Characterizing Dialysis Efficacy, Kidney Failure, and Renal Recovery Using Blood Urea Nitrogen (BUN) Modeling

Characterizing Dialysis Efficacy, Kidney Failure, and Renal Recovery using Blood Urea Nitrogen (BUN) Modeling

Kaniyah Purcell, Annabelle Lint, Gilles Clermont, Robert S. Parker

Observation:

When patients experience renal failure, they require treatments like intermittent hemodialysis. To describe a patient’s renal health, dialysis adequacy (Kt/V) and renal recovery times can be analyzed. However, because Kt/V and renal recovery are not routinely collected, blood urea nitrogen (BUN) concentrations can be used to estimate Kt/V and renal recovery instead. Blood urea nitrogen (BUN) concentration levels can be used to estimate a patient’s Kt/V and renal recovery time. A model was created to estimate dynamic BUN trajectories before, during, and after dialysis using clinical medical data.

Method:

A 2-compartment ordinary differential (ODE) model was created to predict BUN levels before and after dialysis. BUN generation and dialyzer clearance model parameters were fit using a differential evolution algorithm to minimize normalized root mean squared error (RSME) between the predicted and actual trajectories within clinically reasonable parameter bounds. Parameters for BUN levels were updated every dialysis session. Bounds for parameters were established using high-density data simulation results. The model was tested on 4 patients who had no renal function and 2 patients with renal recovery. For patients who experienced renal recovery, additional parameters were included: K, β, and 𝜏. K represents how much the patient recovers, β represents the time that renal recovery begins, and 𝜏 represents the time it takes to reach 63.2% of max Kr.

Results:

For the 4 patients who experienced no renal function, the model fit relatively well. The RMSE for those patients was under 2. Additionally, Patients who experienced renal recovery fit the model relatively well. The RMSE for those patients was under 5, and the parity line between our mathematical model and medical data demonstrated a good fit.

Conclusion:

The developed model predicted BUN trajectories over time and captured variance in BUN clearance and generation in patients with and without renal recovery. The model calculated estimates of dialysis adequacy that could support clinicians through intermittent hemodialysis support systems. Simulations produced using the renal recovery mathematical model demonstrated a direct correlation between levels of BUN decreasing as renal function increases. Simulations produced by the model for patients with no renal function demonstrate that high-adequacy dialysis sessions removed high BUN concentrations and excess fluid volume.