Perfusion-guided virtual element analysis for biomechanical diagnosis of breast cysts and tumors

Abstract Breast cancer remains one of the most common cancers in the world. There is a pressing need for sophisticated diagnostic techniques that can identify anomalies in their earliest, benign stages. Although infrared thermography provides a non-invasive way to monitor surface temperature distributions, the lack of quantitative, parameter-based markers limits its clinical utility. The current study presents a framework that uses quantitative blood perfusion reference ranges as a non-invasive pre-screening diagnostic tool in order to overcome this limitation. We demonstrate the theoretical foundations of the model, such as the derivation of optimal convergence rates, error estimates in the $$L^2$$ -norm, and demonstrations of existence and uniqueness of the discrete solution, in order to guarantee the robustness of VEM. Our methodology incorporates the Pennes bioheat equation into the virtual element method to determine blood perfusion ranges from thermal profiles corresponding to healthy, cystic, and malignant tissues, in contrast to traditional approaches that assume constant perfusion. By methodically mapping these thermal signatures against the selected perfusion ranges, pathological zones are identified, offering a diagnostic approach comparable to the application of biochemical markers in clinical settings. By creating perfusion-based quantitative markers, this framework enhances thermo-graphic diagnostic potential and opens the door to better early identification and characterization of breast tissue abnormalities.