly different between the two groups of people with and without AMR. The eigenvalues for each DSA time series have been calculated and compared between the groups. A higher frequency of oscillation and a faster dissipation rate of antibodies have been found in the AMR group, which demonstrate a potential for intelligent laboratory interrogation of the underlying immunological mechanisms, which at present are entirely opaque.