In biological tissues, coefficients of intracellular and extracellular diffusion (Di and De respectively) and permeability of cell membranes (P) are not exactly known, and these are expected to differ between benign and malignant tumours.

In previous studies it was possible to differentiate between benign and malignant breast tumours with Diffusion Weighted Magnetic Resonance Imaging (DW-MRI), namely using the Apparent Diffusion Coefficient (ADC) estimated from the monoexponential diffusion model.^1,2 However, this model is not able to estimate the Di, De and P values of a chosen region-of-interest in the MR images. Recently tough, Monte-Carlo simulations (MCS) of diffusion processes have shown to be useful in characterizing simulated histological environments at the microstructural level.³ Here, the same method was applied to real histological images corresponding to malignant and benign breast tumours in order to estimate combinations of Di, De and P values that could explain the observed ADC values and thus further characterise tumour tissues.

Histological images were obtained for benign (n=3) and malignant (n=3) tumours from a dataset for breast cancer histopathological image classification⁴. These images were then binarised using Matlab in order to define cellular and extracellular matrix compartments. MCS of diffusion based on the methods used by C-Y Lee et al.³ were performed in each processed image (Fig. 1). Histological images had dimensions ranging from 0.34 mm to 1.35 mm, and had a mean intracellular volume fraction of 0.175. 10,000 dimensionless random walkers with a time-step of 2.5x10^-5 s were placed in the cell environments and performed a walk of 0.0263 s. 10 values of Di and De each ranging between 0 and 3x10^-3 mm²/s were tested in all possible combinations with 10 values of P ranging between 0.001 mm/s and 0.1 mm/s (a total of 1000 combinations). For each lesion, results of MCS for the corresponding histological images were compared with the typical values of ADC, 1.43±0.25 mm²/s for benign tumours and 0.88±0.17 mm²/s for malignant tumours², and possible (Di,De,P) combinations were analysed.

Table 1 shows the average±standard deviation values of Di, De and P obtained from the tested combinations of these parameters in the MCS for each histological image. Any combination of these parameters which falls within the range of the associated uncertainties must result in the expected values of D. Interestingly, there are clearly distinct regions of possible values of De for each lesion (Fig 2). The De obtained for malignant tumors are lower than the values obtained for the benign lesions. This could be explained by the characteristic higher cellularity⁵ of the malignant lesions, leading to an increase in the number of barriers for water diffusion in the extracellular medium and, consequently, reducing the diffusion coefficient of this compartment. Additionally, it is known that malignant tumours are often associated with changes in the extracellular matrix, namely the growth of fibrous or connective tissue (desmoplastic reaction) which results in a further restriction of water molecules’ diffusion⁶. The intracellular environment of cancer cells is not well known, and results did not show significant differences in Di between benign and malignant lesions. Nonetheless, a trend towards smaller values of Di may be observed in malignant tumours, which may be correlated to the cell heterogeneity associated to malignant tumours⁵ and cell mitosis. No significant differences were also observed for P regarding tumour type. A higher variability is nonetheless observed for malignant lesions, which may reflect tumour heterogeneity⁵ and/or changes on cells’ transport dynamics of these tumours⁷.

Overall, it can be observed that the presented approach is able to translate changes in the extracellular medium but is not sufficiently sensitive to depict significant changes in Di and P, which could be expected. This may be the result of the low number of images studied and, especially, of the oversimplified processing of the histological images (binarisation only) prior to MCS.

MCS were used on histological images of benign and malignant breast tumour tissues to estimate the parameters Di, De and P that characterise diffusion in each type of tumor tissue. It was observed that distinct combinations of these parameters correlate with different types of tumors. In particular, De revealed to be very distinct for benign and malignant tumors in agreement with known extracellular matrix differences. Presently, MCS with more images with more complex processing are being done in order to improve the sensitivity to Di and P changes.