Decision-support modelling for liver paired exchange integrating clinical thresholds and operational feasibility

Living donor liver transplantation (LDLT) is limited by donor–recipient incompatibilities in blood type, graft-to-recipient weight ratio (GRWR), and future remnant liver volume (FRLV). Liver Paired Exchange (LPE), adapted from kidney exchange, offers a strategy to expand donor pools, but implementation remains constrained by surgical, logistical, and ethical challenges. We developed an integer linear programming (ILP) model, implemented in OPL/CPLEX, to optimise LPE under combined clinical and operational constraints. Clinical thresholds included ABO compatibility, GRWR ≥ 0.8, and FRLV ≥ 30%. Logistical feasibility was encoded through simultaneous or consecutive operating room scheduling, inter-centre travel distance ≤ 250 km, and surgical team availability. A synthetic cohort of 20 incompatible donor–recipient pairs was generated using clinically realistic parameter distributions derived from published LDLT and LPE programmes. Applying the optimisation model to this simulated dataset, we identified 6 feasible matches (30%), compared with a random allocation baseline of 12.5% (± 4.3%) under the same clinical thresholds and one-to-one assignment rules. All simulated matches complied with ABO, GRWR, and FRLV thresholds, as well as the imposed logistical feasibility filters. In this simulation study, we demonstrate that incorporating operational constraints into an optimisation framework can improve matching efficiency within a synthetic LPE pool. The work provides a transparent, replicable decision-support framework that transplant centres could adapt and prospectively evaluate. The main contributions are: (i) formalising logistical feasibility for LPE within an integer linear programming model, (ii) showing, in a simulated cohort, that optimisation can identify more clinically and logistically feasible exchanges than random allocation, and (iii) illustrating how such a tool could support, but not replace, multidisciplinary decision-making around donor safety, recipient viability, and institutional capacity.