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The current clinical management for TAA is continuous monitoring and surgical replacement once the aortic diameter reaches a specified size or rate of growth. Although operative intervention is often successful in preventing fatal outcomes, not all patients will reach surgical criteria before an aortic event, and the surgery carries significant risk with a potential requirement for reoperation. There is a need for patient-specific diagnostic tools and\/or novel therapeutics to treat TAA. In this review, we discuss fluid and solute transport through the aortic wall (transmural aortic transport), its potential contributions to TAA progression, and possible applications for diagnosis and treatment. We first discuss the structural organization of the aortic wall with a focus on cellular and extracellular matrix (ECM) changes associated with TAA that may alter transmural transport. We then focus on aortic transmural transport processes defined with biphasic and multiphasic theory. Biphasic theory describes fluid interactions with a porous solid (i.e., the aortic wall), whereas multiphasic theory describes fluid and solute(s) interactions with a porous solid. We summarize experimental and computational methods to quantify transport through the aortic wall. Finally, we discuss how transmural transport may be used to diagnose, monitor, or treat TAA. 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