Mathematical modelling of the dynamics of image-informed tumor habitats in a murine model of glioma

Abstract

Tumors exhibit high molecular, phenotypic, and physiological heterogeneity. In this effort, we employ quantitative magnetic resonance imaging (MRI) data to capture this heterogeneity through imaging-based subregions or “habitats” in a murine model of glioma. We then demonstrate the ability to model and predict the growth of the habitats using coupled ordinary differential equations (ODEs) in the presence and absence of radiotherapy. Female Wistar rats (N = 21) were inoculated intracranially with 106 C6 glioma cells, a subset of which received 20 Gy (N = 5) or 40 Gy (N = 8) of radiation. All rats underwent diffusion-weighted and dynamic contrast-enhanced MRI at up to seven time points. All MRI data at each visit were subsequently clustered using k-means to identify physiological tumor habitats. A family of four models consisting of three coupled ODEs were developed and calibrated to the habitat time series of control and treated rats and evaluated for predictive capability. The Akaike Information Criterion was used for model selection, and the normalized sum-of-square-error (SSE) was used to evaluate goodness-of-fit in model calibration and prediction. Three tumor habitats with significantly different imaging data characteristics (p < 0.05) were identified: high-vascularity high-cellularity, low-vascularity high-cellularity, and low-vascularity low-cellularity. Model selection resulted in a five-parameter model whose predictions of habitat dynamics yielded SSEs that were similar to the SSEs from the calibrated model. It is thus feasible to mathematically describe habitat dynamics in a preclinical model of glioma using biology-based ODEs, showing promise for forecasting heterogeneous tumor behavior.

Mechanistic Modelling of Biomass Growth, Glucose Consumption and Ethanol Production by Kluyveromyces marxianus in Batch Fermentation

“…Further, the Akaike Information Criterion ( ) [ 53 , 54 , 55 ] was computed by considering a small sample relative to the number of parameters with a bias correction as indicated below where n is the total number of experimental data points; the experimental data and the approximated value for the residual sum of squares ( ); and K the number of parameters of the system; therefore, . Results, including , and , for the complete trajectory of the system, i.e., for the total of 42 experimental points (14 for each variable) are summarized in Table 4 .…”

Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and Machine Learning Approaches

“…It complements cancer research by providing valuable quantitative predictions to unravel the complexity of cancer and open new avenues for developing effective treatments [25]. Numerous mathematical models, often rooted in ordinary differential equations (ODEs), have explored various aspects of cancer research, including treatment strategies [26][27][28][29][30][31][32][33][34], immune responses [35][36][37][38][39][40][41], treatment sensitivity and resistance [42], the effects of treatment combinations [43][44][45][46][47][48][49], habitat dynamics [50], tumor heterogeneity [51,52], and treatment optimization [53]. Their collective contribution lies in furnishing predictions for optimal dosing, treatment regimens, and scheduling, all while minimizing adverse side effects and maximizing therapeutic gains.…”

Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and AI Algorithms

“…It complements cancer research by providing valuable quantitative predictions to unravel the complexity of cancer and open new avenues for developing effective treatments [25]. Numerous mathematical models, often rooted in ordinary differential equations (ODEs), have explored various aspects of cancer research, including treatment strategies [26][27][28][29][30][31][32][33][34], immune responses [35][36][37][38][39][40][41], treatment sensitivity and resistance [42], the effects of treatment combinations [43][44][45][46][47][48][49], habitat dynamics [50], tumor heterogeneity [51,52], and treatment optimization [53]. Their collective contribution lies in furnishing predictions for optimal dosing, treatment regimens, and scheduling, all while minimizing adverse side effects and maximizing therapeutic gains.…”