Partial Differential Equation (PDE)-Based Spatial Pharmacometrics in NONMEM: Method of Lines (MOL) Implementation...

Spatial heterogeneity in drug distribution, particularly within solid tumors, compromises target engagement, yet is rarely represented in population pharmacokinetic analyses. Standard "well-stirred" models fail to capture intratumoral gradients. Reaction-diffusion partial differential equations (PDEs) mechanistically represent penetration and washout, but routine implementation in nonlinear mixed-effects modeling (NONMEM) is limited by operational complexity. Native numerical templates remain cumbersome, and manual method of lines (MOL) coding is labor-intensive and error-prone. This work presents a streamlined workflow to implement spatial PDEs in NONMEM using AI tools. We utilized AI-assisted code generation to systematically translate continuous spatial models into coupled ordinary differential equation systems directly executable in NONMEM, maintaining transparent $DES block implementations. We illustrate this approach with one-dimensional, spherical, and two-dimensional reaction-diffusion models, providing guidance for iterative refinement via prompt engineering. Although AI does not resolve numerical stiffness or identifiability limitations, it substantially reduces the engineering burden of large MOL systems. Coupled with disciplined verification, AI-assisted code generation makes PDE-based spatial pharmacometrics in NONMEM practical and maintainable, supporting wider adoption to interrogate target-site exposure and penetration-driven efficacy.