Diffusion Simulation on Mammograms: A Technique for Analyzing and Monitoring Breast Tumors

Jonas Borjas, Kay Tucci, Orlando Alvarez-Llamoza () and Carlos Echeverria
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Jonas Borjas: CeSiMo, Facultad de Ingeniería, Universidad de Los Andes, Mérida 5101, Venezuela
Kay Tucci: SUMA, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, Venezuela
Orlando Alvarez-Llamoza: C2MAD-CIITT, Universidad Católica de Cuenca, Cuenca 010101, Ecuador
Carlos Echeverria: CeSiMo, Facultad de Ingeniería, Universidad de Los Andes, Mérida 5101, Venezuela

Mathematics, 2023, vol. 11, issue 24, 1-10

Abstract: We have developed an imaging biomarker for quantitatively monitoring the response to clinical treatment in cancer patients. Similar to other diffusion-weighted imaging DWI techniques, our method allows for the monitoring of breast cancer progression based on the diffusion coefficient values in the affected area. Our technique has the advantage of using images from mammograms and mesoscopic multiparticle collision MPC simulation, making it more affordable and easier to implement compared to other DWI techniques, such as diffusion-weighted MRI. To create our simulation, we start with the region of interest from a mammogram where the lesion is located and build a flat simulation box with impenetrable cylindrical obstacles of varying diameters to represent the tissue’s heterogeneity. The volume of each obstacle is based on the intensity of the mammogram pixels, and the diffusion coefficient is calculated by simulating the behavior of a point particle fluid inside the box using MPC. We tested our technique on two mammograms of a male patient with a moderately differentiated breast ductal carcinoma lesion, taken before and after the first cycle of four chemotherapy sessions. As seen in other DWI studies, our technique demonstrated significant changes in the fluid concentration map of the tumor lesion, and the relative values of the diffusion coefficient showed a clear difference before and after chemotherapy.

Keywords: diffusion-weighted imaging; mesoscopic simulation; apparent diffusion coefficient; mammography image (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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