Multi-patient Inverse Estimation of Effective Membrane Diffusion Coefficients in Calcium-Citrate Hemodialysis

TL;DR

This work provides a physically consistent and computationally tractable framework for multi-patient parameter estimation in dialysis models, and opens perspectives for large-scale personalization through physics-informed surrogate modeling.

Abstract

We propose a multi-patient inverse modeling framework for identifying effective calcium and citrate diffusion coefficients in hollow-fiber hemodialysis devices. The approach relies on a coupled forward model combining axisymmetric fluid dynamics with multi-species convection-reaction-diffusion, together with a derivative-free optimization strategy to estimate membrane transport parameters from outlet concentration measurements. To account for inter-patient variability, physiological input parameters are first generated from clinical data and complemented by a patient-specific hydraulic calibration step, ensuring physical consistency across the synthetic cohort. The inverse problem is formulated as a global least-squares minimization aggregating residuals over multiple patients. Numerical experiments on synthetic data demonstrate multi-patient identifiability of the diffusion coefficients in the exact-data setting. Robustness with respect to measurement noise is subsequently assessed by perturbing observable outputs at various noise levels, and sensitivity analyses are performed to quantify the influence of membrane transport parameters on model predictions. The methodology is then applied to real clinical data obtained from an AK200 Gambro/Nikkiso DBB07 dialysis system. The results indicate that aggregating information from several patients substantially improves parameter identifiability and stability compared to single-patient inversions. Overall, this work provides a physically consistent and computationally tractable framework for multi-patient parameter estimation in dialysis models, and opens perspectives for large-scale personalization through physics-informed surrogate modeling.

Figures (16)

• Figure 1: Axisymmetric representation of a representative hollow fiber: blood region $\Omega_b$, porous membrane $\Omega_m$, and dialysate region $\Omega_d$.
• Figure 2: Evolution of the error in Newton algorithm described in Algorithm \ref{['alg:newton']} for boundary data given in Table \ref{['tab:bd-p1']}.
• Figure 3: Components $c_1$ (corresponding to Calcium) and $c_4$ (corresponding to Citrate) of the numerical approximation of the solution $\boldsymbol{c}$ computed using Newton's method for the initial data in Table \ref{['tab:bd-p1']} and $\boldsymbol{\beta}=(0.2, 0.2)$.
• Figure 4: Components $c_1$ and $c_4$ of the numerical approximation of the solution $\boldsymbol{c}$ for $\beta$ minimizing $\mathcal{J}$.
• Figure 5: The geometry of the functional $\mathcal{J}$ as a function of $\beta = (d_{\mathrm{Ca}},d_{\mathrm{Ci}})$ in logarithmic scale.