The lack of analytical models describing diffusion time dependence at intermediate time scales in complex tissue microstructure limits accurate quantification of extracellular diffusivity and tissue microstructure. Cell membrane water permeability modulates the signal in complex ways and is often disregarded in tumor microstructure models. We introduce TRACED-X, a Monte Carlo-based model that incorporates diffusion time dependence and membrane permeability in cell distributions to quantify pathologically-relevant properties in solid tumors. Monte Carlo simulations of water diffusion in semipermeable spheres were used to train neural network regressors for parameter estimation. A separate neural network was trained to predict the extracellular effective diffusivity, enabling the estimation of extracellular space tortuosity. Diffusion data from eight mixed-grade glioma patients were fitted with TRACED-X and analyzed in conjunction with clinical images. Simulation results demonstrate improved parameter estimation compared to comparator models. TRACED-X enabled the simultaneous in vivo quantification of intracellular volume fraction, cell size distribution, intrinsic extracellular diffusivity, tortuosity, and membrane permeability in glioma patients. Parameter maps show coherence with radiological findings and expected tumor phenotypes. TRACED-X permits the rapid estimate of unique biophysical properties in solid tumors, such as intrinsic extracellular diffusivity, tortuosity, and membrane permeability, in addition to cell microstructure. TRACED-X maps show promise in identifying heterogenous tumor subregions before and after treatment. Neural network implementations of diffusion time-dependence and tortuosity showed behavior consistent with coarse-graining and effective medium theory, respectively. Future work will explore the clinical utility of TRACED-X parameters in additional patients.

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