A Graphical Approach to Visualize and Interpret Biochemically Coupled Biomechanical Models

The last decade has seen the emergence of progressively more complex mechanobiological models, often coupling biochemical and biomechanical components. The complexity of these models makes interpretation difficult, and although computational tools can solve model equations, there is considerable potential value in a simple method to explore the interplay between different model components. Pump and system performance curves, long utilized in centrifugal pump selection and design, inspire the development of a graphical technique to depict visually the performance of biochemically-coupled mechanical models. Our approach is based on a biochemical performance curve (analogous to the classical pump curve) and a biomechanical performance curve (analogous to the system curve). Upon construction of the two curves, their intersection, or lack thereof, describes the coupled model's equilibrium state(s). One can also observe graphically how an applied perturbation shifts one or both curves, and thus how the other component will respond, without rerunning the full model. While the upfront cost of generating the performance curve graphic varies with the efficiency of the model components, the easily interpretable visual depiction of what would otherwise be nonintuitive model behavior is valuable. Herein, we outline how performance curves can be constructed and interpreted for biochemically-coupled biomechanical models and apply the technique to two independent models in the cardiovascular space. The performance curve approach can illustrate and help identify weaknesses in model construction, inform user-applied perturbations and fitting procedures to generate intended behaviors, and improve the efficiency of the model generation and application process.