Modeling BK Virus Infection in Renal Transplant Recipients

Abstract

Kidney transplant recipients require a lifelong protocol of immunosuppressive therapy to prevent graft rejection. However, these same medications leave them susceptible to opportunistic infections. One pathogen of particular concern is human polyomavirus 1, also known as BK virus (BKPyV). This virus attacks kidney tubule epithelial cells and is a direct threat to the health of the graft. Current standard of care in BK virus-infected transplant recipients is reduction in immunosuppressant therapy, to allow the patient's immune system to control the virus. This requires a delicate balance; immune suppression must be strong enough to prevent rejection, yet weak enough to allow viral clearance. We seek to model viral and immune dynamics with the ultimate goal of applying optimal control methods to this problem. In this paper, we begin with a previously published model and make simplifying assumptions that reduce the number of parameters from 20 to 14. We calibrate our model using newly available patient data and a detailed sensitivity analysis. Numerical results for multiple patients are given to show that the newer model reflects observed dynamics well.

Keywords: BKPyV; immunosuppression; kidney; model calibration; modeling; renal; sensitivity; transplant.

Figure 1

Diagram of the model 2 state interactions. There is a cyclical relationship between susceptible cells, infected cells, and BKPyV. The immunosuppression efficacy $ϵ$ affects the growth of the immune cell states and these immune cell states affect the loss terms for their targets, susceptible cells and infected cells. Also, note that creatinine is a biomarker and does not affect the other model states.

Figure 2

All CTOT-19 subset viral load trajectories with representative samples highlighted.

Figure 3

Model fits to EHR patient #4080 data. (a) Model 2 captures the BKPyV increase in the non-censored data better than model 1 and captures the decrease. (b) Both models fit the patient creatinine data equally well. (c) The unobserved model states (dashed lines) are shown here, which the model simulates without corresponding data. (d) The susceptible cell dynamics of model 2 show a plateau effect and stabilization of the allograft once a BKPyV infection is under control. This figure is a zoomed-in effect of the top left panel of (c).

Figure 4

Parameter estimate subset selection based on standard errors for patient #4080. Each number of parameters indicates the best standard errors for a subgroup of that size. The red line indicates where standard errors are greater than their respective parameter values. For patient #4080, at best two parameters can be estimated with acceptable standard errors: ${\delta }_{EH}$ and ${\rho }_V$. Estimating all eight parameters, as shown in Table 6, only has a single parameter with respectable standard error.

Figure 5

Sensitivity analysis for models 1 and 2. (a) The global analysis of model 1 shows half of the parameters have limited or no influence on BKPyV dynamics for a wide range of patients. (b) For patients in this study, the local analysis indicates the relative importance each parameter plays on BKPyV dynamics. There are four parameters that are uniquely identifiable from data in the model. (c) For model 2, the global sensitivity suggests that, again, for a wide range of patients, approximately half of the parameters have limited influence on BKPyV, similar to part (a). (d) The local sensitivity for model 2 shows that after improvements to the model, four parameters are still identifiable. Green sensitivities are identifiable parameters.

Figure 6

Model 2 fit to CTOT patient #287915 data. (a) The original model fit (blue) to the data displays a very early and strong BKPyV infection; the results of which would most likely lead to BKPyV nephropathy (BKPyVAN). For the model fit in red, a simulated data point is added to the dataset and results in more biologically realistic dynamics. (b) Limited creatinine data were available, but they are captured well by both models. (c) All states of the model are shown with both trajectories, where those in blue demonstrate an allograft lost to BKPyVAN, and others in red show a damaged but still functioning organ.

Figure 7

The effect of immunosuppression efficacy value ($ϵ$) on model fits to EHR patient #4947 data. (a) Reducing the efficacy of the immunosuppression treatment from 1 to 0 limits the strength of the BKPyV infection. (b) The effect of immunosuppression efficacy on the other states shows that the balanced immunosuppression approach of $e=0.8$ maintains a healthy graft. The healthy graft is visible through the non-zero $H_S$ trajectory (top left panel) and extended creatinine trajectory below 3 (bottom right panel).