Mathematical Modeling of Cardiovascular Systems: From Physiology to the Clinic

Biomedical research has enjoyed an eruption of reductionism where organs are reduced to tissues, cells and molecules. Although reductionism (including proteomic and genomic) is a powerful approach to provide the components of the system, integration of the components and their interactions are ultimately necessary to reveal organ function and phenotype. Biological integration is inherently complex that requires “gluing” of numerous components of the system with many interacting variables. Physics-based mathematical modeling is well tailored for the task when the number of variables is so great that it eludes intuition. The past several decades have enjoyed enormous advancements in mathematical modeling as computational capabilities have advanced substantially and experimental databases to inform and calibrate the computational models have become available to reduce ad hoc assumptions. Applications of mathematical models have ranged from understanding basic biological system to generate new hypotheses to patient-specific computational models that can aid medical diagnosis and help design optimal treatments. Currently, most computational biomechanics modeling, however, is still in the research and development stage. Furthermore, the progress of mathematical models remains largely unrecognized in the clinic. The objective of this Research Topic is to place the spotlight on integration with emphasis on clinical translation of mathematical models.
Here, we focus on the cardiovascular system which includes the heart and blood vessels as this discipline has been at the frontier of computational modeling both for understanding physiology and disease. For example, it is now clinical practice to compute pressure drop in the coronary arteries using CT (to determine fractional flow reserve), or to non-invasively measure regional heart wall motion and strain in patients by using echocardiography or cardiac MRI in order to diagnose localized contractile disorders. On the latter, there is still no reliable way to directly measure the forces or stresses that produce abnormal heart wall motion. Cardiologists have long been interested in quantification of heart wall stress because it is a primary determinant of coronary blood flow and myocardial oxygen consumption. Moreover, changes in wall stress are believed to be stimuli to cardiac growth and remodeling. Since regional heart wall stress cannot be measured reliably, mathematical modeling based on the conservation laws of continuum mechanics is needed. Because heart wall geometry (including its fibrous architecture) is fully 3D and the mechanical properties of beating myocardium are nonlinear, there are no exact solutions of the governing differential equations of motion. Thus, numerical methods are required to find numerical approximations. The most versatile numerical method is the finite element (FE) method, which is widely used in the automotive and aerospace industries. Most FE models concerned with heart disease include only the left ventricular (LV) heart chamber because it is under the greatest stress (highest pressures) and thus, most prone to failure.
In the spirit of continuing these and other translational efforts, it is important to encourage further computational modeling that range from molecular, to cellular, to tissues and organs. It is our hope that this edition will serve to bring powerful analytical tools to the clinic that improve safety and efficacy and diagnostics and therapeutics.