Transient cryogenic bioheat transfer with localized phase change: An adaptive boundary element–distributed residual case study

Localized cryogenic cooling produces steep temperature gradients, a moving phase-change front, perfusion and metabolic source terms, and latent-heat buffering that challenge conventional volumetric solvers. This case study examines transient freezing-front evolution in a two-dimensional circular tissue domain with radially symmetric loading using an adaptive boundary element-distributed residual formulation. Boundary integrals treat planar conduction, while residual-driven background and locally enriched basis functions reconstruct distributed sources and concentrated probe cooling. An apparent-heat-capacity model represents a finite mushy interval, and backward-Euler integration advances the transient solution. Verification with a smooth manufactured solution gives nearly second-order spatial convergence of the underlying planar BEM discretization; this test is not claimed to establish the nonlinear convergence rate through phase change. Temporal refinement gives first-order behavior. Basis refinement changes the 120 s iceball radius by only 0.1%, and the maximum global energy residual is 0.84%. Under matched geometry, properties, boundary conditions and cooling history, cross-code comparison with a finite-difference enthalpy solver yields differences of 3.2-4.2% in iceball radius, 4.8% in probe-centre temperature and 4.6% in average boundary heat flux. Parametric cases show how conductivity, perfusion, metabolism and probe power affect freezing-front propagation, near-probe gradients and heat-flux recovery. The results demonstrate a mesh-reduced framework for repeated cryogenic thermal-engineering analyses. The study establishes numerical verification and cross-method consistency; experimental validation remains necessary before clinical prediction.