Table 1.

Principal innovation in the continuum mathematical models of gliomagenesis.

Authors	Key Features	Prediction
Owen LN (1969) [28]	Relation between cell kinetics and growth of the gross tumor	Tumor growth and cell production vs. cell loss
Swanson KR (2002) [29]	Quantification of the spatio-temporal growth and invasion of gliomas in three dimensions	Tumor growth and microscopic invasion
Swanson KR (2000) [5]	Augmented diffusion rates of malignant cells in white matter as compared to grey matter	Pattern of microscopic and submicroscopic invasion of the brain by glioma cells
Jbabdi S (2005) [30]	Implementation of modeled glioma diffusion by means of introduction of brain anisotropy, as detectable with diffusion tensor imaging	Pattern of glioma cells migration
Cristini V (2009) [31]	Role of microenvironment vasculature and chemotaxis in glioma invasive behavior	Pattern of tumor invasiveness
Macklin P (2007) [32]	Implementation the role the properties of microenvironment in detecting cancer morphology	Prediction of tumor 3D morphology and malignant properties
Harpold HLP (2007) [21]	Analyzing the relation between tumor growth velocity and cellular proliferation rate	Survival time
Swanson KR (2008) [20]	Analyzing tumor spreading velocity starting from patient-specific MRI	Survival time
Wang CH (2009) [33]	Quantification of patient-specific kinetic rate of malignant cell proliferation since serial preoperative MRI	Diffusion rate and development of GBM for each patient
Rockne R (2010) [34]	Incorporating the effect of radiation therapy in mathematical model of glioma growth	Tumor dimension after RT protocol
Unkelbach J (2014) [35]	Analysis of malignant cell infiltration by means of FLAIR images and prediction of RT response	Optimization of patient-specific radiation therapy and dosing of fall-off rate
Zhao Y (2015) [36]	Role of angiogenesis in tumor development and aggressiveness	Effect of antiangiogenic drugs
Saut O (2014) [37]	Role of hypoxia in tumor development and invasion	Prediction of tumor behavior (proliferative vs. invasive phenotype)
Colombo MC (2015) [23]	Analyzing patient-specific preoperative DTI in revealing personal heterogeneity and anisotropy of brain tissue	Tumor growth
Lipkova J (2019) [38]	Integration complementary information from MRI and FET-PET to infer tumor cell density in GBM patient to tailor radiotherapy	Individual response to RT
Acerbi F (2021) [24]	Introducing in a continuous mechanical model, the heterogeneity and the anisotropicity of the brain bundles from patient-specific DTI	Tumor growth, invasion and recurrence