Generalized integral transform technique (GITT) in tumor dynamics: A technical qualitative review for translational oncology.

Abstract

e13645 Background: Mathematical models of tumor growth, invasion, cell–matrix interactions, and therapeutic response commonly rely on nonlinear partial differential equations (PDEs), which become analytically and numerically challenging under realistic geometry, heterogeneity, anisotropy, and treatment forcing. The Generalized Integral Transform Technique (GITT) provides a semi-analytical framework that projects PDEs onto eigenfunction bases, reducing them to coupled ordinary differential equations (ODEs) while preserving spatial structure and improving analytical transparency in tumor modeling. Methods: A technical narrative review examined GITT-based tumor models, including avascular or vascular growth (41%), chemotaxis/haptotaxis-driven invasion (28%), tumor–immune interactions (19%), and intra- or extracellular drug transport (12%). Qualitative synthesis with descriptive quantitative analysis evaluated the impact of modal projection on PDE restructuring, dimensionality reduction, and interpretable temporal dynamics; Pearson correlation assessed associations among modal truncation efficiency, numerical stability, computational cost, and accuracy preservation. Results: GITT application was consistently associated with methodological advantages. Improved numerical stability in nonlinear regimes was reported in 87% of studies (95% CI 79–93), and reduced computational cost without loss of spatial resolution in 70% (95% CI 60–79). In invasion models, 82% (95% CI 73–90) achieved clearer representation of anisotropy and directional migration. Among tumor–immune and therapy-response models, 74% (95% CI 63–83) enabled improved discrimination of elimination, equilibrium, and escape regimes through dominant spectral modes. Models incorporating fractional operators demonstrated stable behavior in all cases (100%; 95% CI 88–100). Modal truncation efficiency correlated positively with numerical stability (r = 0.58, p < 0.01) and negatively with computational cost relative to accuracy preservation (r = −0.46, p < 0.05). Conclusions: GITT emerges as a robust semi-analytical approach in tumor modeling, enhancing numerical stability, reducing computational burden, and preserving spatial fidelity. Modal decomposition facilitates interpretation of nonlinear dynamics and biologically relevant mechanisms, supporting GITT as a mature tool for comparative and multiscale analyses of tumor dynamics. Summary of GITT contributions in tumor modeling. Component Role GITT Contribution Geometry Spatial constraints Eigenfunction encoding PDEs Transport and reactions Conversion to ODEs Modal structure Space–time separation Stability and interpretability Nonlinearity Growth and taxis Modal coupling Therapy Drug and immune effects Semi-analytical assessment