Apparent diffusion coefficient (ADC) as a single predictor is insufficient to predict cellular density in gliomas

Cellular density (CD) in gliomas is of great clinical importance to guide treatment. Perhaps the most commonly used approach for estimating CD is based on imaging, by using Apparent Diffusion Coefficient (ADC) measurements derived from diffusion MRI. Cell membranes hinder diffusion, positing an inverse theoretic relationship between CD and ADC: as CD rises, ADC is expected to decrease. We set out to assess this relationship empirically.

Spatially localized biopsies (52 evaluable) were collected from 23 patients with untreated gliomas who underwent biopsy as part of a clinical trial, average 2.26 biopsies/patient, CD for each biopsy was measured as number of nuclei/mm² with quantitative histopathology. Our data was overweight for tumor and abnormal brain, and for balance, 52 mirror sites from contralateral normal appearing white matter were selected as "virtual biopsies", with CD inferred from the published literature. CD predicted theoretically was compared to empiric data.

We found the inverse from what was expected theoretically, specifically, CD and ADC were moderately positively correlated. The theoretical approach predicts a negative correlation between cell density and ADC, with a slope of -1.72 x 10⁶ cells·s /mm⁴. The empirical data showed the slope to be + 4.6 x 10⁶ cells·s /mm⁴ (r = 0.48).

Empiric correlations between cellular density and ADC values in glioma are at odds with one commonly used current theoretical framework, with empiric correlations reversed in sign from the expected. Histopathological ground truth is essential to both test current models and inform improvements in the image-based estimation of CD.