Upscaling of fluid flow in spatially heterogeneous bone tumors

Osteosarcoma is a malignant bone tumor that preferentially arises in adolescents and young adults. Like many sarcomas with complex genomics, this type of tumors exhibits strong spatial heterogeneities in terms of micro-architecture or differentiated response to treatments due to localized effect of chemotherapy. Clinical images at a tissue scale such as histological and immunohistological sections, exhibit three phases: fluid, solid, cells populations. Therefore the tumor can be considered as a porous medium. The objective of this work was to develop a mechanical approach based on upscaling methods to study the interstitial flow within the tumor at the tissue scale. The statistical study of the micro-architecture of the media shows that the identification of characteristic lengths is complex and that a separation of spatial scales is not necessarily identified. We therefore chose a special sequential upscaling technique, named Grid-Block approach to solve this problem.